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Nektar::StdRegions::StdExpansion2D Class Reference

#include <StdExpansion2D.h>

Inheritance diagram for Nektar::StdRegions::StdExpansion2D:
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Public Member Functions

 StdExpansion2D ()
 StdExpansion2D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)
 StdExpansion2D (const StdExpansion2D &T)
virtual ~StdExpansion2D ()
void PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d0, Array< OneD, NekDouble > &outarray_d1)
 Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points.
NekDouble Integral (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &w0, const Array< OneD, const NekDouble > &w1)
void BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)
void IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)
- Public Member Functions inherited from Nektar::StdRegions::StdExpansion
 StdExpansion ()
 Default Constructor.
 StdExpansion (const int numcoeffs, const int numbases, const LibUtilities::BasisKey &Ba=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bb=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bc=LibUtilities::NullBasisKey)
 Constructor.
 StdExpansion (const StdExpansion &T)
 Copy Constructor.
virtual ~StdExpansion ()
 Destructor.
int GetNumBases () const
 This function returns the number of 1D bases used in the expansion.
const Array< OneD, const
LibUtilities::BasisSharedPtr > & 		GetBase () const
 This function gets the shared point to basis.
const
LibUtilities::BasisSharedPtr & 		GetBasis (int dir) const
 This function gets the shared point to basis in the dir direction.
int GetNcoeffs (void) const
 This function returns the total number of coefficients used in the expansion.
int GetTotPoints () const
 This function returns the total number of quadrature points used in the element.
LibUtilities::BasisType GetBasisType (const int dir) const
 This function returns the type of basis used in the dir direction.
int GetBasisNumModes (const int dir) const
 This function returns the number of expansion modes in the dir direction.
int EvalBasisNumModesMax (void) const
 This function returns the maximum number of expansion modes over all local directions.
LibUtilities::PointsType GetPointsType (const int dir) const
 This function returns the type of quadrature points used in the dir direction.
int GetNumPoints (const int dir) const
 This function returns the number of quadrature points in the dir direction.
const Array< OneD, const
NekDouble > & 		GetPoints (const int dir) const
 This function returns a pointer to the array containing the quadrature points in dir direction.
int GetNverts () const
 This function returns the number of vertices of the expansion domain.
int GetNedges () const
 This function returns the number of edges of the expansion domain.
int GetEdgeNcoeffs (const int i) const
 This function returns the number of expansion coefficients belonging to the i-th edge.
int GetTotalEdgeIntNcoeffs () const
int GetEdgeNumPoints (const int i) const
 This function returns the number of quadrature points belonging to the i-th edge.
int DetCartesianDirOfEdge (const int edge)
const LibUtilities::BasisKey DetEdgeBasisKey (const int i) const
const LibUtilities::BasisKey DetFaceBasisKey (const int i, const int k) const
int GetFaceNumPoints (const int i) const
 This function returns the number of quadrature points belonging to the i-th face.
int GetFaceNcoeffs (const int i) const
 This function returns the number of expansion coefficients belonging to the i-th face.
int GetFaceIntNcoeffs (const int i) const
int GetTotalFaceIntNcoeffs () const
LibUtilities::PointsKey GetFacePointsKey (const int i, const int j) const
int NumBndryCoeffs (void) const
int NumDGBndryCoeffs (void) const
LibUtilities::BasisType GetEdgeBasisType (const int i) const
 This function returns the type of expansion basis on the i-th edge.
int GetNfaces () const
 This function returns the number of faces of the expansion domain.
LibUtilities::ShapeType DetShapeType () const
 This function returns the shape of the expansion domain.
int GetShapeDimension () const
bool IsBoundaryInteriorExpansion ()
void BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function performs the Backward transformation from coefficient space to physical space.
void FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function performs the Forward transformation from physical space to coefficient space.
void FwdTrans_BndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
NekDouble Integral (const Array< OneD, const NekDouble > &inarray)
 This function integrates the specified function over the domain.
void FillMode (const int mode, Array< OneD, NekDouble > &outarray)
 This function fills the array outarray with the mode-th mode of the expansion.
void IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 this function calculates the inner product of a given function f with the different modes of the expansion
void IProductWRTBase (const Array< OneD, const NekDouble > &base, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int coll_check)
void IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
int GetElmtId ()
 Get the element id of this expansion when used in a list by returning value of m_elmt_id.
void SetElmtId (const int id)
 Set the element id of this expansion when used in a list by returning value of m_elmt_id.
void GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2=NullNekDouble1DArray, Array< OneD, NekDouble > &coords_3=NullNekDouble1DArray)
 this function returns the physical coordinates of the quadrature points of the expansion
void GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)
 given the coordinates of a point of the element in the local collapsed coordinate system, this function calculates the physical coordinates of the point
DNekMatSharedPtr GetStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr GetStdStaticCondMatrix (const StdMatrixKey &mkey)
IndexMapValuesSharedPtr GetIndexMap (const IndexMapKey &ikey)
const Array< OneD, const
NekDouble > & 		GetPhysNormals (void)
void SetPhysNormals (Array< OneD, const NekDouble > &normal)
virtual void SetUpPhysNormals (const int edge)
void NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
DNekScalBlkMatSharedPtr GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
void DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
StdRegions::Orientation GetFaceOrient (int face)
StdRegions::Orientation GetEorient (int edge)
StdRegions::Orientation GetPorient (int point)
StdRegions::Orientation GetCartesianEorient (int edge)
void SetCoeffsToOrientation (Array< OneD, NekDouble > &coeffs, StdRegions::Orientation dir)
void SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
int CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
void ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble *coeffs)
NekDouble StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
void AddEdgeNormBoundaryInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
void AddEdgeNormBoundaryInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
void AddEdgeNormBoundaryBiInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &outarray)
void AddFaceNormBoundaryInt (const int face, boost::shared_ptr< StdExpansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
int GetCoordim ()
void GetBoundaryMap (Array< OneD, unsigned int > &outarray)
void GetInteriorMap (Array< OneD, unsigned int > &outarray)
int GetVertexMap (const int localVertexId, bool useCoeffPacking=false)
void GetEdgeInteriorMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)
void GetFaceInteriorMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)
void GetEdgeToElementMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)
void GetFaceToElementMap (const int fid, const Orientation faceOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, int nummodesA=-1, int nummodesB=-1)
void GetEdgePhysVals (const int edge, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 Extract the physical values along edge edge from inarray into outarray following the local edge orientation and point distribution defined by defined in EdgeExp.
void GetEdgePhysVals (const int edge, const boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void GetTracePhysVals (const int edge, const boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void GetVertexPhysVals (const int vertex, const Array< OneD, const NekDouble > &inarray, NekDouble &outarray)
void GetEdgeInterpVals (const int edge, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void GetEdgeQFactors (const int edge, Array< OneD, NekDouble > &outarray)
 Extract the metric factors to compute the contravariant fluxes along edge edge and stores them into outarray following the local edge orientation (i.e. anticlockwise convention).
void GetFacePhysVals (const int face, const boost::shared_ptr< StdExpansion > &FaceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient=eNoOrientation)
void MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
DNekMatSharedPtr CreateGeneralMatrix (const StdMatrixKey &mkey)
 this function generates the mass matrix $\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}$
void GeneralMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)
void LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void LinearAdvectionDiffusionReactionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
DNekMatSharedPtr GenMatrix (const StdMatrixKey &mkey)
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)
void PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void PhysDeriv_s (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_ds)
void PhysDeriv_n (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dn)
void PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &outarray)
void StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1=NullNekDouble1DArray, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
void StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void AddRobinMassMatrix (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat)
void AddRobinEdgeContribution (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, Array< OneD, NekDouble > &coeffs)
void DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, boost::shared_ptr< StdExpansion > > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray)
NekDouble PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
 This function evaluates the expansion at a single (arbitrary) point of the domain.
NekDouble PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
 This function evaluates the expansion at a single (arbitrary) point of the domain.
void LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
 Convert local cartesian coordinate xi into local collapsed coordinates eta.
const boost::shared_ptr
< SpatialDomains::GeomFactors > & 		GetMetricInfo (void) const
virtual int v_GetElmtId ()
 Get the element id of this expansion when used in a list by returning value of m_elmt_id.
virtual const Array< OneD,
const NekDouble > & 		v_GetPhysNormals (void)
virtual void v_SetPhysNormals (Array< OneD, const NekDouble > &normal)
virtual void v_SetUpPhysNormals (const int edge)
virtual int v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
virtual void v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmode_offset, NekDouble *coeffs)
 Unpack data from input file assuming it comes from the same expansion type.
virtual void v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, const Array< OneD, const NekDouble > &Fz, Array< OneD, NekDouble > &outarray)
virtual DNekScalBlkMatSharedPtr v_GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
virtual void v_DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
virtual StdRegions::Orientation v_GetFaceOrient (int face)
virtual StdRegions::Orientation v_GetEorient (int edge)
virtual StdRegions::Orientation v_GetCartesianEorient (int edge)
virtual StdRegions::Orientation v_GetPorient (int point)
NekDouble Linf (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
 Function to evaluate the discrete $ L_\infty$ error $ |\epsilon|_\infty = \max |u - u_{exact}|$ where $ u_{exact}$ is given by the array sol.
NekDouble L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
 Function to evaluate the discrete $ L_2$ error, $ | \epsilon |_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 dx \right]^{1/2} d\xi_1 $ where $ u_{exact}$ is given by the array sol.
NekDouble H1 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
 Function to evaluate the discrete $ H^1$ error, $ | \epsilon |^1_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 + \nabla(u - u_{exact})\cdot\nabla(u - u_{exact})\cdot dx \right]^{1/2} d\xi_1 $ where $ u_{exact}$ is given by the array sol.
const NormalVector & GetEdgeNormal (const int edge) const
void ComputeEdgeNormal (const int edge)
void NegateEdgeNormal (const int edge)
bool EdgeNormalNegated (const int edge)
void ComputeFaceNormal (const int face)
void NegateFaceNormal (const int face)
void ComputeVertexNormal (const int vertex)
const NormalVector & GetFaceNormal (const int face) const
const NormalVector & GetVertexNormal (const int vertex) const
const NormalVector & GetSurfaceNormal (const int id) const
const LibUtilities::PointsKeyVector GetPointsKeys () const
Array< OneD, unsigned int > GetEdgeInverseBoundaryMap (int eid)
Array< OneD, unsigned int > GetFaceInverseBoundaryMap (int fid, StdRegions::Orientation faceOrient=eNoOrientation)
DNekMatSharedPtr BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)
template<class T >
boost::shared_ptr< T > as ()

