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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>

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Public Member Functions

 ContField2D ()
 The default constructor.
 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.
 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.
 ContField2D (const ContField2D &In, bool DeclareCoeffPhysArrays=true)
 The copy constructor.
virtual ~ContField2D ()
 The default destructor.
void GlobalToLocal (Array< OneD, NekDouble > &outarray) const
 Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$.
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 $\boldsymbol{\hat{u}}_l$.
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 $\boldsymbol{\hat{u}}_l$.
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 $\boldsymbol{\hat{u}}_l$.
const AssemblyMapCGSharedPtr & GetLocalToGlobalMap () const
 Returns the map from local to global level.
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 $\phi_n^e(\boldsymbol{x})$.
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.
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.
void MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 Multiply a solution by the inverse mass matrix.
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.
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.
const Array< OneD, const
MultiRegions::ExpListSharedPtr > & 		GetBndCondExpansions ()
 Returns the boundary conditions expansion.
const Array< OneD, const
SpatialDomains::BoundaryConditionShPtr > & 		GetBndConditions ()
 Returns the boundary conditions.
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.
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} $.
void EvaluateHDGPostProcessing (Array< OneD, NekDouble > &outarray)
 Evaluate HDG post-processing to increase polynomial order of solution.
virtual ExpListSharedPtr & v_GetTrace ()
- Public Member Functions inherited from Nektar::MultiRegions::ExpList2D
 ExpList2D ()
 Default constructor.
 ExpList2D (const ExpList2D &In, const bool DeclareCoeffPhysArrays=true)
 Copy constructor.
 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.
 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.
 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.
 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.
virtual ~ExpList2D ()
 Destructor.
- Public Member Functions inherited from Nektar::MultiRegions::ExpList
 ExpList ()
 The default constructor.
 ExpList (const LibUtilities::SessionReaderSharedPtr &pSession)
 The default constructor.
 ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
 The default constructor.
 ExpList (const ExpList &in, const bool DeclareCoeffPhysArrays=true)
 The copy constructor.
virtual ~ExpList ()
 The default destructor.
int GetNcoeffs (void) const
 Returns the total number of local degrees of freedom $N_{\mathrm{eof}}=\sum_{e=1}^{{N_{\mathrm{el}}}}N^{e}_m$.
int GetNcoeffs (const int eid) const
 Returns the total number of local degrees of freedom for element eid.
ExpansionType GetExpType (void)
 Returns the type of the expansion.
void SetExpType (ExpansionType Type)
 Returns the type of the expansion.
int EvalBasisNumModesMax (void) const
 Evaulates the maximum number of modes in the elemental basis order over all elements.
const Array< OneD, int > EvalBasisNumModesMaxPerExp (void) const
 Returns the vector of the number of modes in the elemental basis order over all elements.
int GetTotPoints (void) const
 Returns the total number of quadrature points m_npoints $=Q_{\mathrm{tot}}$.
int GetTotPoints (const int eid) const
 Returns the total number of quadrature points for eid's element $=Q_{\mathrm{tot}}$.
int GetNpoints (void) const
 Returns the total number of quadrature points m_npoints $=Q_{\mathrm{tot}}$.
int Get1DScaledTotPoints (const NekDouble scale) const
 Returns the total number of qudature points scaled by the factor scale on each 1D direction.
void SetWaveSpace (const bool wavespace)
 Sets the wave space to the one of the possible configuration true or false.
void SetModifiedBasis (const bool modbasis)
 Set Modified Basis for the stability analysis.
void SetPhys (int i, NekDouble val)
 Set the i th value of m_phys to value val.
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.
void SetPhys (const Array< OneD, const NekDouble > &inarray)
 Fills the array m_phys.
void SetPhysArray (Array< OneD, NekDouble > &inarray)
 Sets the array m_phys.
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.
bool GetPhysState (void) const
 This function indicates whether the array of physical values $\boldsymbol{u}_l$ (implemented as m_phys) is filled or not.
NekDouble PhysIntegral (void)
 This function integrates a function $f(\boldsymbol{x})$ over the domain consisting of all the elements of the expansion.
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.
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 $\phi_n^e(\boldsymbol{x})$.
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.
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.
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.
void SmoothField (Array< OneD, NekDouble > &field)
 Smooth a field across elements.
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.
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.
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.
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.
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 $\boldsymbol{x}_i$.
