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Nektar::MultiRegions::ContField2D Class Reference

This class is the abstraction of a global continuous two- dimensional spectral/hp element expansion which approximates the solution of a set of partial differential equations. More...

#include <ContField2D.h>

Inheritance diagram for Nektar::MultiRegions::ContField2D:
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Public Member Functions

 ContField2D ()
 The default constructor. More...
 
 ContField2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph2D, const std::string &variable="DefaultVar", const bool DeclareCoeffPhysArrays=true, const bool CheckIfSingularSystem=false)
 This constructor sets up global continuous field based on an input mesh and boundary conditions. More...
 
 ContField2D (const ContField2D &In, const SpatialDomains::MeshGraphSharedPtr &graph2D, const std::string &variable, const bool DeclareCoeffPhysArrays=true, const bool CheckIfSingularSystem=false)
 Construct a global continuous field with solution type based on another field but using a separate input mesh and boundary conditions. More...
 
 ContField2D (const ContField2D &In, bool DeclareCoeffPhysArrays=true)
 The copy constructor. More...
 
virtual ~ContField2D ()
 The default destructor. More...
 
void GlobalToLocal (Array< OneD, NekDouble > &outarray) const
 Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$. More...
 
void GlobalToLocal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) const
 Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$. More...
 
void LocalToGlobal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) const
 
void Assemble ()
 Assembles the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$. More...
 
void Assemble (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) const
 Assembles the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$. More...
 
const AssemblyMapCGSharedPtrGetLocalToGlobalMap () const
 Returns the map from local to global level. More...
 
void IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 Calculates the inner product of a function $f(\boldsymbol{x})$ with respect to all global expansion modes $\phi_n^e(\boldsymbol{x})$. More...
 
void FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 Performs the global forward transformation of a function $f(\boldsymbol{x})$, subject to the boundary conditions specified. More...
 
void BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 Performs the backward transformation of the spectral/hp element expansion. More...
 
void MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 Multiply a solution by the inverse mass matrix. More...
 
void LaplaceSolve (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray, const Array< OneD, Array< OneD, NekDouble > > &variablecoeffs=NullNekDoubleArrayofArray, NekDouble time=0.0, CoeffState coeffstate=eLocal)
 Solves the two-dimensional Laplace equation, subject to the boundary conditions specified. More...
 
void LinearAdvectionEigs (const NekDouble ax, const NekDouble ay, Array< OneD, NekDouble > &Real, Array< OneD, NekDouble > &Imag, Array< OneD, NekDouble > &Evecs=NullNekDouble1DArray)
 Compute the eigenvalues of the linear advection operator. More...
 
const Array< OneD, const
MultiRegions::ExpListSharedPtr > & 
GetBndCondExpansions ()
 Returns the boundary conditions expansion. More...
 
const Array< OneD, const
SpatialDomains::BoundaryConditionShPtr > & 
GetBndConditions ()
 Returns the boundary conditions. More...
 
int GetGlobalMatrixNnz (const GlobalMatrixKey &gkey)
 
- Public Member Functions inherited from Nektar::MultiRegions::DisContField2D
 DisContField2D ()
 Default constructor. More...
 
 DisContField2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph2D, const std::string &variable, const bool SetUpJustDG=true, const bool DeclareCoeffPhysArrays=true)
 Constructs a global discontinuous field based on an input mesh with boundary conditions. More...
 
 DisContField2D (const DisContField2D &In, const SpatialDomains::MeshGraphSharedPtr &graph2D, const std::string &variable, const bool SetUpJustDG=false, const bool DeclareCoeffPhysArrays=true)
 
 DisContField2D (const DisContField2D &In, const bool DeclareCoeffPhysArrays=true)
 
virtual ~DisContField2D ()
 Default destructor. More...
 
GlobalLinSysSharedPtr GetGlobalBndLinSys (const GlobalLinSysKey &mkey)
 
NekDouble L2_DGDeriv (const int dir, const Array< OneD, const NekDouble > &soln)
 Calculate the $ L^2 $ error of the $ Q_{\rm dir} $ derivative using the consistent DG evaluation of $ Q_{\rm dir} $. More...
 
void EvaluateHDGPostProcessing (Array< OneD, NekDouble > &outarray)
 Evaluate HDG post-processing to increase polynomial order of solution. More...
 
virtual ExpListSharedPtrv_GetTrace ()
 
- Public Member Functions inherited from Nektar::MultiRegions::ExpList2D
 ExpList2D ()
 Default constructor. More...
 
 ExpList2D (const ExpList2D &In, const bool DeclareCoeffPhysArrays=true)
 Copy constructor. More...
 
 ExpList2D (const ExpList2D &In, const std::vector< unsigned int > &eIDs, const bool DeclareCoeffPhysArrays=true)
 Constructor copying only elements defined in eIds. More...
 
 ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph2D, const bool DelcareCoeffPhysArrays=true, const std::string &var="DefaultVar")
 Sets up a list of local expansions based on an input mesh. More...
 
 ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::ExpansionMap &expansions, const bool DeclareCoeffPhysArrays=true)
 Sets up a list of local expansions based on an expansion Map. More...
 
 ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const LibUtilities::BasisKey &TriBa, const LibUtilities::BasisKey &TriBb, const LibUtilities::BasisKey &QuadBa, const LibUtilities::BasisKey &QuadBb, const SpatialDomains::MeshGraphSharedPtr &graph2D, const LibUtilities::PointsType TriNb=LibUtilities::SIZE_PointsType)
 Sets up a list of local expansions based on an input mesh and separately defined basiskeys. More...
 
 ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const Array< OneD, const ExpListSharedPtr > &bndConstraint, const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > &bndCond, const LocalRegions::ExpansionVector &locexp, const SpatialDomains::MeshGraphSharedPtr &graph3D, const PeriodicMap &periodicFaces, const bool DeclareCoeffPhysArrays=true, const std::string variable="DefaultVar")
 
 ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::CompositeMap &domain, const SpatialDomains::MeshGraphSharedPtr &graph3D, const std::string variable="DefaultVar")
 Specialised constructor for Neumann boundary conditions in DisContField3D and ContField3D. More...
 
virtual ~ExpList2D ()
 Destructor. More...
 
- Public Member Functions inherited from Nektar::MultiRegions::ExpList
 ExpList ()
 The default constructor. More...
 
 ExpList (const LibUtilities::SessionReaderSharedPtr &pSession)
 The default constructor. More...
 
 ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
 The default constructor. More...
 
 ExpList (const ExpList &in, const std::vector< unsigned int > &eIDs, const bool DeclareCoeffPhysArrays=true)
 Constructor copying only elements defined in eIds. More...
 
 ExpList (const ExpList &in, const bool DeclareCoeffPhysArrays=true)
 The copy constructor. More...
 
virtual ~ExpList ()
 The default destructor. More...
 
int GetNcoeffs (void) const
 Returns the total number of local degrees of freedom $N_{\mathrm{eof}}=\sum_{e=1}^{{N_{\mathrm{el}}}}N^{e}_m$. More...
 
int GetNcoeffs (const int eid) const
 Returns the total number of local degrees of freedom for element eid. More...
 
ExpansionType GetExpType (void)
 Returns the type of the expansion. More...
 
void SetExpType (ExpansionType Type)
 Returns the type of the expansion. More...
 
int EvalBasisNumModesMax (void) const
 Evaulates the maximum number of modes in the elemental basis order over all elements. More...
 
const Array< OneD, int > EvalBasisNumModesMaxPerExp (void) const
 Returns the vector of the number of modes in the elemental basis order over all elements. More...
 
int GetTotPoints (void) const
 Returns the total number of quadrature points m_npoints $=Q_{\mathrm{tot}}$. More...
 
int GetTotPoints (const int eid) const
 Returns the total number of quadrature points for eid's element $=Q_{\mathrm{tot}}$. More...
 
int GetNpoints (void) const
 Returns the total number of quadrature points m_npoints $=Q_{\mathrm{tot}}$. More...
 
int Get1DScaledTotPoints (const NekDouble scale) const
 Returns the total number of qudature points scaled by the factor scale on each 1D direction. More...
 
void SetWaveSpace (const bool wavespace)
 Sets the wave space to the one of the possible configuration true or false. More...
 
void SetModifiedBasis (const bool modbasis)
 Set Modified Basis for the stability analysis. More...
 
void SetPhys (int i, NekDouble val)
 Set the i th value of m_phys to value val. More...
 
bool GetWaveSpace (void) const
 This function returns the third direction expansion condition, which can be in wave space (coefficient) or not It is stored in the variable m_WaveSpace. More...
 
void SetPhys (const Array< OneD, const NekDouble > &inarray)
 Fills the array m_phys. More...
 
void SetPhysArray (Array< OneD, NekDouble > &inarray)
 Sets the array m_phys. More...
 
void SetPhysState (const bool physState)
 This function manually sets whether the array of physical values $\boldsymbol{u}_l$ (implemented as m_phys) is filled or not. More...
 
bool GetPhysState (void) const
 This function indicates whether the array of physical values $\boldsymbol{u}_l$ (implemented as m_phys) is filled or not. More...
 
NekDouble PhysIntegral (void)
 This function integrates a function $f(\boldsymbol{x})$ over the domain consisting of all the elements of the expansion. More...
 
NekDouble PhysIntegral (const Array< OneD, const NekDouble > &inarray)
 This function integrates a function $f(\boldsymbol{x})$ over the domain consisting of all the elements of the expansion. More...
 
void IProductWRTBase_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function calculates the inner product of a function $f(\boldsymbol{x})$ with respect to all {local} expansion modes $\phi_n^e(\boldsymbol{x})$. More...
 
void IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 
void IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function calculates the inner product of a function $f(\boldsymbol{x})$ with respect to the derivative (in direction. More...
 
void IProductWRTDerivBase (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, NekDouble > &outarray)
 This function calculates the inner product of a function $f(\boldsymbol{x})$ with respect to the derivative (in direction. More...
 
void FwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function elementally evaluates the forward transformation of a function $u(\boldsymbol{x})$ onto the global spectral/hp expansion. More...
 
void FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 
void MultiplyByElmtInvMass (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function elementally mulplies the coefficient space of Sin my the elemental inverse of the mass matrix. More...
 
void MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 
void SmoothField (Array< OneD, NekDouble > &field)
 Smooth a field across elements. More...
 
void HelmSolve (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const FlagList &flags, const StdRegions::ConstFactorMap &factors, const StdRegions::VarCoeffMap &varcoeff=StdRegions::NullVarCoeffMap, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
 Solve helmholtz problem. More...
 
void LinearAdvectionDiffusionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
 Solve Advection Diffusion Reaction. More...
 
void LinearAdvectionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
 Solve Advection Diffusion Reaction. More...
 
void FwdTrans_BndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
void BwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function elementally evaluates the backward transformation of the global spectral/hp element expansion. More...
 
void BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 
void GetCoords (Array< OneD, NekDouble > &coord_0, Array< OneD, NekDouble > &coord_1=NullNekDouble1DArray, Array< OneD, NekDouble > &coord_2=NullNekDouble1DArray)
 This function calculates the coordinates of all the elemental quadrature points $\boldsymbol{x}_i$. More...
 
void HomogeneousFwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true)
 
void HomogeneousBwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true)
 
void DealiasedProd (const Array< OneD, NekDouble > &inarray1, const Array< OneD, NekDouble > &inarray2, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 
void GetBCValues (Array< OneD, NekDouble > &BndVals, const Array< OneD, NekDouble > &TotField, int BndID)
 
void NormVectorIProductWRTBase (Array< OneD, const NekDouble > &V1, Array< OneD, const NekDouble > &V2, Array< OneD, NekDouble > &outarray, int BndID)
 
void NormVectorIProductWRTBase (Array< OneD, Array< OneD, NekDouble > > &V, Array< OneD, NekDouble > &outarray)
 
void ApplyGeomInfo ()
 Apply geometry information to each expansion. More...
 
void Reset ()
 Reset geometry information and reset matrices. More...
 
void WriteTecplotHeader (std::ostream &outfile, std::string var="")
 
void WriteTecplotZone (std::ostream &outfile, int expansion=-1)
 
void WriteTecplotField (std::ostream &outfile, int expansion=-1)
 
void WriteTecplotConnectivity (std::ostream &outfile, int expansion=-1)
 
void WriteVtkHeader (std::ostream &outfile)
 
void WriteVtkFooter (std::ostream &outfile)
 
void WriteVtkPieceHeader (std::ostream &outfile, int expansion, int istrip=0)
 
void WriteVtkPieceFooter (std::ostream &outfile, int expansion)
 
void WriteVtkPieceData (std::ostream &outfile, int expansion, std::string var="v")
 
int GetCoordim (int eid)
 This function returns the dimension of the coordinates of the element eid. More...
 
void SetCoeff (int i, NekDouble val)
 Set the i th coefficiient in m_coeffs to value val. More...
 
void SetCoeffs (int i, NekDouble val)
 Set the i th coefficiient in m_coeffs to value val. More...
 
void SetCoeffsArray (Array< OneD, NekDouble > &inarray)
 Set the m_coeffs array to inarray. More...
 
const Array< OneD, const
NekDouble > & 
GetCoeffs () const
 This function returns (a reference to) the array $\boldsymbol{\hat{u}}_l$ (implemented as m_coeffs) containing all local expansion coefficients. More...
 
void ImposeDirichletConditions (Array< OneD, NekDouble > &outarray)
 Impose Dirichlet Boundary Conditions onto Array. More...
 
void FillBndCondFromField (void)
 Fill Bnd Condition expansion from the values stored in expansion. More...
 
void LocalToGlobal (void)
 Put the coefficients into global ordering using m_coeffs. More...
 
void GlobalToLocal (void)
 Put the coefficients into local ordering and place in m_coeffs. More...
 
