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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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Collaboration 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 ()
 
 DisContField2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph2D, const std::string &variable, const bool SetUpJustDG=true, const bool DeclareCoeffPhysArrays=true)
 
 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 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 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 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::ExpansionVectorGetExp () 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)
 
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 GeneralGetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef, int NumHomoDir=0, int NumHomoStrip=1, Array< OneD, LibUtilities::BasisSharedPtr > &HomoBasis=LibUtilities::NullBasisSharedPtr1DArray, std::vector< NekDouble > &HomoLen=LibUtilities::NullNekDoubleVector, std::vector< unsigned int > &HomoZIDs=LibUtilities::NullUnsignedIntVector, std::vector< unsigned int > &HomoYIDs=LibUtilities::NullUnsignedIntVector)
 
const NekOptimize::GlobalOptParamSharedPtrGetGlobalOptParam (void)
 
map< int, RobinBCInfoSharedPtrGetRobinBCInfo ()
 
void GetPeriodicEntities (PeriodicMap &periodicVerts, PeriodicMap &periodicEdges, PeriodicMap &periodicFaces=NullPeriodicMap)
 
std::vector< LibUtilities::FieldDefinitionsSharedPtrGetFieldDefinitions ()
 
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::SessionReaderGetSession ()
 Returns the session object. More...
 
boost::shared_ptr< LibUtilities::CommGetComm ()
 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...
 

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...
 

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, GlobalLinSysm_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
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_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::ExpListSharedPtrv_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 map< int, RobinBCInfoSharedPtrv_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 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 std::vector< LibUtilities::FieldDefinitionsSharedPtrv_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 NekDoublev_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, MultiRegions::ExpListSharedPtrm_bndCondExpansions
 An object which contains the discretised boundary conditions. More...
 
Array< OneD, SpatialDomains::BoundaryConditionShPtrm_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
 
Array< OneD, Array< OneD, unsigned int > > m_mapEdgeToElmn
 
Array< OneD, Array< OneD, unsigned int > > m_signEdgeToElmn
 
Array< OneD, StdRegions::Orientationm_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...
 
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...
 
vector< int > m_periodicBwdCopy
 
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::ExpansionVectorm_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 86 of file ContField2D.cpp.

86  :
88  m_locToGloMap(),
89  m_globalMat(),
91  boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
92  std::string("GlobalLinSys"))
93  {
94  }
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
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 118 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.

122  :
123  DisContField2D(pSession,graph2D,variable,false,DeclareCoeffPhysArrays),
126  boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
127  std::string("GlobalLinSys"))
128  {
133  CheckIfSingularSystem,
134  variable,
137 
138  if (m_session->DefinesCmdLineArgument("verbose"))
139  {
140  m_locToGloMap->PrintStats(std::cout, variable);
141  }
142  }
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.
General purpose memory allocation routines with the ability to allocate from thread specific memory p...
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
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:887
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:880
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 168 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().

172  :
173  DisContField2D(In,graph2D,variable,false,DeclareCoeffPhysArrays),
176  boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
177  std::string("GlobalLinSys"))
178  {
179  if(!SameTypeOfBoundaryConditions(In) || CheckIfSingularSystem)
180  {
185  CheckIfSingularSystem,
186  variable,
189 
190  if (m_session->DefinesCmdLineArgument("verbose"))
191  {
192  m_locToGloMap->PrintStats(std::cout, variable);
193  }
194  }
195  else
196  {
197  m_locToGloMap = In.m_locToGloMap;
198  }
199  }
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.
General purpose memory allocation routines with the ability to allocate from thread specific memory p...
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)
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:887
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:880
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 208 of file ContField2D.cpp.

208  :
209  DisContField2D(In,DeclareCoeffPhysArrays),
210  m_locToGloMap(In.m_locToGloMap),
211  m_globalMat(In.m_globalMat),
212  m_globalLinSysManager(In.m_globalLinSysManager)
213  {
214  }
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
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 220 of file ContField2D.cpp.

221  {
222  }

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 390 of file ContField2D.h.

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

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

391  {
392  m_locToGloMap->Assemble(m_coeffs,m_coeffs);
393  }
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:909
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 422 of file ContField2D.h.