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.
void WriteTecplotHeader (std::ofstream &outfile, std::string var="")
void WriteTecplotZone (std::ofstream &outfile, int expansion=-1)
void WriteTecplotField (std::ofstream &outfile, int expansion=-1)
void WriteTecplotConnectivity (std::ofstream &outfile, int expansion=-1)
void WriteVtkHeader (std::ofstream &outfile)
void WriteVtkFooter (std::ofstream &outfile)
void WriteVtkPieceHeader (std::ofstream &outfile, int expansion)
void WriteVtkPieceFooter (std::ofstream &outfile, int expansion)
void WriteVtkPieceData (std::ofstream &outfile, int expansion, std::string var="v")
int GetCoordim (int eid)
 This function returns the dimension of the coordinates of the element eid.
void SetCoeff (int i, NekDouble val)
 Set the i th coefficiient in m_coeffs to value val.
void SetCoeffs (int i, NekDouble val)
 Set the i th coefficiient in m_coeffs to value val.
void SetCoeffsArray (Array< OneD, NekDouble > &inarray)
 Set the m_coeffs array to inarray.
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.
void ImposeDirichletConditions (Array< OneD, NekDouble > &outarray)
 Impose Dirichlet Boundary Conditions onto Array.
void FillBndCondFromField (void)
 Fill Bnd Condition expansion from the values stored in expansion.
void LocalToGlobal (void)
 Put the coefficients into global ordering using m_coeffs.
void GlobalToLocal (void)
 Put the coefficients into local ordering and place in m_coeffs.
NekDouble GetCoeff (int i)
 Get the i th value (coefficient) of m_coeffs.
NekDouble GetCoeffs (int i)
 Get the i th value (coefficient) of m_coeffs.
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.
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.
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.
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.
NekDouble Integral (const Array< OneD, const NekDouble > &inarray)
Array< OneD, const NekDouble > HomogeneousEnergy (void)
 This function calculates the energy associated with each one of the modesof a 3D homogeneous nD expansion.
void SetHomo1DSpecVanVisc (Array< OneD, NekDouble > visc)
 This function sets the Spectral Vanishing Viscosity in homogeneous1D expansion.
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.
LibUtilities::TranspositionSharedPtr GetTransposition (void)
 This function returns the transposition class associaed with the homogeneous expansion.
NekDouble GetHomoLen (void)
 This function returns the Width of homogeneous direction associaed with the homogeneous expansion.
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.
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.
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.
int GetExpSize (void)
 This function returns the number of elements in the expansion.
int GetNumElmts (void)
 This function returns the number of elements in the expansion which may be different for a homogeoenous extended expansionp.
const boost::shared_ptr
< LocalRegions::ExpansionVector > 		GetExp () const
 This function returns the vector of elements in the expansion.
LocalRegions::ExpansionSharedPtr & GetExp (int n) const
 This function returns (a shared pointer to) the local elemental expansion of the $n^{\mathrm{th}}$ element.
LocalRegions::ExpansionSharedPtr & GetExp (const Array< OneD, const NekDouble > &gloCoord)
 This function returns (a shared pointer to) the local elemental expansion containing the arbitrary point given by gloCoord.
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.
int GetPhys_Offset (int n) const
 Get the start offset position for a global list of m_phys correspoinding to element n.
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.
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.
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.
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.
void PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d)
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)
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.
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, 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::GlobalOptParamSharedPtr & 		GetGlobalOptParam (void)
map< int, RobinBCInfoSharedPtr > GetRobinBCInfo ()
void GetPeriodicEntities (PeriodicMap &periodicVerts, PeriodicMap &periodicEdges, PeriodicMap &periodicFaces=NullPeriodicMap)
std::vector
< LibUtilities::FieldDefinitionsSharedPtr > 		GetFieldDefinitions ()
void GetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef)
void AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata)
 Append the element data listed in elements fielddef->m_ElementIDs onto fielddata.
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.
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.
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.
void ExtractDataToCoeffs (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, std::string &field, Array< OneD, NekDouble > &coeffs)
 Extract the data in fielddata into the coeffs.
boost::shared_ptr< ExpList > GetSharedThisPtr ()
 Returns a shared pointer to the current object.
boost::shared_ptr
< LibUtilities::SessionReader > 		GetSession ()
 Returns the session object.
boost::shared_ptr
< LibUtilities::Comm > 		GetComm ()
 Returns the comm object.
SpatialDomains::MeshGraphSharedPtr GetGraph ()
LibUtilities::BasisSharedPtr GetHomogeneousBasis (void)
boost::shared_ptr< ExpList > & GetPlane (int n)