NekDouble GetCoeff (int i)
 Get the i th value (coefficient) of m_coeffs. More...
 
NekDouble GetCoeffs (int i)
 Get the i th value (coefficient) of m_coeffs. More...
 
const Array< OneD, const
NekDouble > & 
GetPhys () const
 This function returns (a reference to) the array $\boldsymbol{u}_l$ (implemented as m_phys) containing the function $u^{\delta}(\boldsymbol{x})$ evaluated at the quadrature points. More...
 
NekDouble Linf (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray)
 This function calculates the $L_\infty$ error of the global spectral/hp element approximation. More...
 
NekDouble L2 (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray)
 This function calculates the $L_2$ error with respect to soln of the global spectral/hp element approximation. More...
 
NekDouble H1 (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray)
 Calculates the $H^1$ error of the global spectral/hp element approximation. More...
 
NekDouble Integral (const Array< OneD, const NekDouble > &inarray)
 
Array< OneD, const NekDoubleHomogeneousEnergy (void)
 This function calculates the energy associated with each one of the modesof a 3D homogeneous nD expansion. More...
 
void SetHomo1DSpecVanVisc (Array< OneD, NekDouble > visc)
 This function sets the Spectral Vanishing Viscosity in homogeneous1D expansion. More...
 
Array< OneD, const unsigned int > GetZIDs (void)
 This function returns a vector containing the wave numbers in z-direction associated with the 3D homogenous expansion. Required if a parellelisation is applied in the Fourier direction. More...
 
LibUtilities::TranspositionSharedPtr GetTransposition (void)
 This function returns the transposition class associaed with the homogeneous expansion. More...
 
NekDouble GetHomoLen (void)
 This function returns the Width of homogeneous direction associaed with the homogeneous expansion. More...
 
Array< OneD, const unsigned int > GetYIDs (void)
 This function returns a vector containing the wave numbers in y-direction associated with the 3D homogenous expansion. Required if a parellelisation is applied in the Fourier direction. More...
 
void PhysInterp1DScaled (const NekDouble scale, const Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function interpolates the physical space points in inarray to outarray using the same points defined in the expansion but where the number of points are rescaled by 1DScale. More...
 
void PhysGalerkinProjection1DScaled (const NekDouble scale, const Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function Galerkin projects the physical space points in inarray to outarray where inarray is assumed to be defined in the expansion but where the number of points are rescaled by 1DScale. More...
 
int GetExpSize (void)
 This function returns the number of elements in the expansion. More...
 
int GetNumElmts (void)
 This function returns the number of elements in the expansion which may be different for a homogeoenous extended expansionp. More...
 
const boost::shared_ptr
< LocalRegions::ExpansionVector
GetExp () const
 This function returns the vector of elements in the expansion. More...
 
LocalRegions::ExpansionSharedPtrGetExp (int n) const
 This function returns (a shared pointer to) the local elemental expansion of the $n^{\mathrm{th}}$ element. More...
 
LocalRegions::ExpansionSharedPtrGetExp (const Array< OneD, const NekDouble > &gloCoord)
 This function returns (a shared pointer to) the local elemental expansion containing the arbitrary point given by gloCoord. More...
 
int GetExpIndex (const Array< OneD, const NekDouble > &gloCoord, NekDouble tol=0.0, bool returnNearestElmt=false)
 
int GetExpIndex (const Array< OneD, const NekDouble > &gloCoords, Array< OneD, NekDouble > &locCoords, NekDouble tol=0.0, bool returnNearestElmt=false)
 
int GetCoeff_Offset (int n) const
 Get the start offset position for a global list of m_coeffs correspoinding to element n. More...
 
int GetPhys_Offset (int n) const
 Get the start offset position for a global list of m_phys correspoinding to element n. More...
 
int GetOffset_Elmt_Id (int n) const
 Get the element id associated with the n th consecutive block of data in m_phys and m_coeffs. More...
 
Array< OneD, NekDouble > & UpdateCoeffs ()
 This function returns (a reference to) the array $\boldsymbol{\hat{u}}_l$ (implemented as m_coeffs) containing all local expansion coefficients. More...
 
Array< OneD, NekDouble > & UpdatePhys ()
 This function returns (a reference to) the array $\boldsymbol{u}_l$ (implemented as m_phys) containing the function $u^{\delta}(\boldsymbol{x})$ evaluated at the quadrature points. More...
 
void PhysDeriv (Direction edir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d)
 
void PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
 This function discretely evaluates the derivative of a function $f(\boldsymbol{x})$ on the domain consisting of all elements of the expansion. More...
 
void PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d)
 
const Array< OneD, const
boost::shared_ptr< ExpList > > & 
GetBndCondExpansions ()
 
boost::shared_ptr< ExpList > & UpdateBndCondExpansion (int i)
 
void Upwind (const Array< OneD, const Array< OneD, NekDouble > > &Vec, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)
 
void Upwind (const Array< OneD, const NekDouble > &Vn, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)
 
boost::shared_ptr< ExpList > & GetTrace ()
 
boost::shared_ptr
< AssemblyMapDG > & 
GetTraceMap (void)
 
const Array< OneD, const int > & GetTraceBndMap (void)
 
void GetNormals (Array< OneD, Array< OneD, NekDouble > > &normals)
 
void AddTraceIntegral (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
 
void AddTraceIntegral (const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
 
void AddFwdBwdTraceIntegral (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &outarray)
 
void GetFwdBwdTracePhys (Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)
 
void GetFwdBwdTracePhys (const Array< OneD, const NekDouble > &field, Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)
 
const std::vector< bool > & GetLeftAdjacentFaces (void) const
 
void ExtractTracePhys (Array< OneD, NekDouble > &outarray)
 
void ExtractTracePhys (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
const Array< OneD, const
SpatialDomains::BoundaryConditionShPtr > & 
GetBndConditions ()
 
Array< OneD,
SpatialDomains::BoundaryConditionShPtr > & 
UpdateBndConditions ()
 
void EvaluateBoundaryConditions (const NekDouble time=0.0, const std::string varName="", const NekDouble=NekConstants::kNekUnsetDouble, const NekDouble=NekConstants::kNekUnsetDouble)
 
void GeneralMatrixOp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 This function calculates the result of the multiplication of a matrix of type specified by mkey with a vector given by inarray. More...
 
void GeneralMatrixOp_IterPerExp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
void SetUpPhysNormals ()
 
void GetBoundaryToElmtMap (Array< OneD, int > &ElmtID, Array< OneD, int > &EdgeID)
 
void GetBndElmtExpansion (int i, boost::shared_ptr< ExpList > &result)
 
void ExtractElmtToBndPhys (int i, Array< OneD, NekDouble > &elmt, Array< OneD, NekDouble > &boundary)
 
void ExtractPhysToBndElmt (int i, const Array< OneD, const NekDouble > &phys, Array< OneD, NekDouble > &bndElmt)
 
void GetBoundaryNormals (int i, Array< OneD, Array< OneD, NekDouble > > &normals)
 
void GeneralGetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef, int NumHomoDir=0, Array< OneD, LibUtilities::BasisSharedPtr > &HomoBasis=LibUtilities::NullBasisSharedPtr1DArray, std::vector< NekDouble > &HomoLen=LibUtilities::NullNekDoubleVector, bool homoStrips=false, std::vector< unsigned int > &HomoSIDs=LibUtilities::NullUnsignedIntVector, std::vector< unsigned int > &HomoZIDs=LibUtilities::NullUnsignedIntVector, std::vector< unsigned int > &HomoYIDs=LibUtilities::NullUnsignedIntVector)
 
const
NekOptimize::GlobalOptParamSharedPtr
GetGlobalOptParam (void)
 
std::map< int,
RobinBCInfoSharedPtr
GetRobinBCInfo ()
 
void GetPeriodicEntities (PeriodicMap &periodicVerts, PeriodicMap &periodicEdges, PeriodicMap &periodicFaces=NullPeriodicMap)
 
std::vector
< LibUtilities::FieldDefinitionsSharedPtr
GetFieldDefinitions ()
 
void GetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef)
 
void AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata)
 Append the element data listed in elements fielddef->m_ElementIDs onto fielddata. More...
 
void AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, Array< OneD, NekDouble > &coeffs)
 Append the data in coeffs listed in elements fielddef->m_ElementIDs onto fielddata. More...
 
void ExtractElmtDataToCoeffs (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, std::string &field, Array< OneD, NekDouble > &coeffs)
 Extract the data in fielddata into the coeffs using the basic ExpList Elemental expansions rather than planes in homogeneous case. More...
 
void ExtractCoeffsToCoeffs (const boost::shared_ptr< ExpList > &fromExpList, const Array< OneD, const NekDouble > &fromCoeffs, Array< OneD, NekDouble > &toCoeffs)
 Extract the data from fromField using fromExpList the coeffs using the basic ExpList Elemental expansions rather than planes in homogeneous case. More...
 
void ExtractDataToCoeffs (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, std::string &field, Array< OneD, NekDouble > &coeffs)
 Extract the data in fielddata into the coeffs. More...
 
boost::shared_ptr< ExpListGetSharedThisPtr ()
 Returns a shared pointer to the current object. More...
 
boost::shared_ptr
< LibUtilities::SessionReader
GetSession ()
 Returns the session object. More...
 
boost::shared_ptr
< LibUtilities::Comm
GetComm ()
 Returns the comm object. More...
 
SpatialDomains::MeshGraphSharedPtr GetGraph ()
 
LibUtilities::BasisSharedPtr GetHomogeneousBasis (void)
 
boost::shared_ptr< ExpList > & GetPlane (int n)
 
void CreateCollections (Collections::ImplementationType ImpType=Collections::eNoImpType)
 Construct collections of elements containing a single element type and polynomial order from the list of expansions. More...
 
void ClearGlobalLinSysManager (void)
 

Private Member Functions

void GlobalSolve (const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
 Solves the linear system specified by the key key. More...
 
GlobalMatrixSharedPtr GetGlobalMatrix (const GlobalMatrixKey &mkey)
 Returns the global matrix specified by mkey. More...
 
GlobalLinSysSharedPtr GetGlobalLinSys (const GlobalLinSysKey &mkey)
 Returns the linear system specified by the key mkey. More...
 
GlobalLinSysSharedPtr GenGlobalLinSys (const GlobalLinSysKey &mkey)
 
virtual void v_ImposeDirichletConditions (Array< OneD, NekDouble > &outarray)
 Impose the Dirichlet Boundary Conditions on outarray. More...
 
virtual void v_FillBndCondFromField ()
 
virtual void v_LocalToGlobal (void)
 Gathers the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$. More...
 
virtual void v_GlobalToLocal (void)
 Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$. More...
 
virtual void v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
 Template method virtual forwarder for FwdTrans(). More...
 
virtual void v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
 Template method virtual forwarder for FwdTrans(). More...
 
virtual void v_SmoothField (Array< OneD, NekDouble > &field)
 Template method virtual forwarded for SmoothField(). More...
 
virtual void v_MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
 Template method virtual forwarder for MultiplyByInvMassMatrix(). More...
 
virtual void v_HelmSolve (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const FlagList &flags, const StdRegions::ConstFactorMap &factors, const StdRegions::VarCoeffMap &varcoeff, const Array< OneD, const NekDouble > &dirForcing)
 Solves the two-dimensional Helmholtz equation, subject to the boundary conditions specified. More...
 
virtual void v_GeneralMatrixOp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
 Calculates the result of the multiplication of a global matrix of type specified by mkey with a vector given by inarray. More...
 
virtual void v_LinearAdvectionDiffusionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
 
void v_LinearAdvectionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
 
virtual const Array< OneD,
const
SpatialDomains::BoundaryConditionShPtr > & 
v_GetBndConditions ()
 Template method virtual forwarder for GetBndConditions(). More...
 
virtual void v_ClearGlobalLinSysManager (void)
 

Private Attributes

AssemblyMapCGSharedPtr m_locToGloMap
 (A shared pointer to) the object which contains all the required information for the transformation from local to global degrees of freedom. More...
 
GlobalMatrixMapShPtr m_globalMat
 (A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once. More...
 
LibUtilities::NekManager
< GlobalLinSysKey,
GlobalLinSys
m_globalLinSysManager
 A manager which collects all the global linear systems being assembled, such that they should be constructed only once. More...
 

Additional Inherited Members

- Public Attributes inherited from Nektar::MultiRegions::ExpList
ExpansionType m_expType
 
- Protected Member Functions inherited from Nektar::MultiRegions::DisContField2D
const Array< OneD, const
LibUtilities::BasisSharedPtr > & 
GetBase () const
 This function gets the shared point to basis. More...
 