Protected Member Functions

virtual NekDouble v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
 This function evaluates the expansion at a single (arbitrary) point of the domain.
virtual NekDouble v_PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals)
virtual void v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0
virtual void v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0
virtual void v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)
virtual void v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey)
- Protected Member Functions inherited from Nektar::StdRegions::StdExpansion
DNekMatSharedPtr CreateStdMatrix (const StdMatrixKey &mkey)
DNekBlkMatSharedPtr CreateStdStaticCondMatrix (const StdMatrixKey &mkey)
 Create the static condensation of a matrix when using a boundary interior decomposition.
IndexMapValuesSharedPtr CreateIndexMap (const IndexMapKey &ikey)
 Create an IndexMap which contains mapping information linking any specific element shape with either its boundaries, edges, faces, verteces, etc.
void BwdTrans_MatOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void GeneralMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void MassMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)
void LaplacianMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void LaplacianMatrixOp_MatFree (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void WeakDerivMatrixOp_MatFree (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void WeakDirectionalDerivMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void MassLevelCurvatureMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void LinearAdvectionDiffusionReactionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
void HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
void HelmholtzMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void v_SetCoeffsToOrientation (Array< OneD, NekDouble > &coeffs, StdRegions::Orientation dir)
virtual NekDouble v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals)
virtual void v_AddEdgeNormBoundaryInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void v_AddEdgeNormBoundaryInt (const int edge, boost::shared_ptr< StdExpansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
virtual void v_AddFaceNormBoundaryInt (const int face, boost::shared_ptr< StdExpansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)