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.
GlobalMatrixSharedPtr GetGlobalMatrix (const GlobalMatrixKey &mkey)
 Returns the global matrix specified by mkey.
GlobalLinSysSharedPtr GetGlobalLinSys (const GlobalLinSysKey &mkey)
 Returns the linear system specified by the key mkey.
GlobalLinSysSharedPtr GenGlobalLinSys (const GlobalLinSysKey &mkey)
virtual void v_ImposeDirichletConditions (Array< OneD, NekDouble > &outarray)
 Impose the Dirichlet Boundary Conditions on outarray.
virtual void v_FillBndCondFromField ()
virtual void v_LocalToGlobal (void)
 Gathers the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$.
virtual void v_GlobalToLocal (void)
 Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$.
virtual void v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
 Template method virtual forwarder for FwdTrans().
virtual void v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
 Template method virtual forwarder for FwdTrans().
virtual void v_SmoothField (Array< OneD, NekDouble > &field)
 Template method virtual forwarded for SmoothField().
virtual void v_MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
 Template method virtual forwarder for MultiplyByInvMassMatrix().
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.
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.
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().

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.
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.
LibUtilities::NekManager
< GlobalLinSysKey,
GlobalLinSys > 		m_globalLinSysManager
 A manager which collects all the global linear systems being assembled, such that they should be constructed only once.

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.
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.
void FindPeriodicEdges (const SpatialDomains::BoundaryConditions &bcs, const std::string &variable)
 Determine the periodic edges and vertices for the given graph.
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.
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.
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.
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.
virtual void v_ExtractTracePhys (Array< OneD, NekDouble > &outarray)
virtual void v_FillBndCondFromField ()
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)
virtual void v_GeneralMatrixOp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 Calculates the result of the multiplication of a global matrix of type specified by mkey with a vector given by inarray.
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.
virtual void v_GetPeriodicEntities (PeriodicMap &periodicVerts, PeriodicMap &periodicEdges, PeriodicMap &periodicFaces)
 Obtain a copy of the periodic edges and vertices for this field.
virtual AssemblyMapDGSharedPtr & v_GetTraceMap ()
virtual const Array< OneD,
const
MultiRegions::ExpListSharedPtr > & 		v_GetBndCondExpansions ()
virtual const Array< OneD,
const
SpatialDomains::BoundaryConditionShPtr > & 		v_GetBndConditions ()
virtual
MultiRegions::ExpListSharedPtr & 		v_UpdateBndCondExpansion (int i)
virtual Array< OneD,
SpatialDomains::BoundaryConditionShPtr > & 		v_UpdateBndConditions ()
virtual void v_EvaluateBoundaryConditions (const NekDouble time=0.0, const std::string varName="", const NekDouble x2_in=NekConstants::kNekUnsetDouble, const NekDouble x3_in=NekConstants::kNekUnsetDouble)
virtual map< int,
RobinBCInfoSharedPtr > 		v_GetRobinBCInfo ()
 Search through the edge expansions and identify which ones have Robin/Mixed type boundary conditions.
- 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::ExpListSharedPtr > 		m_bndCondExpansions
 An object which contains the discretised boundary conditions.
Array< OneD,
SpatialDomains::BoundaryConditionShPtr > 		m_bndConditions
 An array which contains the information about the boundary condition on the different boundary regions.
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::Orientation > 		m_edgedir
std::set< int > m_boundaryEdges
 A set storing the global IDs of any boundary edges.
PeriodicMap m_periodicVerts
 A map which identifies groups of periodic vertices.
PeriodicMap m_periodicEdges
 A map which identifies pairs of periodic edges.
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.
vector< int > m_periodicBwdCopy
vector< bool > m_leftAdjacentEdges

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.