LibUtilities::BasisType GetBasisType (const int dir) const
 This function returns the type of basis used in the dir direction. More...
 
void SetUpDG (const std::string="DefaultVar")
 Set up all DG member variables and maps. More...
 
bool SameTypeOfBoundaryConditions (const DisContField2D &In)
 
void GenerateBoundaryConditionExpansion (const SpatialDomains::MeshGraphSharedPtr &graph2D, const SpatialDomains::BoundaryConditions &bcs, const std::string &variable, const bool DeclareCoeffPhysArrays=true)
 This function discretises the boundary conditions by setting up a list of one-dimensional boundary expansions. More...
 
void FindPeriodicEdges (const SpatialDomains::BoundaryConditions &bcs, const std::string &variable)
 Determine the periodic edges and vertices for the given graph. More...
 
bool IsLeftAdjacentEdge (const int n, const int e)
 
virtual void v_GetFwdBwdTracePhys (const Array< OneD, const NekDouble > &field, Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)
 This method extracts the "forward" and "backward" trace data from the array field and puts the data into output vectors Fwd and Bwd. More...
 
virtual void v_GetFwdBwdTracePhys (Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)
 
virtual void v_AddTraceIntegral (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
 
virtual void v_AddTraceIntegral (const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
 Add trace contributions into elemental coefficient spaces. More...
 
virtual void v_AddFwdBwdTraceIntegral (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &outarray)
 Add trace contributions into elemental coefficient spaces. More...
 
virtual void v_ExtractTracePhys (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This method extracts the trace (edges in 2D) from the field inarray and puts the values in outarray. More...
 
virtual void v_ExtractTracePhys (Array< OneD, NekDouble > &outarray)
 
virtual void v_GetBoundaryToElmtMap (Array< OneD, int > &ElmtID, Array< OneD, int > &EdgeID)
 Set up a list of element IDs and edge IDs that link to the boundary conditions. More...
 
virtual void v_GetBndElmtExpansion (int i, boost::shared_ptr< ExpList > &result)
 
virtual void v_Reset ()
 Reset this field, so that geometry information can be updated. More...
 
virtual void v_GetPeriodicEntities (PeriodicMap &periodicVerts, PeriodicMap &periodicEdges, PeriodicMap &periodicFaces)
 Obtain a copy of the periodic edges and vertices for this field. More...
 
virtual AssemblyMapDGSharedPtrv_GetTraceMap ()
 
virtual const Array< OneD,
const
MultiRegions::ExpListSharedPtr > & 
v_GetBndCondExpansions ()
 
virtual
MultiRegions::ExpListSharedPtr
v_UpdateBndCondExpansion (int i)
 
virtual Array< OneD,
SpatialDomains::BoundaryConditionShPtr > & 
v_UpdateBndConditions ()
 
virtual void v_EvaluateBoundaryConditions (const NekDouble time=0.0, const std::string varName="", const NekDouble x2_in=NekConstants::kNekUnsetDouble, const NekDouble x3_in=NekConstants::kNekUnsetDouble)
 
virtual std::map< int,
RobinBCInfoSharedPtr
v_GetRobinBCInfo ()
 Search through the edge expansions and identify which ones have Robin/Mixed type boundary conditions. More...
 
- Protected Member Functions inherited from Nektar::MultiRegions::ExpList2D
void v_Upwind (const Array< OneD, const NekDouble > &Vn, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)
 Upwind the Fwd and Bwd states based on the one- dimensional normal velocity field given by Vn. More...
 
void v_GetNormals (Array< OneD, Array< OneD, NekDouble > > &normals)
 For each local element, copy the normals stored in the element list into the array normals. More...
 
- Protected Member Functions inherited from Nektar::MultiRegions::ExpList
boost::shared_ptr< DNekMatGenGlobalMatrixFull (const GlobalLinSysKey &mkey, const boost::shared_ptr< AssemblyMapCG > &locToGloMap)
 
const DNekScalBlkMatSharedPtr GenBlockMatrix (const GlobalMatrixKey &gkey)
 This function assembles the block diagonal matrix of local matrices of the type mtype. More...
 
const DNekScalBlkMatSharedPtrGetBlockMatrix (const GlobalMatrixKey &gkey)
 
void MultiplyByBlockMatrix (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
boost::shared_ptr< GlobalMatrixGenGlobalMatrix (const GlobalMatrixKey &mkey, const boost::shared_ptr< AssemblyMapCG > &locToGloMap)
 Generates a global matrix from the given key and map. More...
 
void GlobalEigenSystem (const boost::shared_ptr< DNekMat > &Gmat, Array< OneD, NekDouble > &EigValsReal, Array< OneD, NekDouble > &EigValsImag, Array< OneD, NekDouble > &EigVecs=NullNekDouble1DArray)
 
boost::shared_ptr< GlobalLinSysGenGlobalLinSys (const GlobalLinSysKey &mkey, const boost::shared_ptr< AssemblyMapCG > &locToGloMap)
 This operation constructs the global linear system of type mkey. More...
 
boost::shared_ptr< GlobalLinSysGenGlobalBndLinSys (const GlobalLinSysKey &mkey, const AssemblyMapSharedPtr &locToGloMap)
 Generate a GlobalLinSys from information provided by the key "mkey" and the mapping provided in LocToGloBaseMap. More...
 
void ReadGlobalOptimizationParameters ()
 
virtual int v_GetNumElmts (void)
 
virtual void v_Upwind (const Array< OneD, const Array< OneD, NekDouble > > &Vec, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)
 
virtual const Array< OneD,
const int > & 
v_GetTraceBndMap ()
 
virtual const std::vector< bool > & v_GetLeftAdjacentFaces (void) const
 
virtual void v_BwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
virtual void v_FwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
virtual void v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
 
virtual void v_IProductWRTBase_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
virtual void v_GetCoords (Array< OneD, NekDouble > &coord_0, Array< OneD, NekDouble > &coord_1, Array< OneD, NekDouble > &coord_2=NullNekDouble1DArray)
 
virtual void v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2)
 
virtual void v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d)
 
virtual void v_PhysDeriv (Direction edir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d)
 
virtual void v_HomogeneousFwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true)
 
virtual void v_HomogeneousBwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true)
 
virtual void v_DealiasedProd (const Array< OneD, NekDouble > &inarray1, const Array< OneD, NekDouble > &inarray2, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 
virtual void v_GetBCValues (Array< OneD, NekDouble > &BndVals, const Array< OneD, NekDouble > &TotField, int BndID)
 
virtual void v_NormVectorIProductWRTBase (Array< OneD, const NekDouble > &V1, Array< OneD, const NekDouble > &V2, Array< OneD, NekDouble > &outarray, int BndID)
 
virtual void v_NormVectorIProductWRTBase (Array< OneD, Array< OneD, NekDouble > > &V, Array< OneD, NekDouble > &outarray)
 
virtual void v_ExtractElmtToBndPhys (int i, Array< OneD, NekDouble > &elmt, Array< OneD, NekDouble > &boundary)
 
virtual void v_ExtractPhysToBndElmt (int i, const Array< OneD, const NekDouble > &phys, Array< OneD, NekDouble > &bndElmt)
 
virtual void v_GetBoundaryNormals (int i, Array< OneD, Array< OneD, NekDouble > > &normals)
 
virtual std::vector
< LibUtilities::FieldDefinitionsSharedPtr
v_GetFieldDefinitions (void)
 
virtual void v_GetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef)
 
virtual void v_AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata)
 
virtual void v_AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, Array< OneD, NekDouble > &coeffs)
 
virtual void v_ExtractDataToCoeffs (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, std::string &field, Array< OneD, NekDouble > &coeffs)
 Extract data from raw field data into expansion list. More...
 
virtual void v_ExtractCoeffsToCoeffs (const boost::shared_ptr< ExpList > &fromExpList, const Array< OneD, const NekDouble > &fromCoeffs, Array< OneD, NekDouble > &toCoeffs)
 
virtual void v_WriteTecplotHeader (std::ostream &outfile, std::string var="")
 
virtual void v_WriteTecplotZone (std::ostream &outfile, int expansion)
 
virtual void v_WriteTecplotField (std::ostream &outfile, int expansion)
 
virtual void v_WriteTecplotConnectivity (std::ostream &outfile, int expansion)
 
virtual void v_WriteVtkPieceData (std::ostream &outfile, int expansion, std::string var)
 
virtual NekDouble v_L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray)
 
virtual NekDouble v_Integral (const Array< OneD, const NekDouble > &inarray)
 
virtual Array< OneD, const
NekDouble
v_HomogeneousEnergy (void)
 
virtual
LibUtilities::TranspositionSharedPtr 
v_GetTransposition (void)
 
virtual NekDouble v_GetHomoLen (void)
 
virtual Array< OneD, const
unsigned int > 
v_GetZIDs (void)
 
virtual Array< OneD, const
unsigned int > 
v_GetYIDs (void)
 
void ExtractFileBCs (const std::string &fileName, const std::string &varName, const boost::shared_ptr< ExpList > locExpList)
 
- Static Protected Member Functions inherited from Nektar::MultiRegions::ExpList
static
SpatialDomains::BoundaryConditionShPtr 
GetBoundaryCondition (const SpatialDomains::BoundaryConditionCollection &collection, unsigned int index, const std::string &variable)
 
- Protected Attributes inherited from Nektar::MultiRegions::DisContField2D
Array< OneD,
LibUtilities::BasisSharedPtr
m_base
 
Array< OneD,
MultiRegions::ExpListSharedPtr
m_bndCondExpansions
 An object which contains the discretised boundary conditions. More...
 
Array< OneD,
SpatialDomains::BoundaryConditionShPtr
m_bndConditions
 An array which contains the information about the boundary condition on the different boundary regions. More...
 
GlobalLinSysMapShPtr m_globalBndMat
 
ExpListSharedPtr m_trace
 
AssemblyMapDGSharedPtr m_traceMap
 
LocTraceToTraceMapSharedPtr m_locTraceToTraceMap
 
Array< OneD, Array< OneD,
unsigned int > > 
m_mapEdgeToElmn
 
Array< OneD, Array< OneD,
unsigned int > > 
m_signEdgeToElmn
 
Array< OneD,
StdRegions::Orientation
m_edgedir
 
std::set< int > m_boundaryEdges
 A set storing the global IDs of any boundary edges. More...
 
PeriodicMap m_periodicVerts
 A map which identifies groups of periodic vertices. More...
 
PeriodicMap m_periodicEdges
 A map which identifies pairs of periodic edges. More...
 
std::vector< int > m_periodicFwdCopy
 A vector indicating degress of freedom which need to be copied from forwards to backwards space in case of a periodic boundary condition. More...
 
std::vector< int > m_periodicBwdCopy
 
std::vector< bool > m_leftAdjacentEdges
 
- Protected Attributes inherited from Nektar::MultiRegions::ExpList
LibUtilities::CommSharedPtr m_comm
 Communicator. More...
 
LibUtilities::SessionReaderSharedPtr m_session
 Session. More...
 
SpatialDomains::MeshGraphSharedPtr m_graph
 Mesh associated with this expansion list. More...
 
int m_ncoeffs
 The total number of local degrees of freedom. m_ncoeffs $=N_{\mathrm{eof}}=\sum_{e=1}^{{N_{\mathrm{el}}}}N^{e}_l$. More...
 
int m_npoints
 
Array< OneD, NekDoublem_coeffs
 Concatenation of all local expansion coefficients. More...
 
Array< OneD, NekDoublem_phys
 The global expansion evaluated at the quadrature points. More...
 
bool m_physState
 The state of the array m_phys. More...
 
boost::shared_ptr
< LocalRegions::ExpansionVector
m_exp
 The list of local expansions. More...
 
Collections::CollectionVector m_collections
 
std::vector< int > m_coll_coeff_offset
 Offset of elemental data into the array m_coeffs. More...
 
std::vector< int > m_coll_phys_offset
 Offset of elemental data into the array m_phys. More...
 
Array< OneD, int > m_coeff_offset
 Offset of elemental data into the array m_coeffs. More...
 
Array< OneD, int > m_phys_offset
 Offset of elemental data into the array m_phys. More...
 
Array< OneD, int > m_offset_elmt_id
 Array containing the element id m_offset_elmt_id[n] that the n^th consecutive block of data in m_coeffs and m_phys is associated, i.e. for an array of constant expansion size and single shape elements m_phys[n*m_npoints] is the data related to m_exp[m_offset_elmt_id[n]];. More...
 
NekOptimize::GlobalOptParamSharedPtr m_globalOptParam
 
BlockMatrixMapShPtr m_blockMat
 
bool m_WaveSpace
 

Detailed Description

This class is the abstraction of a global continuous two- dimensional spectral/hp element expansion which approximates the solution of a set of partial differential equations.

The class ContField2D is able to incorporate the boundary conditions imposed to the problem to be solved. Therefore, the class is equipped with three additional data members:

The first data structure, m_bndCondExpansions, contains the one-dimensional spectral/hp expansion on the boundary, #m_bndTypes stores information about the type of boundary condition on the different parts of the boundary while #m_bndCondEquations holds the equation of the imposed boundary conditions.