References m_locToGloMap.

425  {
426  m_locToGloMap->Assemble(inarray,outarray);
427  }
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 498 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().

502  {
503  if(coeffstate == eGlobal)
504  {
505  bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
507 
508  if(doGlobalOp)
509  {
510  GlobalMatrixKey gkey(StdRegions::eBwdTrans,m_locToGloMap);
512  mat->Multiply(inarray,outarray);
513  }
514  else
515  {
517  GlobalToLocal(inarray,wsp);
518  BwdTrans_IterPerExp(wsp,outarray);
519  }
520  }
521  else
522  {
523  BwdTrans_IterPerExp(inarray,outarray);
524  }
525  }
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:971
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:1568
int m_ncoeffs
The total number of local degrees of freedom. m_ncoeffs .
Definition: ExpList.h:887
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:1796
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 242 of file ContField2D.cpp.

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

Referenced by v_FwdTrans().

246  {
247  // Inner product of forcing
248  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
249  Array<OneD,NekDouble> wsp(contNcoeffs);
250  IProductWRTBase(inarray,wsp,eGlobal);
251 
252  // Solve the system
253  GlobalLinSysKey key(StdRegions::eMass, m_locToGloMap);
254 
255  if(coeffstate == eGlobal)
256  {
257  GlobalSolve(key,wsp,outarray);
258  }
259  else
260  {
261  Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
262  GlobalSolve(key,wsp,tmp);
263  GlobalToLocal(tmp,outarray);
264  }
265  }
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:452
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1796
GlobalLinSysSharedPtr Nektar::MultiRegions::ContField2D::GenGlobalLinSys ( const GlobalLinSysKey mkey)
private

Definition at line 599 of file ContField2D.cpp.

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

601  {
602  ASSERTL1(mkey.LocToGloMapIsDefined(),
603  "To use method must have a AssemblyMap "
604  "attached to key");
606  }
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:1133
#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 528 of file ContField2D.h.

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

529  {
530  return m_bndCondExpansions;
531  }
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 534 of file ContField2D.h.

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

Referenced by v_GetBndConditions().

535  {
536  return m_bndConditions;
537  }
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 593 of file ContField2D.cpp.

References m_globalLinSysManager.

Referenced by GlobalSolve().

595  {
596  return m_globalLinSysManager[mkey];
597  }
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 561 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().

563  {
564  ASSERTL1(mkey.LocToGloMapIsDefined(),
565  "To use method must have a AssemblyMap "
566  "attached to key");
567 
568  GlobalMatrixSharedPtr glo_matrix;
569  GlobalMatrixMap::iterator matrixIter = m_globalMat->find(mkey);
570 
571  if(matrixIter == m_globalMat->end())
572  {
573  glo_matrix = GenGlobalMatrix(mkey,m_locToGloMap);
574  (*m_globalMat)[mkey] = glo_matrix;
575  }
576  else
577  {
578  glo_matrix = matrixIter->second;
579  }
580 
581  return glo_matrix;
582  }
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:855
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 539 of file ContField2D.h.

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

540  {
541  ASSERTL1(gkey.LocToGloMapIsDefined(),
542  "To use method must have a AssemblyMap "
543  "attached to key");
544 
545  GlobalMatrixMap::iterator matrixIter = m_globalMat->find(gkey);
546 
547  if(matrixIter == m_globalMat->end())
548  {
549  return 0;
550  }
551  else
552  {
553  return matrixIter->second->GetNumNonZeroEntries();
554  }
555 
556  return 0;
557  }
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 431 of file ContField2D.h.

References m_locToGloMap.

432  {
433  return m_locToGloMap;
434  }
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 532 of file ContField2D.cpp.

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

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

537  {
538  int NumDirBcs = m_locToGloMap->GetNumGlobalDirBndCoeffs();
539  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
540 
541  // STEP 1: SET THE DIRICHLET DOFS TO THE RIGHT VALUE
542  // IN THE SOLUTION ARRAY
544 
545  // STEP 2: CALCULATE THE HOMOGENEOUS COEFFICIENTS
546  if(contNcoeffs - NumDirBcs > 0)
547  {
549  LinSys->Solve(rhs,inout,m_locToGloMap,dirForcing);
550  }
551  }
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:51
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 318 of file ContField2D.h.