:
DisContField2D(),
m_locToGloMap(),
m_globalMat(),
m_globalLinSysManager(
boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
std::string("GlobalLinSys"))
{
}
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::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.

:
DisContField2D(pSession,graph2D,variable,false,DeclareCoeffPhysArrays),
m_globalMat(MemoryManager<GlobalMatrixMap>::AllocateSharedPtr()),
m_globalLinSysManager(
boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
std::string("GlobalLinSys"))
{
m_locToGloMap = MemoryManager<AssemblyMapCG2D>
::AllocateSharedPtr(m_session,m_ncoeffs,*this,
m_bndCondExpansions,
m_bndConditions,
m_periodicVerts,
m_periodicEdges,
CheckIfSingularSystem,
variable);
if (m_session->DefinesCmdLineArgument("verbose"))
{
m_locToGloMap->PrintStats(std::cout, variable);
}
}
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::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().

:
DisContField2D(In,graph2D,variable,false,DeclareCoeffPhysArrays),
m_globalMat (MemoryManager<GlobalMatrixMap>::AllocateSharedPtr()),
m_globalLinSysManager(
boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
std::string("GlobalLinSys"))
{
if(!SameTypeOfBoundaryConditions(In) || CheckIfSingularSystem)
{
m_locToGloMap = MemoryManager<AssemblyMapCG2D>
::AllocateSharedPtr(m_session, m_ncoeffs,*this,
m_bndCondExpansions,
m_bndConditions,
m_periodicVerts,
m_periodicEdges,
CheckIfSingularSystem);
if (m_session->DefinesCmdLineArgument("verbose"))
{
m_locToGloMap->PrintStats(std::cout, variable);
}
}
else
{
m_locToGloMap = In.m_locToGloMap;
}
}
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 207 of file ContField2D.cpp.

:
DisContField2D(In,DeclareCoeffPhysArrays),
m_locToGloMap(In.m_locToGloMap),
m_globalMat(In.m_globalMat),
m_globalLinSysManager(In.m_globalLinSysManager)
{
}
Nektar::MultiRegions::ContField2D::~ContField2D ( )
virtual

The default destructor.

Definition at line 219 of file ContField2D.cpp.

{
}

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().

{
m_locToGloMap->Assemble(m_coeffs,m_coeffs);
}
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.

{
m_locToGloMap->Assemble(inarray,outarray);
}
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.

Reimplemented from Nektar::MultiRegions::ExpList.

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().

{
if(coeffstate == eGlobal)
{
bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
StdRegions::eBwdTrans);
if(doGlobalOp)
{
GlobalMatrixKey gkey(StdRegions::eBwdTrans,m_locToGloMap);
GlobalMatrixSharedPtr mat = GetGlobalMatrix(gkey);
mat->Multiply(inarray,outarray);
}
else
{
Array<OneD, NekDouble> wsp(m_ncoeffs);
GlobalToLocal(inarray,wsp);
BwdTrans_IterPerExp(wsp,outarray);
}
}
else
{
BwdTrans_IterPerExp(inarray,outarray);
}
}
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.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 241 of file ContField2D.cpp.

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

Referenced by v_FwdTrans().

{
// Inner product of forcing
int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
Array<OneD,NekDouble> wsp(contNcoeffs);
IProductWRTBase(inarray,wsp,eGlobal);
// Solve the system
GlobalLinSysKey key(StdRegions::eMass, m_locToGloMap);
if(coeffstate == eGlobal)
{
GlobalSolve(key,wsp,outarray);
}
else
{
Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
GlobalSolve(key,wsp,tmp);
GlobalToLocal(tmp,outarray);
}
}
GlobalLinSysSharedPtr Nektar::MultiRegions::ContField2D::GenGlobalLinSys ( const GlobalLinSysKey &  mkey)
private

Definition at line 598 of file ContField2D.cpp.