Furthermore, in case of Dirichlet boundary conditions, this class is capable of lifting a known solution satisfying these boundary conditions. If we denote the unknown solution by $u^{\mathcal{H}}(\boldsymbol{x})$ and the known Dirichlet boundary conditions by $u^{\mathcal{D}}(\boldsymbol{x})$, the expansion then can be decomposed as

\[ u^{\delta}(\boldsymbol{x}_i)=u^{\mathcal{D}}(\boldsymbol{x}_i)+ u^{\mathcal{H}}(\boldsymbol{x}_i)=\sum_{n=0}^{N^{\mathcal{D}}-1} \hat{u}_n^{\mathcal{D}}\Phi_n(\boldsymbol{x}_i)+ \sum_{n={N^{\mathcal{D}}}}^{N_{\mathrm{dof}}-1} \hat{u}_n^{\mathcal{H}} \Phi_n(\boldsymbol{x}_i).\]

This lifting is accomplished by ordering the known global degrees of freedom, prescribed by the Dirichlet boundary conditions, first in the global array $\boldsymbol{\hat{u}}$, that is,

\[\boldsymbol{\hat{u}}=\left[ \begin{array}{c} \boldsymbol{\hat{u}}^{\mathcal{D}}\\ \boldsymbol{\hat{u}}^{\mathcal{H}} \end{array} \right].\]

Such kind of expansions are also referred to as continuous fields. This class should be used when solving 2D problems using a standard Galerkin approach.

Definition at line 56 of file ContField2D.h.

Constructor & Destructor Documentation

Nektar::MultiRegions::ContField2D::ContField2D ( )

The default constructor.

Definition at line 88 of file ContField2D.cpp.

88  :
90  m_locToGloMap(),
91  m_globalMat(),
93  boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
94  std::string("GlobalLinSys"))
95  {
96  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
GlobalLinSysSharedPtr GenGlobalLinSys(const GlobalLinSysKey &mkey)
LibUtilities::NekManager< GlobalLinSysKey, GlobalLinSys > m_globalLinSysManager
A manager which collects all the global linear systems being assembled, such that they should be cons...
Definition: ContField2D.h:192
DisContField2D()
Default constructor.
GlobalMatrixMapShPtr m_globalMat
(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once.
Definition: ContField2D.h:187
Nektar::MultiRegions::ContField2D::ContField2D ( const LibUtilities::SessionReaderSharedPtr pSession,
const SpatialDomains::MeshGraphSharedPtr graph2D,
const std::string &  variable = "DefaultVar",
const bool  DeclareCoeffPhysArrays = true,
const bool  CheckIfSingularSystem = false 
)

This constructor sets up global continuous field based on an input mesh and boundary conditions.

Given a mesh graph2D, containing information about the domain and the spectral/hp element expansion, this constructor fills the list of local expansions m_exp with the proper expansions, calculates the total number of quadrature points $\boldsymbol{x}_i$ and local expansion coefficients $\hat{u}^e_n$ and allocates memory for the arrays m_coeffs and m_phys. Furthermore, it constructs the mapping array (contained in m_locToGloMap) for the transformation between local elemental level and global level, it calculates the total number global expansion coefficients $\hat{u}_n$ and allocates memory for the array #m_contCoeffs. The constructor also discretises the boundary conditions, specified by the argument bcs, by expressing them in terms of the coefficient of the expansion on the boundary.

Parameters
graph2DA mesh, containing information about the domain and the spectral/hp element expansion.
bcsThe boundary conditions.
variableAn optional parameter to indicate for which variable the field should be constructed.

Definition at line 120 of file ContField2D.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Nektar::MultiRegions::DisContField2D::m_periodicEdges, Nektar::MultiRegions::DisContField2D::m_periodicVerts, and Nektar::MultiRegions::ExpList::m_session.

124  :
125  DisContField2D(pSession,graph2D,variable,false,DeclareCoeffPhysArrays),
126  m_globalMat(MemoryManager<GlobalMatrixMap>::AllocateSharedPtr()),
128  boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
129  std::string("GlobalLinSys"))
130  {
135  CheckIfSingularSystem,
136  variable,
139 
140  if (m_session->DefinesCmdLineArgument("verbose"))
141  {
142  m_locToGloMap->PrintStats(std::cout, variable);
143  }
144  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
static boost::shared_ptr< DataType > AllocateSharedPtr()
Allocate a shared pointer from the memory pool.
GlobalLinSysSharedPtr GenGlobalLinSys(const GlobalLinSysKey &mkey)
PeriodicMap m_periodicEdges
A map which identifies pairs of periodic edges.
PeriodicMap m_periodicVerts
A map which identifies groups of periodic vertices.
LibUtilities::NekManager< GlobalLinSysKey, GlobalLinSys > m_globalLinSysManager
A manager which collects all the global linear systems being assembled, such that they should be cons...
Definition: ContField2D.h:192
DisContField2D()
Default constructor.
Array< OneD, MultiRegions::ExpListSharedPtr > m_bndCondExpansions
An object which contains the discretised boundary conditions.
int m_ncoeffs
The total number of local degrees of freedom. m_ncoeffs .
Definition: ExpList.h:917
GlobalMatrixMapShPtr m_globalMat
(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once.
Definition: ContField2D.h:187
LibUtilities::SessionReaderSharedPtr m_session
Session.
Definition: ExpList.h:910
Array< OneD, SpatialDomains::BoundaryConditionShPtr > m_bndConditions
An array which contains the information about the boundary condition on the different boundary region...
Nektar::MultiRegions::ContField2D::ContField2D ( const ContField2D In,
const SpatialDomains::MeshGraphSharedPtr graph2D,
const std::string &  variable,
const bool  DeclareCoeffPhysArrays = true,
const bool  CheckIfSingularSystem = false 
)

Construct a global continuous field with solution type based on another field but using a separate input mesh and boundary conditions.

Given a mesh graph2D, containing information about the domain and the spectral/hp element expansion, this constructor fills the list of local expansions m_exp with the proper expansions, calculates the total number of quadrature points $\boldsymbol{x}_i$ and local expansion coefficients $\hat{u}^e_n$ and allocates memory for the arrays m_coeffs and m_phys. Furthermore, it constructs the mapping array (contained in m_locToGloMap) for the transformation between local elemental level and global level, it calculates the total number global expansion coefficients $\hat{u}_n$ and allocates memory for the array m_coeffs. The constructor also discretises the boundary conditions, specified by the argument bcs, by expressing them in terms of the coefficient of the expansion on the boundary.

Parameters
InExisting ContField2D object used to provide the local to global mapping information and global solution type.
graph2DA mesh, containing information about the domain and the spectral/hp element expansion.
bcsThe boundary conditions.
bc_loc

Definition at line 170 of file ContField2D.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Nektar::MultiRegions::DisContField2D::m_periodicEdges, Nektar::MultiRegions::DisContField2D::m_periodicVerts, Nektar::MultiRegions::ExpList::m_session, and Nektar::MultiRegions::DisContField2D::SameTypeOfBoundaryConditions().

174  :
175  DisContField2D(In,graph2D,variable,false,DeclareCoeffPhysArrays),
176  m_globalMat (MemoryManager<GlobalMatrixMap>::AllocateSharedPtr()),
178  boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
179  std::string("GlobalLinSys"))
180  {
181  if(!SameTypeOfBoundaryConditions(In) || CheckIfSingularSystem)
182  {
187  CheckIfSingularSystem,
188  variable,
191 
192  if (m_session->DefinesCmdLineArgument("verbose"))
193  {
194  m_locToGloMap->PrintStats(std::cout, variable);
195  }
196  }
197  else
198  {
199  m_locToGloMap = In.m_locToGloMap;
200  }
201  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
static boost::shared_ptr< DataType > AllocateSharedPtr()
Allocate a shared pointer from the memory pool.
GlobalLinSysSharedPtr GenGlobalLinSys(const GlobalLinSysKey &mkey)
PeriodicMap m_periodicEdges
A map which identifies pairs of periodic edges.
PeriodicMap m_periodicVerts
A map which identifies groups of periodic vertices.
LibUtilities::NekManager< GlobalLinSysKey, GlobalLinSys > m_globalLinSysManager
A manager which collects all the global linear systems being assembled, such that they should be cons...
Definition: ContField2D.h:192
bool SameTypeOfBoundaryConditions(const DisContField2D &In)
DisContField2D()
Default constructor.
Array< OneD, MultiRegions::ExpListSharedPtr > m_bndCondExpansions
An object which contains the discretised boundary conditions.
int m_ncoeffs
The total number of local degrees of freedom. m_ncoeffs .
Definition: ExpList.h:917
GlobalMatrixMapShPtr m_globalMat
(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once.
Definition: ContField2D.h:187
LibUtilities::SessionReaderSharedPtr m_session
Session.
Definition: ExpList.h:910
Array< OneD, SpatialDomains::BoundaryConditionShPtr > m_bndConditions
An array which contains the information about the boundary condition on the different boundary region...
Nektar::MultiRegions::ContField2D::ContField2D ( const ContField2D In,
bool  DeclareCoeffPhysArrays = true 
)

The copy constructor.

Initialises the object as a copy of an existing ContField2D object.

Parameters
InExisting ContField2D object.
DeclareCoeffPhysArraysbool to declare if m_phys and m_coeffs should be declared. Default is true

Definition at line 210 of file ContField2D.cpp.

210  :
211  DisContField2D(In,DeclareCoeffPhysArrays),
212  m_locToGloMap(In.m_locToGloMap),
213  m_globalMat(In.m_globalMat),
214  m_globalLinSysManager(In.m_globalLinSysManager)
215  {
216  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
LibUtilities::NekManager< GlobalLinSysKey, GlobalLinSys > m_globalLinSysManager
A manager which collects all the global linear systems being assembled, such that they should be cons...
Definition: ContField2D.h:192
DisContField2D()
Default constructor.
GlobalMatrixMapShPtr m_globalMat
(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once.
Definition: ContField2D.h:187
Nektar::MultiRegions::ContField2D::~ContField2D ( )
virtual

The default destructor.

Definition at line 222 of file ContField2D.cpp.

223  {
224  }

Member Function Documentation

void Nektar::MultiRegions::ContField2D::Assemble ( )
inline

Assembles the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$.

This operation is evaluated as:

\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}_g[\mbox{map}[e][i]] = \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]+\mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}^{e}[i]$\\ \> \> continue\\ \> continue \end{tabbing}

where map $[e][i]$ is the mapping array and sign $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the gather operation $\boldsymbol{\hat{u}}_g=\mathcal{A}^{T}\boldsymbol{\hat{u}}_l$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

Note
The array m_coeffs should be filled with the local coefficients $\boldsymbol{\hat{u}}_l$ and that the resulting global coefficients $\boldsymbol{\hat{u}}_g$ will be stored in m_coeffs.

Definition at line 392 of file ContField2D.h.

References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.

Referenced by IProductWRTBase(), MultiplyByInvMassMatrix(), and v_GeneralMatrixOp().

393  {
394  m_locToGloMap->Assemble(m_coeffs,m_coeffs);
395  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
Array< OneD, NekDouble > m_coeffs
Concatenation of all local expansion coefficients.
Definition: ExpList.h:939
void Nektar::MultiRegions::ContField2D::Assemble ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
) const
inline

Assembles the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$.

This operation is evaluated as:

\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}_g[\mbox{map}[e][i]] = \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]+\mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}^{e}[i]$\\ \> \> continue\\ \> continue \end{tabbing}

where map $[e][i]$ is the mapping array and sign $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the gather operation $\boldsymbol{\hat{u}}_g=\mathcal{A}^{T}\boldsymbol{\hat{u}}_l$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

Parameters
inarrayAn array of size $N_\mathrm{eof}$ containing the local degrees of freedom $\boldsymbol{x}_l$.
outarrayThe resulting global degrees of freedom $\boldsymbol{x}_g$ will be stored in this array of size $N_\mathrm{dof}$.

Definition at line 424 of file ContField2D.h.

References m_locToGloMap.

427  {
428  m_locToGloMap->Assemble(inarray,outarray);
429  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
void Nektar::MultiRegions::ContField2D::BwdTrans ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
CoeffState  coeffstate = eLocal 
)
inline

Performs the backward transformation of the spectral/hp element expansion.

Given the coefficients of an expansion, this function evaluates the spectral/hp expansion $u^{\delta}(\boldsymbol{x})$ at the quadrature points $\boldsymbol{x}_i$. This operation is evaluated locally by the function ExpList::BwdTrans.

The coefficients of the expansion should be contained in the variable m_coeffs of the ExpList object In. The resulting physical values at the quadrature points $u^{\delta}(\boldsymbol{x}_i)$ are stored in the array m_phys.

Parameters
InAn ExpList, containing the local coefficients $\hat{u}_n^e$ in its array m_coeffs.

Definition at line 500 of file ContField2D.h.

References Nektar::MultiRegions::ExpList::BwdTrans_IterPerExp(), Nektar::StdRegions::eBwdTrans, Nektar::MultiRegions::eGlobal, GetGlobalMatrix(), Nektar::MultiRegions::ExpList::GlobalToLocal(), Nektar::MultiRegions::ExpList::m_globalOptParam, m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.

Referenced by v_BwdTrans(), and v_SmoothField().