Private Member Functions

virtual int v_GetShapeDimension () const
virtual int v_GetNfaces () const
virtual int v_GetCoordim (void)

Additional Inherited Members

- Protected Attributes inherited from Nektar::StdRegions::StdExpansion
Array< OneD,
LibUtilities::BasisSharedPtr > 		m_base
int m_elmt_id
int m_ncoeffs
LibUtilities::NekManager
< StdMatrixKey, DNekMat,
StdMatrixKey::opLess > 		m_stdMatrixManager
LibUtilities::NekManager
< StdMatrixKey, DNekBlkMat,
StdMatrixKey::opLess > 		m_stdStaticCondMatrixManager
LibUtilities::NekManager
< IndexMapKey, IndexMapValues,
IndexMapKey::opLess > 		m_IndexMapManager

Detailed Description

Definition at line 49 of file StdExpansion2D.h.

Constructor & Destructor Documentation

Nektar::StdRegions::StdExpansion2D::StdExpansion2D ( )

Definition at line 49 of file StdExpansion2D.cpp.

{
}
Nektar::StdRegions::StdExpansion2D::StdExpansion2D ( int  numcoeffs,
const LibUtilities::BasisKey &  Ba,
const LibUtilities::BasisKey &  Bb 
)

Definition at line 53 of file StdExpansion2D.cpp.

:
StdExpansion(numcoeffs,2, Ba, Bb)
{
}
Nektar::StdRegions::StdExpansion2D::StdExpansion2D ( const StdExpansion2D &  T)

Definition at line 60 of file StdExpansion2D.cpp.

:
StdExpansion(T)
{
}
Nektar::StdRegions::StdExpansion2D::~StdExpansion2D ( )
virtual

Definition at line 65 of file StdExpansion2D.cpp.

{
}

Member Function Documentation

void Nektar::StdRegions::StdExpansion2D::BwdTrans_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0 = true,
bool  doCheckCollDir1 = true 
)

Definition at line 188 of file StdExpansion2D.cpp.

References v_BwdTrans_SumFacKernel().

Referenced by Nektar::StdRegions::StdTriExp::v_BwdTrans_SumFac(), Nektar::StdRegions::StdQuadExp::v_BwdTrans_SumFac(), v_HelmholtzMatrixOp_MatFree(), and v_LaplacianMatrixOp_MatFree().

{
v_BwdTrans_SumFacKernel(base0, base1, inarray, outarray, wsp, doCheckCollDir0, doCheckCollDir1);
}
NekDouble Nektar::StdRegions::StdExpansion2D::Integral ( const Array< OneD, const NekDouble > &  inarray,
const Array< OneD, const NekDouble > &  w0,
const Array< OneD, const NekDouble > &  w1 
)

Definition at line 161 of file StdExpansion2D.cpp.

References Nektar::StdRegions::StdExpansion::m_base, Vmath::Vmul(), and Vmath::Vsum().

Referenced by Nektar::StdRegions::StdTriExp::v_Integral(), and Nektar::StdRegions::StdQuadExp::v_Integral().