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

{
ASSERTL1(mkey.LocToGloMapIsDefined(),
"To use method must have a AssemblyMap "
"attached to key");
return ExpList::GenGlobalLinSys(mkey, m_locToGloMap);
}
const Array< OneD, const MultiRegions::ExpListSharedPtr > & Nektar::MultiRegions::ContField2D::GetBndCondExpansions ( )
inline

Returns the boundary conditions expansion.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 528 of file ContField2D.h.

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

{
return m_bndCondExpansions;
}
const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField2D::GetBndConditions ( )
inline

Returns the boundary conditions.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 534 of file ContField2D.h.

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

Referenced by v_GetBndConditions().

{
return m_bndConditions;
}
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 592 of file ContField2D.cpp.

References m_globalLinSysManager.

Referenced by GlobalSolve().

{
return m_globalLinSysManager[mkey];
}
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 560 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().

{
ASSERTL1(mkey.LocToGloMapIsDefined(),
"To use method must have a AssemblyMap "
"attached to key");
GlobalMatrixSharedPtr glo_matrix;
GlobalMatrixMap::iterator matrixIter = m_globalMat->find(mkey);
if(matrixIter == m_globalMat->end())
{
glo_matrix = GenGlobalMatrix(mkey,m_locToGloMap);
(*m_globalMat)[mkey] = glo_matrix;
}
else
{
glo_matrix = matrixIter->second;
}
return glo_matrix;
}
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.

{
ASSERTL1(gkey.LocToGloMapIsDefined(),
"To use method must have a AssemblyMap "
"attached to key");
GlobalMatrixMap::iterator matrixIter = m_globalMat->find(gkey);
if(matrixIter == m_globalMat->end())
{
return 0;
}
else
{
return matrixIter->second->GetNumNonZeroEntries();
}
return 0;
}
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.

{
return m_locToGloMap;
}
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 531 of file ContField2D.cpp.

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

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

{
int NumDirBcs = m_locToGloMap->GetNumGlobalDirBndCoeffs();
int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
// STEP 1: SET THE DIRICHLET DOFS TO THE RIGHT VALUE
// IN THE SOLUTION ARRAY
v_ImposeDirichletConditions(inout);
// STEP 2: CALCULATE THE HOMOGENEOUS COEFFICIENTS
if(contNcoeffs - NumDirBcs > 0)
{
GlobalLinSysSharedPtr LinSys = GetGlobalLinSys(key);
LinSys->Solve(rhs,inout,m_locToGloMap,dirForcing);
}
}
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.

{
m_locToGloMap->GlobalToLocal(m_coeffs,outarray);
}
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.

{
m_locToGloMap->GlobalToLocal(inarray,outarray);
}
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.

Reimplemented from Nektar::MultiRegions::ExpList.

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().

{
if(coeffstate == eGlobal)
{
bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
StdRegions::eIProductWRTBase);
if(doGlobalOp)
{
GlobalMatrixKey gkey(StdRegions::eIProductWRTBase,
m_locToGloMap);
GlobalMatrixSharedPtr mat = GetGlobalMatrix(gkey);
mat->Multiply(inarray,outarray);
m_locToGloMap->UniversalAssemble(outarray);
}
else
{
Array<OneD, NekDouble> wsp(m_ncoeffs);
IProductWRTBase_IterPerExp(inarray,wsp);
Assemble(wsp,outarray);
}
}
else
{
IProductWRTBase_IterPerExp(inarray,outarray);
}
}
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 382 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().

{
// Inner product of forcing
int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
Array<OneD,NekDouble> wsp(contNcoeffs);
IProductWRTBase(inarray,wsp,eGlobal);
// Note -1.0 term necessary to invert forcing function to
// be consistent with matrix definition
Vmath::Neg(m_ncoeffs, wsp, 1);
// Forcing function with weak boundary conditions
int i,j;
int bndcnt=0;
for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
{
if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
{
for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
{
wsp[m_locToGloMap
->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
+= (m_bndCondExpansions[i]->GetCoeffs())[j];
}
}
else
{
bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
}
}
StdRegions::VarCoeffMap varcoeffs;
varcoeffs[StdRegions::eVarCoeffD00] = variablecoeffs[0];
varcoeffs[StdRegions::eVarCoeffD11] = variablecoeffs[3];
varcoeffs[StdRegions::eVarCoeffD22] = variablecoeffs[5];
StdRegions::ConstFactorMap factors;
factors[StdRegions::eFactorTime] = time;
// Solve the system
GlobalLinSysKey key(StdRegions::eLaplacian,m_locToGloMap,factors,
varcoeffs);
if(coeffstate == eGlobal)
{
GlobalSolve(key,wsp,outarray,dirForcing);
}
else
{
Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
GlobalSolve(key,wsp,tmp,dirForcing);
GlobalToLocal(tmp,outarray);
}
}
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 452 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.