504  {
505  if(coeffstate == eGlobal)
506  {
507  bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
509 
510  if(doGlobalOp)
511  {
512  GlobalMatrixKey gkey(StdRegions::eBwdTrans,m_locToGloMap);
514  mat->Multiply(inarray,outarray);
515  }
516  else
517  {
518  Array<OneD, NekDouble> wsp(m_ncoeffs);
519  GlobalToLocal(inarray,wsp);
520  BwdTrans_IterPerExp(wsp,outarray);
521  }
522  }
523  else
524  {
525  BwdTrans_IterPerExp(inarray,outarray);
526  }
527  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
NekOptimize::GlobalOptParamSharedPtr m_globalOptParam
Definition: ExpList.h:1001
boost::shared_ptr< GlobalMatrix > GlobalMatrixSharedPtr
Shared pointer to a GlobalMatrix object.
Definition: GlobalMatrix.h:89
Global coefficients.
void BwdTrans_IterPerExp(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
This function elementally evaluates the backward transformation of the global spectral/hp element exp...
Definition: ExpList.h:1620
int m_ncoeffs
The total number of local degrees of freedom. m_ncoeffs .
Definition: ExpList.h:917
GlobalMatrixSharedPtr GetGlobalMatrix(const GlobalMatrixKey &mkey)
Returns the global matrix specified by mkey.
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1855
void Nektar::MultiRegions::ContField2D::FwdTrans ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
CoeffState  coeffstate = eLocal 
)

Performs the global forward transformation of a function $f(\boldsymbol{x})$, subject to the boundary conditions specified.

Given a function $f(\boldsymbol{x})$ defined at the quadrature points, this function determines the unknown global coefficients $\boldsymbol{\hat{u}}^{\mathcal{H}}$ employing a discrete Galerkin projection from physical space to coefficient space. The operation is evaluated by the function GlobalSolve using the global mass matrix.

The values of the function $f(\boldsymbol{x})$ evaluated at the quadrature points $\boldsymbol{x}_i$ should be contained in the variable m_phys of the ExpList object Sin. The resulting global coefficients $\hat{u}_g$ are stored in the array m_coeffs.

Parameters
SinAn ExpList, containing the discrete evaluation of $f(\boldsymbol{x})$ at the quadrature points in its array m_phys.

Definition at line 244 of file ContField2D.cpp.

References Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eMass, GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), and m_locToGloMap.

Referenced by v_FwdTrans().

248  {
249  // Inner product of forcing
250  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
251  Array<OneD,NekDouble> wsp(contNcoeffs);
252  IProductWRTBase(inarray,wsp,eGlobal);
253 
254  // Solve the system
255  GlobalLinSysKey key(StdRegions::eMass, m_locToGloMap);
256 
257  if(coeffstate == eGlobal)
258  {
259  GlobalSolve(key,wsp,outarray);
260  }
261  else
262  {
263  Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
264  GlobalSolve(key,wsp,tmp);
265  GlobalToLocal(tmp,outarray);
266  }
267  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
Global coefficients.
void GlobalSolve(const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
Solves the linear system specified by the key key.
void IProductWRTBase(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Calculates the inner product of a function with respect to all global expansion modes ...
Definition: ContField2D.h:454
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1855
GlobalLinSysSharedPtr Nektar::MultiRegions::ContField2D::GenGlobalLinSys ( const GlobalLinSysKey mkey)
private

Definition at line 601 of file ContField2D.cpp.

References ASSERTL1, Nektar::MultiRegions::ExpList::GenGlobalLinSys(), Nektar::MultiRegions::GlobalMatrixKey::LocToGloMapIsDefined(), and m_locToGloMap.

603  {
604  ASSERTL1(mkey.LocToGloMapIsDefined(),
605  "To use method must have a AssemblyMap "
606  "attached to key");
608  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
boost::shared_ptr< GlobalLinSys > GenGlobalLinSys(const GlobalLinSysKey &mkey, const boost::shared_ptr< AssemblyMapCG > &locToGloMap)
This operation constructs the global linear system of type mkey.
Definition: ExpList.cpp:1175
#define ASSERTL1(condition, msg)
Assert Level 1 – Debugging which is used whether in FULLDEBUG or DEBUG compilation mode...
Definition: ErrorUtil.hpp:191
const Array< OneD, const MultiRegions::ExpListSharedPtr > & Nektar::MultiRegions::ContField2D::GetBndCondExpansions ( )
inline

Returns the boundary conditions expansion.

Definition at line 530 of file ContField2D.h.

References Nektar::MultiRegions::DisContField2D::m_bndCondExpansions.

531  {
532  return m_bndCondExpansions;
533  }
Array< OneD, MultiRegions::ExpListSharedPtr > m_bndCondExpansions
An object which contains the discretised boundary conditions.
const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField2D::GetBndConditions ( )
inline

Returns the boundary conditions.

Definition at line 536 of file ContField2D.h.

References Nektar::MultiRegions::DisContField2D::m_bndConditions.

Referenced by v_GetBndConditions().

537  {
538  return m_bndConditions;
539  }
Array< OneD, SpatialDomains::BoundaryConditionShPtr > m_bndConditions
An array which contains the information about the boundary condition on the different boundary region...
GlobalLinSysSharedPtr Nektar::MultiRegions::ContField2D::GetGlobalLinSys ( const GlobalLinSysKey mkey)
private

Returns the linear system specified by the key mkey.

The function searches the map #m_globalLinSys to see if the global matrix has been created before. If not, it calls the function GenGlobalLinSys to generate the requested global system.

Parameters
mkeyThis key uniquely defines the requested linear system.

Definition at line 595 of file ContField2D.cpp.

References m_globalLinSysManager.

Referenced by GlobalSolve().

597  {
598  return m_globalLinSysManager[mkey];
599  }
LibUtilities::NekManager< GlobalLinSysKey, GlobalLinSys > m_globalLinSysManager
A manager which collects all the global linear systems being assembled, such that they should be cons...
Definition: ContField2D.h:192
GlobalMatrixSharedPtr Nektar::MultiRegions::ContField2D::GetGlobalMatrix ( const GlobalMatrixKey mkey)
private

Returns the global matrix specified by mkey.

Returns the global matrix associated with the given GlobalMatrixKey. If the global matrix has not yet been constructed on this field, it is first constructed using GenGlobalMatrix().

Parameters
mkeyGlobal matrix key.
Returns
Assocated global matrix.

Definition at line 563 of file ContField2D.cpp.

References ASSERTL1, Nektar::MultiRegions::ExpList::GenGlobalMatrix(), Nektar::iterator, Nektar::MultiRegions::GlobalMatrixKey::LocToGloMapIsDefined(), m_globalMat, and m_locToGloMap.

Referenced by BwdTrans(), IProductWRTBase(), and v_GeneralMatrixOp().

565  {
566  ASSERTL1(mkey.LocToGloMapIsDefined(),
567  "To use method must have a AssemblyMap "
568  "attached to key");
569 
570  GlobalMatrixSharedPtr glo_matrix;
571  GlobalMatrixMap::iterator matrixIter = m_globalMat->find(mkey);
572 
573  if(matrixIter == m_globalMat->end())
574  {
575  glo_matrix = GenGlobalMatrix(mkey,m_locToGloMap);
576  (*m_globalMat)[mkey] = glo_matrix;
577  }
578  else
579  {
580  glo_matrix = matrixIter->second;
581  }
582 
583  return glo_matrix;
584  }
boost::shared_ptr< GlobalMatrix > GenGlobalMatrix(const GlobalMatrixKey &mkey, const boost::shared_ptr< AssemblyMapCG > &locToGloMap)
Generates a global matrix from the given key and map.
Definition: ExpList.cpp:897
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
boost::shared_ptr< GlobalMatrix > GlobalMatrixSharedPtr
Shared pointer to a GlobalMatrix object.
Definition: GlobalMatrix.h:89
GlobalMatrixMapShPtr m_globalMat
(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once.
Definition: ContField2D.h:187
StandardMatrixTag boost::call_traits< LhsDataType >::const_reference rhs typedef NekMatrix< LhsDataType, StandardMatrixTag >::iterator iterator
#define ASSERTL1(condition, msg)
Assert Level 1 – Debugging which is used whether in FULLDEBUG or DEBUG compilation mode...
Definition: ErrorUtil.hpp:191
int Nektar::MultiRegions::ContField2D::GetGlobalMatrixNnz ( const GlobalMatrixKey gkey)
inline

Definition at line 541 of file ContField2D.h.

References ASSERTL1, Nektar::iterator, Nektar::MultiRegions::GlobalMatrixKey::LocToGloMapIsDefined(), and m_globalMat.

542  {
543  ASSERTL1(gkey.LocToGloMapIsDefined(),
544  "To use method must have a AssemblyMap "
545  "attached to key");
546 
547  GlobalMatrixMap::iterator matrixIter = m_globalMat->find(gkey);
548 
549  if(matrixIter == m_globalMat->end())
550  {
551  return 0;
552  }
553  else
554  {
555  return matrixIter->second->GetNumNonZeroEntries();
556  }
557 
558  return 0;
559  }
GlobalMatrixMapShPtr m_globalMat
(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once.
Definition: ContField2D.h:187
StandardMatrixTag boost::call_traits< LhsDataType >::const_reference rhs typedef NekMatrix< LhsDataType, StandardMatrixTag >::iterator iterator
#define ASSERTL1(condition, msg)
Assert Level 1 – Debugging which is used whether in FULLDEBUG or DEBUG compilation mode...
Definition: ErrorUtil.hpp:191
const AssemblyMapCGSharedPtr & Nektar::MultiRegions::ContField2D::GetLocalToGlobalMap ( ) const
inline

Returns the map from local to global level.

Definition at line 433 of file ContField2D.h.

References m_locToGloMap.

434  {
435  return m_locToGloMap;
436  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
void Nektar::MultiRegions::ContField2D::GlobalSolve ( const GlobalLinSysKey key,
const Array< OneD, const NekDouble > &  rhs,
Array< OneD, NekDouble > &  inout,
const Array< OneD, const NekDouble > &  dirForcing = NullNekDouble1DArray 
)
private

Solves the linear system specified by the key key.

Given a linear system specified by the key key,

\[\boldsymbol{M}\boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}},\]

this function solves this linear system taking into account the boundary conditions specified in the data member m_bndCondExpansions. Therefore, it adds an array $\boldsymbol{\hat{g}}$ which represents the non-zero surface integral resulting from the weak boundary conditions (e.g. Neumann boundary conditions) to the right hand side, that is,

\[\boldsymbol{M}\boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}}+ \boldsymbol{\hat{g}}.\]

Furthermore, it lifts the known degrees of freedom which are prescribed by the Dirichlet boundary conditions. As these known coefficients $\boldsymbol{\hat{u}}^{\mathcal{D}}$ are numbered first in the global coefficient array $\boldsymbol{\hat{u}}_g$, the linear system can be decomposed as,

\[\left[\begin{array}{cc} \boldsymbol{M}^{\mathcal{DD}}&\boldsymbol{M}^{\mathcal{DH}}\\ \boldsymbol{M}^{\mathcal{HD}}&\boldsymbol{M}^{\mathcal{HH}} \end{array}\right] \left[\begin{array}{c} \boldsymbol{\hat{u}}^{\mathcal{D}}\\ \boldsymbol{\hat{u}}^{\mathcal{H}} \end{array}\right]= \left[\begin{array}{c} \boldsymbol{\hat{f}}^{\mathcal{D}}\\ \boldsymbol{\hat{f}}^{\mathcal{H}} \end{array}\right]+ \left[\begin{array}{c} \boldsymbol{\hat{g}}^{\mathcal{D}}\\ \boldsymbol{\hat{g}}^{\mathcal{H}} \end{array}\right] \]

which will then be solved for the unknown coefficients $\boldsymbol{\hat{u}}^{\mathcal{H}}$ as,

\[ \boldsymbol{M}^{\mathcal{HH}}\boldsymbol{\hat{u}}^{\mathcal{H}}= \boldsymbol{\hat{f}}^{\mathcal{H}}+ \boldsymbol{\hat{g}}^{\mathcal{H}}- \boldsymbol{M}^{\mathcal{HD}}\boldsymbol{\hat{u}}^{\mathcal{D}}\]

Parameters
mkeyThis key uniquely defines the linear system to be solved.
SinAn ExpList, containing the discrete evaluation of the forcing function $f(\boldsymbol{x})$ at the quadrature points in its array m_phys.
ScaleForcingAn optional parameter with which the forcing vector $\boldsymbol{\hat{f}}$ should be multiplied.
Note
inout contains initial guess and final output.

Definition at line 534 of file ContField2D.cpp.

References GetGlobalLinSys(), m_locToGloMap, and v_ImposeDirichletConditions().

Referenced by FwdTrans(), LaplaceSolve(), MultiplyByInvMassMatrix(), v_HelmSolve(), v_LinearAdvectionDiffusionReactionSolve(), and v_LinearAdvectionReactionSolve().

539  {
540  int NumDirBcs = m_locToGloMap->GetNumGlobalDirBndCoeffs();
541  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
542 
543  // STEP 1: SET THE DIRICHLET DOFS TO THE RIGHT VALUE
544  // IN THE SOLUTION ARRAY
546 
547  // STEP 2: CALCULATE THE HOMOGENEOUS COEFFICIENTS
548  if(contNcoeffs - NumDirBcs > 0)
549  {
551  LinSys->Solve(rhs,inout,m_locToGloMap,dirForcing);
552  }
553  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
virtual void v_ImposeDirichletConditions(Array< OneD, NekDouble > &outarray)
Impose the Dirichlet Boundary Conditions on outarray.
boost::shared_ptr< GlobalLinSys > GlobalLinSysSharedPtr
Pointer to a GlobalLinSys object.
Definition: GlobalLinSys.h:52
GlobalLinSysSharedPtr GetGlobalLinSys(const GlobalLinSysKey &mkey)
Returns the linear system specified by the key mkey.
void Nektar::MultiRegions::ContField2D::GlobalToLocal ( Array< OneD, NekDouble > &  outarray) const
inline

Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$.