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

320  {
321  m_locToGloMap->GlobalToLocal(m_coeffs,outarray);
322  }
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:909
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 351 of file ContField2D.h.

References m_locToGloMap.

354  {
355  m_locToGloMap->GlobalToLocal(inarray,outarray);
356  }
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 452 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().

457  {
458  if(coeffstate == eGlobal)
459  {
460  bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
462 
463  if(doGlobalOp)
464  {
465  GlobalMatrixKey gkey(StdRegions::eIProductWRTBase,
466  m_locToGloMap);
468  mat->Multiply(inarray,outarray);
469  m_locToGloMap->UniversalAssemble(outarray);
470  }
471  else
472  {
474  IProductWRTBase_IterPerExp(inarray,wsp);
475  Assemble(wsp,outarray);
476  }
477  }
478  else
479  {
480  IProductWRTBase_IterPerExp(inarray,outarray);
481  }
482  }
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:971
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:1518
int m_ncoeffs
The total number of local degrees of freedom. m_ncoeffs .
Definition: ExpList.h:887
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:390
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 383 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().

390  {
391  // Inner product of forcing
392  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
393  Array<OneD,NekDouble> wsp(contNcoeffs);
394  IProductWRTBase(inarray,wsp,eGlobal);
395  // Note -1.0 term necessary to invert forcing function to
396  // be consistent with matrix definition
397  Vmath::Neg(m_ncoeffs, wsp, 1);
398 
399  // Forcing function with weak boundary conditions
400  int i,j;
401  int bndcnt=0;
402  for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
403  {
404  if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
405  {
406  for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
407  {
408  wsp[m_locToGloMap
409  ->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
410  += (m_bndCondExpansions[i]->GetCoeffs())[j];
411  }
412  }
413  else
414  {
415  bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
416  }
417  }
418 
419  StdRegions::VarCoeffMap varcoeffs;
420  varcoeffs[StdRegions::eVarCoeffD00] = variablecoeffs[0];
421  varcoeffs[StdRegions::eVarCoeffD11] = variablecoeffs[3];
422  varcoeffs[StdRegions::eVarCoeffD22] = variablecoeffs[5];
424  factors[StdRegions::eFactorTime] = time;
425 
426  // Solve the system
427  GlobalLinSysKey key(StdRegions::eLaplacian,m_locToGloMap,factors,
428  varcoeffs);
429 
430  if(coeffstate == eGlobal)
431  {
432  GlobalSolve(key,wsp,outarray,dirForcing);
433  }
434  else
435  {
436  Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
437  GlobalSolve(key,wsp,tmp,dirForcing);
438  GlobalToLocal(tmp,outarray);
439  }
440  }
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:248
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:225
int m_ncoeffs
The total number of local degrees of freedom. m_ncoeffs .
Definition: ExpList.h:887
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:452
int GetNcoeffs(void) const
Returns the total number of local degrees of freedom .
Definition: ExpList.h:1351
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1796
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 453 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.

458  {
459  // Solve the system
463  vel[0] = vel_x;
464  vel[1] = vel_y;
465 
466  StdRegions::VarCoeffMap varcoeffs;
470  factors[StdRegions::eFactorTime] = 0.0;
472  factors,varcoeffs);
473 
475  Gmat->EigenSolve(Real,Imag,Evecs);
476  }
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:992
std::map< ConstFactorType, NekDouble > ConstFactorMap
Definition: StdRegions.hpp:248
boost::shared_ptr< DNekMat > DNekMatSharedPtr
Definition: NekTypeDefs.hpp:70
std::map< StdRegions::VarCoeffType, Array< OneD, NekDouble > > VarCoeffMap
Definition: StdRegions.hpp:225
void Nektar::MultiRegions::ContField2D::LocalToGlobal ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
) const
inline

Definition at line 358 of file ContField2D.h.

References m_locToGloMap.

361  {
362  m_locToGloMap->LocalToGlobal(inarray, outarray);
363  }
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 293 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().