{
int i;
NekDouble Int = 0.0;
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
Array<OneD, NekDouble> tmp(nquad0 * nquad1);
// multiply by integration constants
for (i = 0; i < nquad1; ++i)
{
Vmath::Vmul(nquad0, &inarray[0] + i*nquad0, 1, w0.get(),
1, &tmp[0] + i*nquad0, 1);
}
for (i = 0; i < nquad0; ++i)
{
Vmath::Vmul(nquad1, &tmp[0]+ i, nquad0, w1.get(), 1,
&tmp[0] + i, nquad0);
}
Int = Vmath::Vsum(nquad0 * nquad1, tmp, 1);
return Int;
}
void Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0 = true,
bool  doCheckCollDir1 = true 
)

Definition at line 200 of file StdExpansion2D.cpp.

References v_IProductWRTBase_SumFacKernel().

Referenced by Nektar::LocalRegions::NodalTriExp::IProductWRTBase_SumFac(), Nektar::LocalRegions::NodalTriExp::IProductWRTDerivBase_SumFac(), v_HelmholtzMatrixOp_MatFree(), Nektar::LocalRegions::TriExp::v_IProductWRTBase_SumFac(), Nektar::LocalRegions::QuadExp::v_IProductWRTBase_SumFac(), Nektar::StdRegions::StdQuadExp::v_IProductWRTBase_SumFac(), Nektar::StdRegions::StdTriExp::v_IProductWRTBase_SumFac(), Nektar::LocalRegions::TriExp::v_IProductWRTDerivBase_SumFac(), Nektar::LocalRegions::QuadExp::v_IProductWRTDerivBase_SumFac(), Nektar::StdRegions::StdQuadExp::v_IProductWRTDerivBase_SumFac(), Nektar::StdRegions::StdTriExp::v_IProductWRTDerivBase_SumFac(), Nektar::LocalRegions::TriExp::v_LaplacianMatrixOp_MatFree_Kernel(), and Nektar::LocalRegions::QuadExp::v_LaplacianMatrixOp_MatFree_Kernel().

{
v_IProductWRTBase_SumFacKernel(base0, base1, inarray, outarray, wsp, doCheckCollDir0, doCheckCollDir1);
}
void Nektar::StdRegions::StdExpansion2D::PhysTensorDeriv ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray_d0,
Array< OneD, NekDouble > &  outarray_d1 
)

Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points.

This function is independent of the expansion basis and can therefore be defined for all tensor product distribution of quadrature points in a generic manner. The key operations are:

Parameters
inarrayarray of physical points to be differentiated
outarray_d0the resulting array of derivative in the $\eta_1$ direction will be stored in outarray_d0 as output of the function
outarray_d1the resulting array of derivative in the $\eta_2$ direction will be stored in outarray_d1 as output of the function

Recall that: $ \hspace{1cm} \begin{array}{llll} \mbox{Shape} & \mbox{Cartesian coordinate range} & \mbox{Collapsed coord.} & \mbox{Collapsed coordinate definition}\\ \mbox{Quadrilateral} & -1 \leq \xi_1,\xi_2 \leq 1 & -1 \leq \eta_1,\eta_2 \leq 1 & \eta_1 = \xi_1, \eta_2 = \xi_2\\ \mbox{Triangle} & -1 \leq \xi_1,\xi_2; \xi_1+\xi_2 \leq 0 & -1 \leq \eta_1,\eta_2 \leq 1 & \eta_1 = \frac{2(1+\xi_1)}{(1-\xi_2)}-1, \eta_2 = \xi_2 \\ \end{array} $

Definition at line 72 of file StdExpansion2D.cpp.

References Nektar::StdRegions::StdExpansion::m_base, and Vmath::Vcopy().

Referenced by Nektar::LocalRegions::TriExp::v_LaplacianMatrixOp_MatFree_Kernel(), Nektar::LocalRegions::QuadExp::v_LaplacianMatrixOp_MatFree_Kernel(), Nektar::StdRegions::StdTriExp::v_PhysDeriv(), and Nektar::StdRegions::StdQuadExp::v_PhysDeriv().