{
// Solve the system
Array<OneD, Array<OneD, NekDouble> > vel(2);
Array<OneD, NekDouble> vel_x(m_npoints,ax);
Array<OneD, NekDouble> vel_y(m_npoints,ay);
vel[0] = vel_x;
vel[1] = vel_y;
StdRegions::VarCoeffMap varcoeffs;
varcoeffs[StdRegions::eVarCoeffVelX] = Array<OneD, NekDouble>(m_npoints,ax);
varcoeffs[StdRegions::eVarCoeffVelY] = Array<OneD, NekDouble>(m_npoints,ay);
StdRegions::ConstFactorMap factors;
factors[StdRegions::eFactorTime] = 0.0;
GlobalLinSysKey key(StdRegions::eLinearAdvectionReaction,m_locToGloMap,
factors,varcoeffs);
DNekMatSharedPtr Gmat = GenGlobalMatrixFull(key,m_locToGloMap);
Gmat->EigenSolve(Real,Imag,Evecs);
}
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.

{
m_locToGloMap->LocalToGlobal(inarray, outarray);
}
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.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 292 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().

{
GlobalLinSysKey key(StdRegions::eMass,m_locToGloMap);
int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
if(coeffstate == eGlobal)
{
if(inarray.data() == outarray.data())
{
Array<OneD, NekDouble> tmp(contNcoeffs,0.0);
Vmath::Vcopy(contNcoeffs,inarray,1,tmp,1);
GlobalSolve(key,tmp,outarray);
}
else
{
GlobalSolve(key,inarray,outarray);
}
}
else
{
Array<OneD, NekDouble> globaltmp(contNcoeffs,0.0);
if(inarray.data() == outarray.data())
{
Array<OneD,NekDouble> tmp(inarray.num_elements());
Vmath::Vcopy(inarray.num_elements(),inarray,1,tmp,1);
Assemble(tmp,outarray);
}
else
{
Assemble(inarray,outarray);
}
GlobalSolve(key,outarray,globaltmp);
GlobalToLocal(globaltmp,outarray);
}
}
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().

Definition at line 611 of file ContField2D.cpp.

References BwdTrans().

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

Definition at line 690 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.

{
NekDouble sign;
int bndcnt = 0;
const Array<OneD,const int> &bndMap =
m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap();
Array<OneD, NekDouble> tmp(m_locToGloMap->GetNumGlobalCoeffs());
LocalToGlobal(m_coeffs,tmp);
// Now fill in all other Dirichlet coefficients.
for(int i = 0; i < m_bndCondExpansions.num_elements(); ++i)
{
Array<OneD, NekDouble>& coeffs = m_bndCondExpansions[i]->UpdateCoeffs();
for(int j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
{
sign = m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsSign(bndcnt);
coeffs[j] = sign * tmp[bndMap[bndcnt++]];
}
}
}
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().

Definition at line 623 of file ContField2D.cpp.

References FwdTrans().

{
FwdTrans(inarray,outarray,coeffstate);
}
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 $N_{\mathrm{dof}}$.

Definition at line 892 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.

{
if(coeffstate == eGlobal)
{
bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
gkey.GetMatrixType());
if(doGlobalOp)
{
GlobalMatrixSharedPtr mat = GetGlobalMatrix(gkey);
mat->Multiply(inarray,outarray);
m_locToGloMap->UniversalAssemble(outarray);
}
else
{
Array<OneD,NekDouble> tmp1(2*m_ncoeffs);
Array<OneD,NekDouble> tmp2(tmp1+m_ncoeffs);
GlobalToLocal(inarray,tmp1);
GeneralMatrixOp_IterPerExp(gkey,tmp1,tmp2);
Assemble(tmp2,outarray);
}
}
else
{
GeneralMatrixOp_IterPerExp(gkey,inarray,outarray);
}
}
const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField2D::v_GetBndConditions ( void  )
privatevirtual

Template method virtual forwarder for GetBndConditions().