This operation is evaluated as:

\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}^{e}[i] = \mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]$ \\ \> \> continue \\ \> continue \end{tabbing}

where map $[e][i]$ is the mapping array and sign $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the scatter operation $\boldsymbol{\hat{u}}_l=\mathcal{A}\boldsymbol{\hat{u}}_g$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

Parameters
outarrayThe resulting local degrees of freedom $\boldsymbol{x}_l$ will be stored in this array of size $N_\mathrm{eof}$.

Definition at line 320 of file ContField2D.h.

References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.

322  {
323  m_locToGloMap->GlobalToLocal(m_coeffs,outarray);
324  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
Array< OneD, NekDouble > m_coeffs
Concatenation of all local expansion coefficients.
Definition: ExpList.h:939
void Nektar::MultiRegions::ContField2D::GlobalToLocal ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
) const
inline

Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$.

This operation is evaluated as:

\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}^{e}[i] = \mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]$ \\ \> \> continue \\ \> continue \end{tabbing}

where map $[e][i]$ is the mapping array and sign $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the scatter operation $\boldsymbol{\hat{u}}_l=\mathcal{A}\boldsymbol{\hat{u}}_g$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

Parameters
inarrayAn array of size $N_\mathrm{dof}$ containing the global degrees of freedom $\boldsymbol{x}_g$.
outarrayThe resulting local degrees of freedom $\boldsymbol{x}_l$ will be stored in this array of size $N_\mathrm{eof}$.

Definition at line 353 of file ContField2D.h.

References m_locToGloMap.

356  {
357  m_locToGloMap->GlobalToLocal(inarray,outarray);
358  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
void Nektar::MultiRegions::ContField2D::IProductWRTBase ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
CoeffState  coeffstate = eLocal 
)
inline

Calculates the inner product of a function $f(\boldsymbol{x})$ with respect to all global expansion modes $\phi_n^e(\boldsymbol{x})$.

The operation is evaluated locally (i.e. with respect to all local expansion modes) by the function ExpList::IProductWRTBase. The inner product with respect to the global expansion modes is than obtained by a global assembly operation.

The values of the function $f(\boldsymbol{x})$ evaluated at the quadrature points $\boldsymbol{x}_i$ should be contained in the variable m_phys of the ExpList object in. The result is stored in the array m_coeffs.

Parameters
InAn ExpList, containing the discrete evaluation of $f(\boldsymbol{x})$ at the quadrature points in its array m_phys.

Definition at line 454 of file ContField2D.h.

References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eIProductWRTBase, GetGlobalMatrix(), Nektar::MultiRegions::ExpList::IProductWRTBase_IterPerExp(), Nektar::MultiRegions::ExpList::m_globalOptParam, m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.

Referenced by FwdTrans(), LaplaceSolve(), v_HelmSolve(), v_LinearAdvectionDiffusionReactionSolve(), v_LinearAdvectionReactionSolve(), and v_SmoothField().

459  {
460  if(coeffstate == eGlobal)
461  {
462  bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
464 
465  if(doGlobalOp)
466  {
467  GlobalMatrixKey gkey(StdRegions::eIProductWRTBase,
468  m_locToGloMap);
470  mat->Multiply(inarray,outarray);
471  m_locToGloMap->UniversalAssemble(outarray);
472  }
473  else
474  {
475  Array<OneD, NekDouble> wsp(m_ncoeffs);
476  IProductWRTBase_IterPerExp(inarray,wsp);
477  Assemble(wsp,outarray);
478  }
479  }
480  else
481  {
482  IProductWRTBase_IterPerExp(inarray,outarray);
483  }
484  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
NekOptimize::GlobalOptParamSharedPtr m_globalOptParam
Definition: ExpList.h:1001
boost::shared_ptr< GlobalMatrix > GlobalMatrixSharedPtr
Shared pointer to a GlobalMatrix object.
Definition: GlobalMatrix.h:89
Global coefficients.
void IProductWRTBase_IterPerExp(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
This function calculates the inner product of a function with respect to all {local} expansion modes...
Definition: ExpList.h:1570
int m_ncoeffs
The total number of local degrees of freedom. m_ncoeffs .
Definition: ExpList.h:917
GlobalMatrixSharedPtr GetGlobalMatrix(const GlobalMatrixKey &mkey)
Returns the global matrix specified by mkey.
void Assemble()
Assembles the global coefficients from the local coefficients .
Definition: ContField2D.h:392
void Nektar::MultiRegions::ContField2D::LaplaceSolve ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const Array< OneD, const NekDouble > &  dirForcing = NullNekDouble1DArray,
const Array< OneD, Array< OneD, NekDouble > > &  variablecoeffs = NullNekDoubleArrayofArray,
NekDouble  time = 0.0,
CoeffState  coeffstate = eLocal 
)

Solves the two-dimensional Laplace equation, subject to the boundary conditions specified.

Consider the two dimensional Laplace equation,

\[\nabla\cdot\left(\boldsymbol{\sigma}\nabla u(\boldsymbol{x})\right) = f(\boldsymbol{x}),\]

supplemented with appropriate boundary conditions (which are contained in the data member m_bndCondExpansions). In the equation above $\boldsymbol{\sigma}$ is the (symmetric positive definite) diffusion tensor:

\[ \sigma = \left[ \begin{array}{cc} \sigma_{00}(\boldsymbol{x},t) & \sigma_{01}(\boldsymbol{x},t) \\ \sigma_{01}(\boldsymbol{x},t) & \sigma_{11}(\boldsymbol{x},t) \end{array} \right]. \]

Applying a $C^0$ continuous Galerkin discretisation, this equation leads to the following linear system:

\[\boldsymbol{L} \boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}}\]

where $\boldsymbol{L}$ is the Laplacian matrix. This function solves the system above for the global coefficients $\boldsymbol{\hat{u}}$ by a call to the function GlobalSolve.

The values of the function $f(\boldsymbol{x})$ evaluated at the quadrature points $\boldsymbol{x}_i$ should be contained in the variable m_phys of the ExpList object Sin. The resulting global coefficients $\boldsymbol{\hat{u}}_g$ are stored in the array m_coeffs.

Parameters
SinAn ExpList, containing the discrete evaluation of the forcing function $f(\boldsymbol{x})$ at the quadrature points in its array m_phys.
variablecoeffsThe (optional) parameter containing the coefficients evaluated at the quadrature points. It is an Array of (three) arrays which stores the laplacian coefficients in the following way

\[\mathrm{variablecoeffs} = \left[ \begin{array}{c} \left[\sigma_{00}(\boldsymbol{x_i},t)\right]_i \\ \left[\sigma_{01}(\boldsymbol{x_i},t)\right]_i \\ \left[\sigma_{11}(\boldsymbol{x_i},t)\right]_i \end{array}\right] \]

If this argument is not passed to the function, the following equation will be solved:

\[\nabla^2u(\boldsymbol{x}) = f(\boldsymbol{x}),\]

timeThe time-level at which the coefficients are evaluated

Definition at line 385 of file ContField2D.cpp.

References Nektar::SpatialDomains::eDirichlet, Nektar::StdRegions::eFactorTime, Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eLaplacian, Nektar::StdRegions::eVarCoeffD00, Nektar::StdRegions::eVarCoeffD11, Nektar::StdRegions::eVarCoeffD22, Nektar::MultiRegions::ExpList::GetNcoeffs(), GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, and Vmath::Neg().

392  {
393  // Inner product of forcing
394  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
395  Array<OneD,NekDouble> wsp(contNcoeffs);
396  IProductWRTBase(inarray,wsp,eGlobal);
397  // Note -1.0 term necessary to invert forcing function to
398  // be consistent with matrix definition
399  Vmath::Neg(m_ncoeffs, wsp, 1);
400 
401  // Forcing function with weak boundary conditions
402  int i,j;
403  int bndcnt=0;
404  for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
405  {
406  if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
407  {
408  for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
409  {
410  wsp[m_locToGloMap
411  ->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
412  += (m_bndCondExpansions[i]->GetCoeffs())[j];
413  }
414  }
415  else
416  {
417  bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
418  }
419  }
420 
421  StdRegions::VarCoeffMap varcoeffs;
422  varcoeffs[StdRegions::eVarCoeffD00] = variablecoeffs[0];
423  varcoeffs[StdRegions::eVarCoeffD11] = variablecoeffs[3];
424  varcoeffs[StdRegions::eVarCoeffD22] = variablecoeffs[5];
426  factors[StdRegions::eFactorTime] = time;
427 
428  // Solve the system
429  GlobalLinSysKey key(StdRegions::eLaplacian,m_locToGloMap,factors,
430  varcoeffs);
431 
432  if(coeffstate == eGlobal)
433  {
434  GlobalSolve(key,wsp,outarray,dirForcing);
435  }
436  else
437  {
438  Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
439  GlobalSolve(key,wsp,tmp,dirForcing);
440  GlobalToLocal(tmp,outarray);
441  }
442  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
std::map< ConstFactorType, NekDouble > ConstFactorMap
Definition: StdRegions.hpp:251
Global coefficients.
Array< OneD, MultiRegions::ExpListSharedPtr > m_bndCondExpansions
An object which contains the discretised boundary conditions.
std::map< StdRegions::VarCoeffType, Array< OneD, NekDouble > > VarCoeffMap
Definition: StdRegions.hpp:226
int m_ncoeffs
The total number of local degrees of freedom. m_ncoeffs .
Definition: ExpList.h:917
void GlobalSolve(const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
Solves the linear system specified by the key key.
void Neg(int n, T *x, const int incx)
Negate x = -x.
Definition: Vmath.cpp:382
Array< OneD, SpatialDomains::BoundaryConditionShPtr > m_bndConditions
An array which contains the information about the boundary condition on the different boundary region...
void IProductWRTBase(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Calculates the inner product of a function with respect to all global expansion modes ...
Definition: ContField2D.h:454
int GetNcoeffs(void) const
Returns the total number of local degrees of freedom .
Definition: ExpList.h:1403
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1855
void Nektar::MultiRegions::ContField2D::LinearAdvectionEigs ( const NekDouble  ax,
const NekDouble  ay,
Array< OneD, NekDouble > &  Real,
Array< OneD, NekDouble > &  Imag,
Array< OneD, NekDouble > &  Evecs = NullNekDouble1DArray 
)

Compute the eigenvalues of the linear advection operator.

Constructs the GlobalLinearSysKey for the linear advection operator with the supplied parameters, and computes the eigenvectors and eigenvalues of the associated matrix.

Parameters
axAdvection parameter, x.
ayAdvection parameter, y.
RealComputed eigenvalues, real component.
ImagComputed eigenvalues, imag component.
EvecsComputed eigenvectors.

Definition at line 455 of file ContField2D.cpp.

References Nektar::StdRegions::eFactorTime, Nektar::StdRegions::eLinearAdvectionReaction, Nektar::StdRegions::eVarCoeffVelX, Nektar::StdRegions::eVarCoeffVelY, Nektar::MultiRegions::ExpList::GenGlobalMatrixFull(), m_locToGloMap, and Nektar::MultiRegions::ExpList::m_npoints.

460  {
461  // Solve the system
462  Array<OneD, Array<OneD, NekDouble> > vel(2);
463  Array<OneD, NekDouble> vel_x(m_npoints,ax);
464  Array<OneD, NekDouble> vel_y(m_npoints,ay);
465  vel[0] = vel_x;
466  vel[1] = vel_y;
467 
468  StdRegions::VarCoeffMap varcoeffs;
469  varcoeffs[StdRegions::eVarCoeffVelX] = Array<OneD, NekDouble>(m_npoints,ax);
470  varcoeffs[StdRegions::eVarCoeffVelY] = Array<OneD, NekDouble>(m_npoints,ay);
472  factors[StdRegions::eFactorTime] = 0.0;
474  factors,varcoeffs);
475 
477  Gmat->EigenSolve(Real,Imag,Evecs);
478  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
boost::shared_ptr< DNekMat > GenGlobalMatrixFull(const GlobalLinSysKey &mkey, const boost::shared_ptr< AssemblyMapCG > &locToGloMap)
Definition: ExpList.cpp:1034
std::map< ConstFactorType, NekDouble > ConstFactorMap
Definition: StdRegions.hpp:251
boost::shared_ptr< DNekMat > DNekMatSharedPtr
Definition: NekTypeDefs.hpp:70
std::map< StdRegions::VarCoeffType, Array< OneD, NekDouble > > VarCoeffMap
Definition: StdRegions.hpp:226
void Nektar::MultiRegions::ContField2D::LocalToGlobal ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
) const
inline

Definition at line 360 of file ContField2D.h.

References m_locToGloMap.

363  {
364  m_locToGloMap->LocalToGlobal(inarray, outarray);
365  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
void Nektar::MultiRegions::ContField2D::MultiplyByInvMassMatrix ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
CoeffState  coeffstate = eLocal 
)

Multiply a solution by the inverse mass matrix.

Computes the matrix vector product $ \mathbf{y} = \mathbf{M}^{-1}\mathbf{x} $. If coeffstate == eGlobal is set then the elemental system is used directly. If not set, the global system is assembled, the system is solved, and mapped back to the local elemental system.