{
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
if (outarray_d0.num_elements() > 0) // calculate du/dx_0
{
DNekMatSharedPtr D0 = m_base[0]->GetD();
if(inarray.data() == outarray_d0.data())
{
Array<OneD, NekDouble> wsp(nquad0 * nquad1);
Vmath::Vcopy(nquad0 * nquad1,inarray.get(),1,wsp.get(),1);
Blas::Dgemm('N', 'N', nquad0, nquad1, nquad0, 1.0,
&(D0->GetPtr())[0], nquad0, &wsp[0], nquad0, 0.0,
&outarray_d0[0], nquad0);
}
else
{
Blas::Dgemm('N', 'N', nquad0, nquad1, nquad0, 1.0,
&(D0->GetPtr())[0], nquad0, &inarray[0], nquad0, 0.0,
&outarray_d0[0], nquad0);
}
}
if (outarray_d1.num_elements() > 0) // calculate du/dx_1
{
DNekMatSharedPtr D1 = m_base[1]->GetD();
if(inarray.data() == outarray_d1.data())
{
Array<OneD, NekDouble> wsp(nquad0 * nquad1);
Vmath::Vcopy(nquad0 * nquad1,inarray.get(),1,wsp.get(),1);
Blas:: Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0, &wsp[0], nquad0,
&(D1->GetPtr())[0], nquad1, 0.0, &outarray_d1[0], nquad0);
}
else
{
Blas:: Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0, &inarray[0], nquad0,
&(D1->GetPtr())[0], nquad1, 0.0, &outarray_d1[0], nquad0);
}
}
}
virtual void Nektar::StdRegions::StdExpansion2D::v_BwdTrans_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0,
bool  doCheckCollDir1 
)
protectedpure virtual

Implemented in Nektar::StdRegions::StdQuadExp, and Nektar::StdRegions::StdTriExp.

Referenced by BwdTrans_SumFacKernel().

virtual int Nektar::StdRegions::StdExpansion2D::v_GetCoordim ( void  )
inlineprivatevirtual

Reimplemented in Nektar::LocalRegions::QuadExp, and Nektar::LocalRegions::TriExp.

Definition at line 192 of file StdExpansion2D.h.

{
return 2;
}
virtual int Nektar::StdRegions::StdExpansion2D::v_GetNfaces ( ) const
inlineprivatevirtual

Definition at line 187 of file StdExpansion2D.h.

{
return 0;
}
virtual int Nektar::StdRegions::StdExpansion2D::v_GetShapeDimension ( ) const
inlineprivatevirtual

Definition at line 182 of file StdExpansion2D.h.

{
return 2;
}
void Nektar::StdRegions::StdExpansion2D::v_HelmholtzMatrixOp_MatFree ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const StdRegions::StdMatrixKey &  mkey 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 259 of file StdExpansion2D.cpp.

References BwdTrans_SumFacKernel(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdMatrixKey::GetNVarCoeff(), Nektar::StdRegions::StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(), IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_Kernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), and Vmath::Svtvp().

Referenced by Nektar::StdRegions::StdQuadExp::v_HelmholtzMatrixOp(), and Nektar::StdRegions::StdTriExp::v_HelmholtzMatrixOp().