Definition at line 1042 of file ContField2D.cpp.

References GetBndConditions().

{
return GetBndConditions();
}
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.

Definition at line 737 of file ContField2D.cpp.

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

{
m_locToGloMap->GlobalToLocal(m_coeffs,m_coeffs);
}
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

Definition at line 814 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().

{
//----------------------------------
// Setup RHS Inner product
//----------------------------------
// Inner product of forcing
int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
Array<OneD,NekDouble> wsp(contNcoeffs);
IProductWRTBase(inarray,wsp,eGlobal);
// Note -1.0 term necessary to invert forcing function to
// be consistent with matrix definition
Vmath::Neg(contNcoeffs, wsp, 1);
// Fill weak boundary conditions
int i,j;
int bndcnt=0;
Array<OneD, NekDouble> gamma(contNcoeffs, 0.0);
for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
{
if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
{
for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
{
gamma[m_locToGloMap
->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
+= (m_bndCondExpansions[i]->GetCoeffs())[j];
}
}
else
{
bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
}
}
m_locToGloMap->UniversalAssemble(gamma);
// Add weak boundary conditions to forcing
Vmath::Vadd(contNcoeffs, wsp, 1, gamma, 1, wsp, 1);
GlobalLinSysKey key(StdRegions::eHelmholtz,m_locToGloMap,factors,varcoeff);
if(flags.isSet(eUseGlobal))
{
GlobalSolve(key,wsp,outarray,dirForcing);
}
else
{
Array<OneD,NekDouble> tmp(contNcoeffs);
LocalToGlobal(outarray,tmp);
GlobalSolve(key,wsp,tmp,dirForcing);
GlobalToLocal(tmp,outarray);
}
}
void Nektar::MultiRegions::ContField2D::v_ImposeDirichletConditions ( Array< OneD, NekDouble > &  outarray)
privatevirtual

Impose the Dirichlet Boundary Conditions on outarray.

Definition at line 631 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().

{
int i,j;
int bndcnt=0;
int nDir = m_locToGloMap->GetNumGlobalDirBndCoeffs();
// STEP 1: SET THE DIRICHLET DOFS TO THE RIGHT VALUE IN THE SOLUTION
// ARRAY
NekDouble sign;
const Array<OneD,const int> &bndMap =
m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap();
Array<OneD, NekDouble> tmp(
m_locToGloMap->GetNumGlobalBndCoeffs(), 0.0);
// Fill in Dirichlet coefficients that are to be sent to
// other processors. This code block uses a
// tuple<int,int.NekDouble> which stores the local id of
// coefficent the global id of the data location and the
// inverse of the values of the data (arising from
// periodic boundary conditiosn)
map<int, vector<ExtraDirDof> > &extraDirDofs =
m_locToGloMap->GetExtraDirDofs();
map<int, vector<ExtraDirDof> >::iterator it;
for (it = extraDirDofs.begin(); it != extraDirDofs.end(); ++it)
{
for (i = 0; i < it->second.size(); ++i)
{
tmp[it->second.at(i).get<1>()] =
m_bndCondExpansions[it->first]->GetCoeffs()[
it->second.at(i).get<0>()]*it->second.at(i).get<2>();
}
}
m_locToGloMap->UniversalAssembleBnd(tmp);
// Now fill in all other Dirichlet coefficients.
for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
{
if(m_bndConditions[i]->GetBoundaryConditionType() ==
SpatialDomains::eDirichlet)
{
const Array<OneD,const NekDouble>& coeffs =
m_bndCondExpansions[i]->GetCoeffs();
for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
{
sign = m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsSign(
bndcnt);
tmp[bndMap[bndcnt++]] = sign * coeffs[j];
}
}
else
{
bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
}
}
Vmath::Vcopy(nDir, tmp, 1, outarray, 1);
}
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.

Definition at line 936 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().