298  {
299  GlobalLinSysKey key(StdRegions::eMass,m_locToGloMap);
300  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
301 
302  if(coeffstate == eGlobal)
303  {
304  if(inarray.data() == outarray.data())
305  {
306  Array<OneD, NekDouble> tmp(contNcoeffs,0.0);
307  Vmath::Vcopy(contNcoeffs,inarray,1,tmp,1);
308  GlobalSolve(key,tmp,outarray);
309  }
310  else
311  {
312  GlobalSolve(key,inarray,outarray);
313  }
314  }
315  else
316  {
317  Array<OneD, NekDouble> globaltmp(contNcoeffs,0.0);
318 
319  if(inarray.data() == outarray.data())
320  {
321  Array<OneD,NekDouble> tmp(inarray.num_elements());
322  Vmath::Vcopy(inarray.num_elements(),inarray,1,tmp,1);
323  Assemble(tmp,outarray);
324  }
325  else
326  {
327  Assemble(inarray,outarray);
328  }
329 
330  GlobalSolve(key,outarray,globaltmp);
331  GlobalToLocal(globaltmp,outarray);
332  }
333  }
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:390
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1796
void Vcopy(int n, const T *x, const int incx, T *y, const int incy)
Definition: Vmath.cpp:1038
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 612 of file ContField2D.cpp.

References BwdTrans().

616  {
617  BwdTrans(inarray,outarray,coeffstate);
618  }
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:498
void Nektar::MultiRegions::ContField2D::v_FillBndCondFromField ( void  )
privatevirtual

Reimplemented from Nektar::MultiRegions::DisContField2D.

Definition at line 691 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.

692  {
693  NekDouble sign;
694  int bndcnt = 0;
695  const Array<OneD,const int> &bndMap =
696  m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap();
697 
698  Array<OneD, NekDouble> tmp(m_locToGloMap->GetNumGlobalCoeffs());
699  LocalToGlobal(m_coeffs,tmp);
700 
701  // Now fill in all other Dirichlet coefficients.
702  for(int i = 0; i < m_bndCondExpansions.num_elements(); ++i)
703  {
704  Array<OneD, NekDouble>& coeffs = m_bndCondExpansions[i]->UpdateCoeffs();
705 
706  for(int j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
707  {
708  sign = m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsSign(bndcnt);
709  coeffs[j] = sign * tmp[bndMap[bndcnt++]];
710  }
711  }
712  }
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:909
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:1791
int GetNcoeffs(void) const
Returns the total number of local degrees of freedom .
Definition: ExpList.h:1351
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 624 of file ContField2D.cpp.

References FwdTrans().

628  {
629  FwdTrans(inarray,outarray,coeffstate);
630  }
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 893 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.

898  {
899  if(coeffstate == eGlobal)
900  {
901  bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
902  gkey.GetMatrixType());
903 
904  if(doGlobalOp)
905  {
907  mat->Multiply(inarray,outarray);
908  m_locToGloMap->UniversalAssemble(outarray);
909  }
910  else
911  {
913  Array<OneD,NekDouble> tmp2(tmp1+m_ncoeffs);
914  GlobalToLocal(inarray,tmp1);
915  GeneralMatrixOp_IterPerExp(gkey,tmp1,tmp2);
916  Assemble(tmp2,outarray);
917  }
918  }
919  else
920  {
921  GeneralMatrixOp_IterPerExp(gkey,inarray,outarray);
922  }
923  }
void GeneralMatrixOp_IterPerExp(const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Definition: ExpList.cpp:787
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:971
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:887
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:390
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1796
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 1043 of file ContField2D.cpp.

References GetBndConditions().

1044  {
1045  return GetBndConditions();
1046  }
const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & GetBndConditions()
Returns the boundary conditions.
Definition: ContField2D.h:534
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 738 of file ContField2D.cpp.

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

739  {
740  m_locToGloMap->GlobalToLocal(m_coeffs,m_coeffs);
741  }
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:909
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.
lambdaThe parameter $\lambda$ of the Helmholtz equation

Reimplemented from Nektar::MultiRegions::DisContField2D.

Definition at line 815 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().