Parameters
inarrayInput vector $\mathbf{x}$.
outarrayOutput vector $\mathbf{y}$.
coeffStateFlag for using global system.

Definition at line 295 of file ContField2D.cpp.

References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eMass, GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), m_locToGloMap, and Vmath::Vcopy().

Referenced by v_MultiplyByInvMassMatrix(), and v_SmoothField().

300  {
301  GlobalLinSysKey key(StdRegions::eMass,m_locToGloMap);
302  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
303 
304  if(coeffstate == eGlobal)
305  {
306  if(inarray.data() == outarray.data())
307  {
308  Array<OneD, NekDouble> tmp(contNcoeffs,0.0);
309  Vmath::Vcopy(contNcoeffs,inarray,1,tmp,1);
310  GlobalSolve(key,tmp,outarray);
311  }
312  else
313  {
314  GlobalSolve(key,inarray,outarray);
315  }
316  }
317  else
318  {
319  Array<OneD, NekDouble> globaltmp(contNcoeffs,0.0);
320 
321  if(inarray.data() == outarray.data())
322  {
323  Array<OneD,NekDouble> tmp(inarray.num_elements());
324  Vmath::Vcopy(inarray.num_elements(),inarray,1,tmp,1);
325  Assemble(tmp,outarray);
326  }
327  else
328  {
329  Assemble(inarray,outarray);
330  }
331 
332  GlobalSolve(key,outarray,globaltmp);
333  GlobalToLocal(globaltmp,outarray);
334  }
335  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
Global coefficients.
void GlobalSolve(const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
Solves the linear system specified by the key key.
void Assemble()
Assembles the global coefficients from the local coefficients .
Definition: ContField2D.h:392
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1855
void Vcopy(int n, const T *x, const int incx, T *y, const int incy)
Definition: Vmath.cpp:1047
void Nektar::MultiRegions::ContField2D::v_BwdTrans ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
CoeffState  coeffstate 
)
privatevirtual

Template method virtual forwarder for FwdTrans().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 614 of file ContField2D.cpp.

References BwdTrans().

618  {
619  BwdTrans(inarray,outarray,coeffstate);
620  }
void BwdTrans(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Performs the backward transformation of the spectral/hp element expansion.
Definition: ContField2D.h:500
void Nektar::MultiRegions::ContField2D::v_ClearGlobalLinSysManager ( void  )
privatevirtual

Reset the GlobalLinSys Manager

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 1054 of file ContField2D.cpp.

References m_globalLinSysManager.

1055  {
1056  m_globalLinSysManager.ClearManager("GlobalLinSys");
1057  }
LibUtilities::NekManager< GlobalLinSysKey, GlobalLinSys > m_globalLinSysManager
A manager which collects all the global linear systems being assembled, such that they should be cons...
Definition: ContField2D.h:192
void Nektar::MultiRegions::ContField2D::v_FillBndCondFromField ( void  )
privatevirtual

Reimplemented from Nektar::MultiRegions::DisContField2D.

Definition at line 693 of file ContField2D.cpp.

References Nektar::MultiRegions::ExpList::GetNcoeffs(), Nektar::MultiRegions::ExpList::LocalToGlobal(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::ExpList::m_coeffs, m_locToGloMap, and sign.

694  {
695  NekDouble sign;
696  int bndcnt = 0;
697  const Array<OneD,const int> &bndMap =
698  m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap();
699 
700  Array<OneD, NekDouble> tmp(m_locToGloMap->GetNumGlobalCoeffs());
701  LocalToGlobal(m_coeffs,tmp);
702 
703  // Now fill in all other Dirichlet coefficients.
704  for(int i = 0; i < m_bndCondExpansions.num_elements(); ++i)
705  {
706  Array<OneD, NekDouble>& coeffs = m_bndCondExpansions[i]->UpdateCoeffs();
707 
708  for(int j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
709  {
710  sign = m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsSign(bndcnt);
711  coeffs[j] = sign * tmp[bndMap[bndcnt++]];
712  }
713  }
714  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
#define sign(a, b)
return the sign(b)*a
Definition: Polylib.cpp:22
Array< OneD, NekDouble > m_coeffs
Concatenation of all local expansion coefficients.
Definition: ExpList.h:939
Array< OneD, MultiRegions::ExpListSharedPtr > m_bndCondExpansions
An object which contains the discretised boundary conditions.
double NekDouble
void LocalToGlobal(void)
Put the coefficients into global ordering using m_coeffs.
Definition: ExpList.h:1850
int GetNcoeffs(void) const
Returns the total number of local degrees of freedom .
Definition: ExpList.h:1403
void Nektar::MultiRegions::ContField2D::v_FwdTrans ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
CoeffState  coeffstate 
)
privatevirtual

Template method virtual forwarder for FwdTrans().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 626 of file ContField2D.cpp.

References FwdTrans().

630  {
631  FwdTrans(inarray,outarray,coeffstate);
632  }
void FwdTrans(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Performs the global forward transformation of a function , subject to the boundary conditions specifi...
void Nektar::MultiRegions::ContField2D::v_GeneralMatrixOp ( const GlobalMatrixKey gkey,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
CoeffState  coeffstate 
)
privatevirtual

Calculates the result of the multiplication of a global matrix of type specified by mkey with a vector given by inarray.

This is equivalent to the operation:

\[\boldsymbol{M\hat{u}}_g\]

where $\boldsymbol{M}$ is the global matrix of type specified by mkey. After scattering the global array inarray to local level, this operation is evaluated locally by the function ExpList::GeneralMatrixOp. The global result is then obtained by a global assembly procedure.

Parameters
mkeyThis key uniquely defines the type matrix required for the operation.
inarrayThe vector $\boldsymbol{\hat{u}}_g$ of size $N_{\mathrm{dof}}$.
outarrayThe resulting vector of size $N_{\mathrm{dof}}$.

Reimplemented from Nektar::MultiRegions::DisContField2D.

Definition at line 895 of file ContField2D.cpp.

References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::MultiRegions::ExpList::GeneralMatrixOp_IterPerExp(), GetGlobalMatrix(), Nektar::MultiRegions::GlobalMatrixKey::GetMatrixType(), Nektar::MultiRegions::ExpList::GlobalToLocal(), Nektar::MultiRegions::ExpList::m_globalOptParam, m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.

900  {
901  if(coeffstate == eGlobal)
902  {
903  bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
904  gkey.GetMatrixType());
905 
906  if(doGlobalOp)
907  {
909  mat->Multiply(inarray,outarray);
910  m_locToGloMap->UniversalAssemble(outarray);
911  }
912  else
913  {
914  Array<OneD,NekDouble> tmp1(2*m_ncoeffs);
915  Array<OneD,NekDouble> tmp2(tmp1+m_ncoeffs);
916  GlobalToLocal(inarray,tmp1);
917  GeneralMatrixOp_IterPerExp(gkey,tmp1,tmp2);
918  Assemble(tmp2,outarray);
919  }
920  }
921  else
922  {
923  GeneralMatrixOp_IterPerExp(gkey,inarray,outarray);
924  }
925  }
void GeneralMatrixOp_IterPerExp(const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Definition: ExpList.cpp:829
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
NekOptimize::GlobalOptParamSharedPtr m_globalOptParam
Definition: ExpList.h:1001
boost::shared_ptr< GlobalMatrix > GlobalMatrixSharedPtr
Shared pointer to a GlobalMatrix object.
Definition: GlobalMatrix.h:89
Global coefficients.
int m_ncoeffs
The total number of local degrees of freedom. m_ncoeffs .
Definition: ExpList.h:917
GlobalMatrixSharedPtr GetGlobalMatrix(const GlobalMatrixKey &mkey)
Returns the global matrix specified by mkey.
void Assemble()
Assembles the global coefficients from the local coefficients .
Definition: ContField2D.h:392
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1855
const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField2D::v_GetBndConditions ( void  )
privatevirtual

Template method virtual forwarder for GetBndConditions().

Reimplemented from Nektar::MultiRegions::DisContField2D.

Definition at line 1045 of file ContField2D.cpp.

References GetBndConditions().

1046  {
1047  return GetBndConditions();
1048  }
const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & GetBndConditions()
Returns the boundary conditions.
Definition: ContField2D.h:536
void Nektar::MultiRegions::ContField2D::v_GlobalToLocal ( void  )
privatevirtual

Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$.

This operation is evaluated as:

\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}^{e}[i] = \mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]$ \\ \> \> continue \\ \> continue \end{tabbing}

where map $[e][i]$ is the mapping array and sign $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the scatter operation $\boldsymbol{\hat{u}}_l=\mathcal{A}\boldsymbol{\hat{u}}_g$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

Note
The array m_coeffs should be filled with the global coefficients $\boldsymbol{\hat{u}}_g$ and that the resulting local coefficients $\boldsymbol{\hat{u}}_l$ will be stored in m_coeffs.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 740 of file ContField2D.cpp.

References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.

741  {
742  m_locToGloMap->GlobalToLocal(m_coeffs,m_coeffs);
743  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
Array< OneD, NekDouble > m_coeffs
Concatenation of all local expansion coefficients.
Definition: ExpList.h:939
void Nektar::MultiRegions::ContField2D::v_HelmSolve ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const FlagList flags,
const StdRegions::ConstFactorMap factors,
const StdRegions::VarCoeffMap varcoeff,
const Array< OneD, const NekDouble > &  dirForcing 
)
privatevirtual

Solves the two-dimensional Helmholtz equation, subject to the boundary conditions specified.

Consider the two dimensional Helmholtz equation,

\[\nabla^2u(\boldsymbol{x})-\lambda u(\boldsymbol{x}) = f(\boldsymbol{x}),\]

supplemented with appropriate boundary conditions (which are contained in the data member m_bndCondExpansions). Applying a $C^0$ continuous Galerkin discretisation, this equation leads to the following linear system:

\[\left(\boldsymbol{L}+\lambda\boldsymbol{M}\right) \boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}}\]

where $\boldsymbol{L}$ and $\boldsymbol{M}$ are the Laplacian and mass matrix respectively. This function solves the system above for the global coefficients $\boldsymbol{\hat{u}}$ by a call to the function GlobalSolve. It is assumed #m_coeff contains an initial estimate for the solution.

The values of the function $f(\boldsymbol{x})$ evaluated at the quadrature points $\boldsymbol{x}_i$ should be contained in the variable m_phys of the ExpList object inarray. The resulting global coefficients $\boldsymbol{\hat{u}}_g$ are stored in the array #m_contCoeffs or m_coeffs depending on whether coeffstate is eGlobal or eLocal

Parameters
inarrayAn ExpList, containing the discrete evaluation of the forcing function $f(\boldsymbol{x})$ at the quadrature points in its array m_phys.
factorsThe parameter $\lambda$ of the Helmholtz equation is specified through the factors map

Reimplemented from Nektar::MultiRegions::DisContField2D.

Definition at line 817 of file ContField2D.cpp.

References Nektar::SpatialDomains::eDirichlet, Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eHelmholtz, Nektar::eUseGlobal, Nektar::MultiRegions::ExpList::GetNcoeffs(), GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), Nektar::FlagList::isSet(), Nektar::MultiRegions::ExpList::LocalToGlobal(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Vmath::Neg(), and Vmath::Vadd().

824  {
825  //----------------------------------
826  // Setup RHS Inner product
827  //----------------------------------
828  // Inner product of forcing
829  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
830  Array<OneD,NekDouble> wsp(contNcoeffs);
831  IProductWRTBase(inarray,wsp,eGlobal);
832  // Note -1.0 term necessary to invert forcing function to
833  // be consistent with matrix definition
834  Vmath::Neg(contNcoeffs, wsp, 1);
835 
836  // Fill weak boundary conditions
837  int i,j;
838  int bndcnt=0;
839  Array<OneD, NekDouble> gamma(contNcoeffs, 0.0);
840 
841  for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
842  {
843  if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
844  {
845  for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
846  {
847  gamma[m_locToGloMap
848  ->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
849  += (m_bndCondExpansions[i]->GetCoeffs())[j];
850  }
851  }
852  else
853  {
854  bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
855  }
856  }
857 
858  m_locToGloMap->UniversalAssemble(gamma);
859 
860  // Add weak boundary conditions to forcing
861  Vmath::Vadd(contNcoeffs, wsp, 1, gamma, 1, wsp, 1);
862 
863  GlobalLinSysKey key(StdRegions::eHelmholtz,m_locToGloMap,factors,varcoeff);
864 
865  if(flags.isSet(eUseGlobal))
866  {
867  GlobalSolve(key,wsp,outarray,dirForcing);
868  }
869  else
870  {
871  Array<OneD,NekDouble> tmp(contNcoeffs);
872  LocalToGlobal(outarray,tmp);
873  GlobalSolve(key,wsp,tmp,dirForcing);
874  GlobalToLocal(tmp,outarray);
875  }
876  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
Global coefficients.
Array< OneD, MultiRegions::ExpListSharedPtr > m_bndCondExpansions
An object which contains the discretised boundary conditions.
void GlobalSolve(const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
Solves the linear system specified by the key key.
void Neg(int n, T *x, const int incx)
Negate x = -x.
Definition: Vmath.cpp:382
Array< OneD, SpatialDomains::BoundaryConditionShPtr > m_bndConditions
An array which contains the information about the boundary condition on the different boundary region...
void IProductWRTBase(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Calculates the inner product of a function with respect to all global expansion modes ...
Definition: ContField2D.h:454
void LocalToGlobal(void)
Put the coefficients into global ordering using m_coeffs.
Definition: ExpList.h:1850
int GetNcoeffs(void) const
Returns the total number of local degrees of freedom .
Definition: ExpList.h:1403
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1855
void Vadd(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Add vector z = x+y.
Definition: Vmath.cpp:285
void Nektar::MultiRegions::ContField2D::v_ImposeDirichletConditions ( Array< OneD, NekDouble > &  outarray)
privatevirtual

Impose the Dirichlet Boundary Conditions on outarray.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 634 of file ContField2D.cpp.