{
// Inner product of forcing
int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
Array<OneD,NekDouble> wsp(contNcoeffs);
IProductWRTBase(inarray,wsp,eGlobal);
// Note -1.0 term necessary to invert forcing function to
// be consistent with matrix definition
Vmath::Neg(contNcoeffs, wsp, 1);
// Forcing function with weak boundary conditions
int i,j;
int bndcnt=0;
Array<OneD, NekDouble> gamma(contNcoeffs, 0.0);
for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
{
if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
{
for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
{
gamma[m_locToGloMap
->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
+= (m_bndCondExpansions[i]->GetCoeffs())[j];
}
}
else
{
bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
}
}
m_locToGloMap->UniversalAssemble(wsp);
// Add weak boundary conditions to forcing
Vmath::Vadd(contNcoeffs, wsp, 1, gamma, 1, wsp, 1);
// Solve the system
StdRegions::ConstFactorMap factors;
factors[StdRegions::eFactorLambda] = lambda;
StdRegions::VarCoeffMap varcoeffs;
varcoeffs[StdRegions::eVarCoeffVelX] = velocity[0];
varcoeffs[StdRegions::eVarCoeffVelY] = velocity[1];
GlobalLinSysKey key(StdRegions::eLinearAdvectionDiffusionReaction,m_locToGloMap,factors,varcoeffs);
if(coeffstate == eGlobal)
{
GlobalSolve(key,wsp,outarray,dirForcing);
}
else
{
Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
GlobalSolve(key,wsp,tmp,dirForcing);
GlobalToLocal(tmp,outarray);
}
}
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 
)
private

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.

Definition at line 1005 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.

{
// Inner product of forcing
int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
Array<OneD,NekDouble> wsp(contNcoeffs);
IProductWRTBase(inarray,wsp,eGlobal);
// Solve the system
StdRegions::ConstFactorMap factors;
factors[StdRegions::eFactorLambda] = lambda;
StdRegions::VarCoeffMap varcoeffs;
varcoeffs[StdRegions::eVarCoeffVelX] = velocity[0];
varcoeffs[StdRegions::eVarCoeffVelY] = velocity[1];
GlobalLinSysKey key(StdRegions::eLinearAdvectionReaction,m_locToGloMap,factors,varcoeffs);
if(coeffstate == eGlobal)
{
GlobalSolve(key,wsp,outarray,dirForcing);
}
else
{
Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
GlobalSolve(key,wsp,tmp,dirForcing);
GlobalToLocal(tmp,outarray);
}
}
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.

Definition at line 768 of file ContField2D.cpp.

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

{
m_locToGloMap->LocalToGlobal(m_coeffs,m_coeffs);
}
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().

Definition at line 776 of file ContField2D.cpp.

References MultiplyByInvMassMatrix().

{
MultiplyByInvMassMatrix(inarray,outarray,coeffstate);
}
void Nektar::MultiRegions::ContField2D::v_SmoothField ( Array< OneD, NekDouble > &  field)
privatevirtual

Template method virtual forwarded for SmoothField().

Definition at line 269 of file ContField2D.cpp.

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

{
int gloNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
Array<OneD,NekDouble> tmp1(gloNcoeffs);
Array<OneD,NekDouble> tmp2(gloNcoeffs);
IProductWRTBase(field,tmp1,eGlobal);
MultiplyByInvMassMatrix(tmp1,tmp2,eGlobal);
BwdTrans(tmp2,field,eGlobal);
}

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

(A shared pointer to) the object which contains all the required information for the transformation from local to global degrees of freedom.

Definition at line 182 of file ContField2D.h.

Referenced by Assemble(), BwdTrans(), ContField2D(), FwdTrans(), GenGlobalLinSys(), GetGlobalMatrix(), GetLocalToGlobalMap(), GlobalSolve(), GlobalToLocal(), IProductWRTBase(), LaplaceSolve(), LinearAdvectionEigs(), LocalToGlobal(), MultiplyByInvMassMatrix(), v_FillBndCondFromField(), v_GeneralMatrixOp(), v_GlobalToLocal(), v_HelmSolve(), v_ImposeDirichletConditions(), v_LinearAdvectionDiffusionReactionSolve(), v_LinearAdvectionReactionSolve(), v_LocalToGlobal(), and v_SmoothField().

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