822  {
823  //----------------------------------
824  // Setup RHS Inner product
825  //----------------------------------
826  // Inner product of forcing
827  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
828  Array<OneD,NekDouble> wsp(contNcoeffs);
829  IProductWRTBase(inarray,wsp,eGlobal);
830  // Note -1.0 term necessary to invert forcing function to
831  // be consistent with matrix definition
832  Vmath::Neg(contNcoeffs, wsp, 1);
833 
834  // Fill weak boundary conditions
835  int i,j;
836  int bndcnt=0;
837  Array<OneD, NekDouble> gamma(contNcoeffs, 0.0);
838 
839  for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
840  {
841  if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
842  {
843  for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
844  {
845  gamma[m_locToGloMap
846  ->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
847  += (m_bndCondExpansions[i]->GetCoeffs())[j];
848  }
849  }
850  else
851  {
852  bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
853  }
854  }
855 
856  m_locToGloMap->UniversalAssemble(gamma);
857 
858  // Add weak boundary conditions to forcing
859  Vmath::Vadd(contNcoeffs, wsp, 1, gamma, 1, wsp, 1);
860 
861  GlobalLinSysKey key(StdRegions::eHelmholtz,m_locToGloMap,factors,varcoeff);
862 
863  if(flags.isSet(eUseGlobal))
864  {
865  GlobalSolve(key,wsp,outarray,dirForcing);
866  }
867  else
868  {
869  Array<OneD,NekDouble> tmp(contNcoeffs);
870  LocalToGlobal(outarray,tmp);
871  GlobalSolve(key,wsp,tmp,dirForcing);
872  GlobalToLocal(tmp,outarray);
873  }
874  }
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.
bool isSet(const FlagType &key) const
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:452
void LocalToGlobal(void)
Put the coefficients into global ordering using m_coeffs.
Definition: ExpList.h:1791
int GetNcoeffs(void) const
Returns the total number of local degrees of freedom .
Definition: ExpList.h:1351
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1796
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 632 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().

633  {
634  int i,j;
635  int bndcnt=0;
636  int nDir = m_locToGloMap->GetNumGlobalDirBndCoeffs();
637 
638  // STEP 1: SET THE DIRICHLET DOFS TO THE RIGHT VALUE IN THE SOLUTION
639  // ARRAY
640  NekDouble sign;
641  const Array<OneD,const int> &bndMap =
642  m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap();
643 
645  m_locToGloMap->GetNumGlobalBndCoeffs(), 0.0);
646 
647  // Fill in Dirichlet coefficients that are to be sent to
648  // other processors. This code block uses a
649  // tuple<int,int.NekDouble> which stores the local id of
650  // coefficent the global id of the data location and the
651  // inverse of the values of the data (arising from
652  // periodic boundary conditiosn)
653  map<int, vector<ExtraDirDof> > &extraDirDofs =
654  m_locToGloMap->GetExtraDirDofs();
655  map<int, vector<ExtraDirDof> >::iterator it;
656  for (it = extraDirDofs.begin(); it != extraDirDofs.end(); ++it)
657  {
658  for (i = 0; i < it->second.size(); ++i)
659  {
660  tmp[it->second.at(i).get<1>()] =
661  m_bndCondExpansions[it->first]->GetCoeffs()[
662  it->second.at(i).get<0>()]*it->second.at(i).get<2>();
663  }
664  }
665  m_locToGloMap->UniversalAssembleBnd(tmp);
666 
667  // Now fill in all other Dirichlet coefficients.
668  for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
669  {
670  if(m_bndConditions[i]->GetBoundaryConditionType() ==
672  {
673  const Array<OneD,const NekDouble>& coeffs =
674  m_bndCondExpansions[i]->GetCoeffs();
675  for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
676  {
677  sign = m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsSign(
678  bndcnt);
679  tmp[bndMap[bndcnt++]] = sign * coeffs[j];
680  }
681  }
682  else
683  {
684  bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
685  }
686  }
687 
688  Vmath::Vcopy(nDir, tmp, 1, outarray, 1);
689  }
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:1351
void Vcopy(int n, const T *x, const int incx, T *y, const int incy)
Definition: Vmath.cpp:1038
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 937 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().