References Nektar::SpatialDomains::eDirichlet, Nektar::MultiRegions::ExpList::GetNcoeffs(), Nektar::iterator, Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, sign, and Vmath::Vcopy().

Referenced by GlobalSolve().

635  {
636  int i,j;
637  int bndcnt=0;
638  int nDir = m_locToGloMap->GetNumGlobalDirBndCoeffs();
639 
640  // STEP 1: SET THE DIRICHLET DOFS TO THE RIGHT VALUE IN THE SOLUTION
641  // ARRAY
642  NekDouble sign;
643  const Array<OneD,const int> &bndMap =
644  m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap();
645 
646  Array<OneD, NekDouble> tmp(
647  m_locToGloMap->GetNumGlobalBndCoeffs(), 0.0);
648 
649  // Fill in Dirichlet coefficients that are to be sent to
650  // other processors. This code block uses a
651  // tuple<int,int.NekDouble> which stores the local id of
652  // coefficent the global id of the data location and the
653  // inverse of the values of the data (arising from
654  // periodic boundary conditiosn)
655  map<int, vector<ExtraDirDof> > &extraDirDofs =
656  m_locToGloMap->GetExtraDirDofs();
657  map<int, vector<ExtraDirDof> >::iterator it;
658  for (it = extraDirDofs.begin(); it != extraDirDofs.end(); ++it)
659  {
660  for (i = 0; i < it->second.size(); ++i)
661  {
662  tmp[it->second.at(i).get<1>()] =
663  m_bndCondExpansions[it->first]->GetCoeffs()[
664  it->second.at(i).get<0>()]*it->second.at(i).get<2>();
665  }
666  }
667  m_locToGloMap->UniversalAssembleBnd(tmp);
668 
669  // Now fill in all other Dirichlet coefficients.
670  for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
671  {
672  if(m_bndConditions[i]->GetBoundaryConditionType() ==
674  {
675  const Array<OneD,const NekDouble>& coeffs =
676  m_bndCondExpansions[i]->GetCoeffs();
677  for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
678  {
679  sign = m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsSign(
680  bndcnt);
681  tmp[bndMap[bndcnt++]] = sign * coeffs[j];
682  }
683  }
684  else
685  {
686  bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
687  }
688  }
689 
690  Vmath::Vcopy(nDir, tmp, 1, outarray, 1);
691  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
#define sign(a, b)
return the sign(b)*a
Definition: Polylib.cpp:22
Array< OneD, MultiRegions::ExpListSharedPtr > m_bndCondExpansions
An object which contains the discretised boundary conditions.
double NekDouble
Array< OneD, SpatialDomains::BoundaryConditionShPtr > m_bndConditions
An array which contains the information about the boundary condition on the different boundary region...
StandardMatrixTag boost::call_traits< LhsDataType >::const_reference rhs typedef NekMatrix< LhsDataType, StandardMatrixTag >::iterator iterator
int GetNcoeffs(void) const
Returns the total number of local degrees of freedom .
Definition: ExpList.h:1403
void Vcopy(int n, const T *x, const int incx, T *y, const int incy)
Definition: Vmath.cpp:1047
void Nektar::MultiRegions::ContField2D::v_LinearAdvectionDiffusionReactionSolve ( const Array< OneD, Array< OneD, NekDouble > > &  velocity,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const NekDouble  lambda,
CoeffState  coeffstate = eLocal,
const Array< OneD, const NekDouble > &  dirForcing = NullNekDouble1DArray 
)
privatevirtual

First compute the inner product of forcing function with respect to base, and then solve the system with the linear advection operator.

Parameters
velocityArray of advection velocities in physical space
inarrayForcing function.
outarrayResult.
lambdareaction coefficient
coeffstateState of Coefficients, Local or Global
dirForcingDirichlet Forcing.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 939 of file ContField2D.cpp.

References Nektar::SpatialDomains::eDirichlet, Nektar::StdRegions::eFactorLambda, Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eLinearAdvectionDiffusionReaction, Nektar::StdRegions::eVarCoeffVelX, Nektar::StdRegions::eVarCoeffVelY, Nektar::MultiRegions::ExpList::GetNcoeffs(), GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Vmath::Neg(), and Vmath::Vadd().

945  {
946  // Inner product of forcing
947  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
948  Array<OneD,NekDouble> wsp(contNcoeffs);
949  IProductWRTBase(inarray,wsp,eGlobal);
950  // Note -1.0 term necessary to invert forcing function to
951  // be consistent with matrix definition
952  Vmath::Neg(contNcoeffs, wsp, 1);
953 
954  // Forcing function with weak boundary conditions
955  int i,j;
956  int bndcnt=0;
957  Array<OneD, NekDouble> gamma(contNcoeffs, 0.0);
958  for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
959  {
960  if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
961  {
962  for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
963  {
964  gamma[m_locToGloMap
965  ->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
966  += (m_bndCondExpansions[i]->GetCoeffs())[j];
967  }
968  }
969  else
970  {
971  bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
972  }
973  }
974  m_locToGloMap->UniversalAssemble(wsp);
975  // Add weak boundary conditions to forcing
976  Vmath::Vadd(contNcoeffs, wsp, 1, gamma, 1, wsp, 1);
977 
978  // Solve the system
980  factors[StdRegions::eFactorLambda] = lambda;
981  StdRegions::VarCoeffMap varcoeffs;
982  varcoeffs[StdRegions::eVarCoeffVelX] = velocity[0];
983  varcoeffs[StdRegions::eVarCoeffVelY] = velocity[1];
984  GlobalLinSysKey key(StdRegions::eLinearAdvectionDiffusionReaction,m_locToGloMap,factors,varcoeffs);
985 
986  if(coeffstate == eGlobal)
987  {
988  GlobalSolve(key,wsp,outarray,dirForcing);
989  }
990  else
991  {
992  Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
993  GlobalSolve(key,wsp,tmp,dirForcing);
994  GlobalToLocal(tmp,outarray);
995  }
996  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
std::map< ConstFactorType, NekDouble > ConstFactorMap
Definition: StdRegions.hpp:251
Global coefficients.
Array< OneD, MultiRegions::ExpListSharedPtr > m_bndCondExpansions
An object which contains the discretised boundary conditions.
std::map< StdRegions::VarCoeffType, Array< OneD, NekDouble > > VarCoeffMap
Definition: StdRegions.hpp:226
void GlobalSolve(const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
Solves the linear system specified by the key key.
void Neg(int n, T *x, const int incx)
Negate x = -x.
Definition: Vmath.cpp:382
Array< OneD, SpatialDomains::BoundaryConditionShPtr > m_bndConditions
An array which contains the information about the boundary condition on the different boundary region...
void IProductWRTBase(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Calculates the inner product of a function with respect to all global expansion modes ...
Definition: ContField2D.h:454
int GetNcoeffs(void) const
Returns the total number of local degrees of freedom .
Definition: ExpList.h:1403
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1855
void Vadd(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Add vector z = x+y.
Definition: Vmath.cpp:285
void Nektar::MultiRegions::ContField2D::v_LinearAdvectionReactionSolve ( const Array< OneD, Array< OneD, NekDouble > > &  velocity,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const NekDouble  lambda,
CoeffState  coeffstate = eLocal,
const Array< OneD, const NekDouble > &  dirForcing = NullNekDouble1DArray 
)
privatevirtual

First compute the inner product of forcing function with respect to base, and then solve the system with the linear advection operator.

Parameters
velocityArray of advection velocities in physical space
inarrayForcing function.
outarrayResult.
lambdareaction coefficient
coeffstateState of Coefficients, Local or Global
dirForcingDirichlet Forcing.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 1008 of file ContField2D.cpp.

References Nektar::StdRegions::eFactorLambda, Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eLinearAdvectionReaction, Nektar::StdRegions::eVarCoeffVelX, Nektar::StdRegions::eVarCoeffVelY, GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), and m_locToGloMap.

1014  {
1015  // Inner product of forcing
1016  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
1017  Array<OneD,NekDouble> wsp(contNcoeffs);
1018  IProductWRTBase(inarray,wsp,eGlobal);
1019 
1020  // Solve the system
1022  factors[StdRegions::eFactorLambda] = lambda;
1023  StdRegions::VarCoeffMap varcoeffs;
1024  varcoeffs[StdRegions::eVarCoeffVelX] = velocity[0];
1025  varcoeffs[StdRegions::eVarCoeffVelY] = velocity[1];
1026  GlobalLinSysKey key(StdRegions::eLinearAdvectionReaction,m_locToGloMap,factors,varcoeffs);
1027 
1028  if(coeffstate == eGlobal)
1029  {
1030  GlobalSolve(key,wsp,outarray,dirForcing);
1031  }
1032  else
1033  {
1034  Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
1035  GlobalSolve(key,wsp,tmp,dirForcing);
1036  GlobalToLocal(tmp,outarray);
1037  }
1038  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
std::map< ConstFactorType, NekDouble > ConstFactorMap
Definition: StdRegions.hpp:251
Global coefficients.
std::map< StdRegions::VarCoeffType, Array< OneD, NekDouble > > VarCoeffMap
Definition: StdRegions.hpp:226
void GlobalSolve(const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
Solves the linear system specified by the key key.
void IProductWRTBase(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Calculates the inner product of a function with respect to all global expansion modes ...
Definition: ContField2D.h:454
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1855
void Nektar::MultiRegions::ContField2D::v_LocalToGlobal ( void  )
privatevirtual

Gathers the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$.

This operation is evaluated as:

\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}_g[\mbox{map}[e][i]] = \mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}^{e}[i]$\\ \> \> continue\\ \> continue \end{tabbing}

where map $[e][i]$ is the mapping array and sign $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the gather operation $\boldsymbol{\hat{u}}_g=\mathcal{A}^{-1}\boldsymbol{\hat{u}}_l$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

Note
The array m_coeffs should be filled with the local coefficients $\boldsymbol{\hat{u}}_l$ and that the resulting global coefficients $\boldsymbol{\hat{u}}_g$ will be stored in m_coeffs.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 771 of file ContField2D.cpp.

References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.

772  {
773  m_locToGloMap->LocalToGlobal(m_coeffs,m_coeffs);
774  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
Array< OneD, NekDouble > m_coeffs
Concatenation of all local expansion coefficients.
Definition: ExpList.h:939
void Nektar::MultiRegions::ContField2D::v_MultiplyByInvMassMatrix ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
CoeffState  coeffstate 
)
privatevirtual

Template method virtual forwarder for MultiplyByInvMassMatrix().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 779 of file ContField2D.cpp.

References MultiplyByInvMassMatrix().

783  {
784  MultiplyByInvMassMatrix(inarray,outarray,coeffstate);
785  }
void MultiplyByInvMassMatrix(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Multiply a solution by the inverse mass matrix.
void Nektar::MultiRegions::ContField2D::v_SmoothField ( Array< OneD, NekDouble > &  field)
privatevirtual

Template method virtual forwarded for SmoothField().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 272 of file ContField2D.cpp.

References BwdTrans(), Nektar::MultiRegions::eGlobal, IProductWRTBase(), m_locToGloMap, and MultiplyByInvMassMatrix().

273  {
274  int gloNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
275  Array<OneD,NekDouble> tmp1(gloNcoeffs);
276  Array<OneD,NekDouble> tmp2(gloNcoeffs);
277 
278  IProductWRTBase(field,tmp1,eGlobal);
279  MultiplyByInvMassMatrix(tmp1,tmp2,eGlobal);
280  BwdTrans(tmp2,field,eGlobal);
281  }
AssemblyMapCGSharedPtr m_locToGloMap
(A shared pointer to) the object which contains all the required information for the transformation f...
Definition: ContField2D.h:182
void BwdTrans(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Performs the backward transformation of the spectral/hp element expansion.
Definition: ContField2D.h:500
Global coefficients.
void IProductWRTBase(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Calculates the inner product of a function with respect to all global expansion modes ...
Definition: ContField2D.h:454
void MultiplyByInvMassMatrix(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
Multiply a solution by the inverse mass matrix.

Member Data Documentation

LibUtilities::NekManager<GlobalLinSysKey, GlobalLinSys> Nektar::MultiRegions::ContField2D::m_globalLinSysManager
private

A manager which collects all the global linear systems being assembled, such that they should be constructed only once.

Definition at line 192 of file ContField2D.h.

Referenced by GetGlobalLinSys(), and v_ClearGlobalLinSysManager().

GlobalMatrixMapShPtr Nektar::MultiRegions::ContField2D::m_globalMat
private

(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once.

Definition at line 187 of file ContField2D.h.

Referenced by GetGlobalMatrix(), and GetGlobalMatrixNnz().

AssemblyMapCGSharedPtr Nektar::MultiRegions::ContField2D::m_locToGloMap
private