943  {
944  // Inner product of forcing
945  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
946  Array<OneD,NekDouble> wsp(contNcoeffs);
947  IProductWRTBase(inarray,wsp,eGlobal);
948  // Note -1.0 term necessary to invert forcing function to
949  // be consistent with matrix definition
950  Vmath::Neg(contNcoeffs, wsp, 1);
951 
952  // Forcing function with weak boundary conditions
953  int i,j;
954  int bndcnt=0;
955  Array<OneD, NekDouble> gamma(contNcoeffs, 0.0);
956  for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
957  {
958  if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
959  {
960  for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
961  {
962  gamma[m_locToGloMap
963  ->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
964  += (m_bndCondExpansions[i]->GetCoeffs())[j];
965  }
966  }
967  else
968  {
969  bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
970  }
971  }
972  m_locToGloMap->UniversalAssemble(wsp);
973  // Add weak boundary conditions to forcing
974  Vmath::Vadd(contNcoeffs, wsp, 1, gamma, 1, wsp, 1);
975 
976  // Solve the system
978  factors[StdRegions::eFactorLambda] = lambda;
979  StdRegions::VarCoeffMap varcoeffs;
980  varcoeffs[StdRegions::eVarCoeffVelX] = velocity[0];
981  varcoeffs[StdRegions::eVarCoeffVelY] = velocity[1];
982  GlobalLinSysKey key(StdRegions::eLinearAdvectionDiffusionReaction,m_locToGloMap,factors,varcoeffs);
983 
984  if(coeffstate == eGlobal)
985  {
986  GlobalSolve(key,wsp,outarray,dirForcing);
987  }
988  else
989  {
990  Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
991  GlobalSolve(key,wsp,tmp,dirForcing);
992  GlobalToLocal(tmp,outarray);
993  }
994  }
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:248
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:225
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:452
int GetNcoeffs(void) const
Returns the total number of local degrees of freedom .
Definition: ExpList.h:1351
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1796
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 1006 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.

1012  {
1013  // Inner product of forcing
1014  int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
1015  Array<OneD,NekDouble> wsp(contNcoeffs);
1016  IProductWRTBase(inarray,wsp,eGlobal);
1017 
1018  // Solve the system
1020  factors[StdRegions::eFactorLambda] = lambda;
1021  StdRegions::VarCoeffMap varcoeffs;
1022  varcoeffs[StdRegions::eVarCoeffVelX] = velocity[0];
1023  varcoeffs[StdRegions::eVarCoeffVelY] = velocity[1];
1024  GlobalLinSysKey key(StdRegions::eLinearAdvectionReaction,m_locToGloMap,factors,varcoeffs);
1025 
1026  if(coeffstate == eGlobal)
1027  {
1028  GlobalSolve(key,wsp,outarray,dirForcing);
1029  }
1030  else
1031  {
1032  Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
1033  GlobalSolve(key,wsp,tmp,dirForcing);
1034  GlobalToLocal(tmp,outarray);
1035  }
1036  }
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:248
Global coefficients.
std::map< StdRegions::VarCoeffType, Array< OneD, NekDouble > > VarCoeffMap
Definition: StdRegions.hpp:225
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:452
void GlobalToLocal(void)
Put the coefficients into local ordering and place in m_coeffs.
Definition: ExpList.h:1796
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 769 of file ContField2D.cpp.

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

770  {
771  m_locToGloMap->LocalToGlobal(m_coeffs,m_coeffs);
772  }
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:909
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 777 of file ContField2D.cpp.

References MultiplyByInvMassMatrix().

781  {
782  MultiplyByInvMassMatrix(inarray,outarray,coeffstate);
783  }
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 270 of file ContField2D.cpp.

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

271  {
272  int gloNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
273  Array<OneD,NekDouble> tmp1(gloNcoeffs);
274  Array<OneD,NekDouble> tmp2(gloNcoeffs);
275 
276  IProductWRTBase(field,tmp1,eGlobal);
277  MultiplyByInvMassMatrix(tmp1,tmp2,eGlobal);
278  BwdTrans(tmp2,field,eGlobal);
279  }
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:498
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:452
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().

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