{
if (mkey.GetNVarCoeff() == 0
&&!mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
{
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
int nqtot = nquad0*nquad1;
int nmodes0 = m_base[0]->GetNumModes();
int nmodes1 = m_base[1]->GetNumModes();
int wspsize = max(max(max(nqtot,m_ncoeffs),nquad1*nmodes0),
nquad0*nmodes1);
NekDouble lambda =
mkey.GetConstFactor(StdRegions::eFactorLambda);
const Array<OneD, const NekDouble>& base0 = m_base[0]->GetBdata();
const Array<OneD, const NekDouble>& base1 = m_base[1]->GetBdata();
// Allocate temporary storage
Array<OneD,NekDouble> wsp0(5*wspsize); // size wspsize
Array<OneD,NekDouble> wsp1(wsp0 + wspsize); // size wspsize
Array<OneD,NekDouble> wsp2(wsp0 + 2*wspsize);// size 3*wspsize
if (!(m_base[0]->Collocation() && m_base[1]->Collocation()))
{
// MASS MATRIX OPERATION
// The following is being calculated:
// wsp0 = B * u_hat = u
// wsp1 = W * wsp0
// outarray = B^T * wsp1 = B^T * W * B * u_hat = M * u_hat
BwdTrans_SumFacKernel (base0, base1, inarray,
wsp0, wsp2,true,true);
MultiplyByQuadratureMetric (wsp0, wsp1);
IProductWRTBase_SumFacKernel(base0, base1, wsp1, outarray,
wsp2, true, true);
LaplacianMatrixOp_MatFree_Kernel(wsp0, wsp1, wsp2);
}
else
{
MultiplyByQuadratureMetric(inarray,outarray);
LaplacianMatrixOp_MatFree_Kernel(inarray, wsp1, wsp2);
}
// outarray = lambda * outarray + wsp1
// = (lambda * M + L ) * u_hat
Vmath::Svtvp(m_ncoeffs, lambda, &outarray[0], 1,
&wsp1[0], 1, &outarray[0], 1);
}
else
{
StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(
inarray,outarray,mkey);
}
}
virtual void Nektar::StdRegions::StdExpansion2D::v_IProductWRTBase_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0,
bool  doCheckCollDir1 
)
protectedpure virtual

Implemented in Nektar::StdRegions::StdQuadExp, and Nektar::StdRegions::StdTriExp.

Referenced by IProductWRTBase_SumFacKernel().

void Nektar::StdRegions::StdExpansion2D::v_LaplacianMatrixOp_MatFree ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const StdRegions::StdMatrixKey &  mkey 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 212 of file StdExpansion2D.cpp.

References BwdTrans_SumFacKernel(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::StdMatrixKey::GetNVarCoeff(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_Kernel(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::m_ncoeffs.

Referenced by Nektar::StdRegions::StdQuadExp::v_LaplacianMatrixOp(), and Nektar::StdRegions::StdTriExp::v_LaplacianMatrixOp().

{
if (mkey.GetNVarCoeff() == 0
&&!mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
{
// This implementation is only valid when there are no
// coefficients associated to the Laplacian operator
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
int nqtot = nquad0*nquad1;
int nmodes0 = m_base[0]->GetNumModes();
int nmodes1 = m_base[1]->GetNumModes();
int wspsize = max(max(max(nqtot,m_ncoeffs),nquad1*nmodes0),nquad0*nmodes1);
const Array<OneD, const NekDouble>& base0 = m_base[0]->GetBdata();
const Array<OneD, const NekDouble>& base1 = m_base[1]->GetBdata();
// Allocate temporary storage
Array<OneD,NekDouble> wsp0(4*wspsize); // size wspsize
Array<OneD,NekDouble> wsp1(wsp0+wspsize); // size 3*wspsize
if(!(m_base[0]->Collocation() && m_base[1]->Collocation()))
{
// LAPLACIAN MATRIX OPERATION
// wsp0 = u = B * u_hat
// wsp1 = du_dxi1 = D_xi1 * wsp0 = D_xi1 * u
// wsp2 = du_dxi2 = D_xi2 * wsp0 = D_xi2 * u
BwdTrans_SumFacKernel(base0,base1,inarray,wsp0,wsp1,true,true);
LaplacianMatrixOp_MatFree_Kernel(wsp0, outarray, wsp1);
}
else
{
LaplacianMatrixOp_MatFree_Kernel(inarray, outarray, wsp1);
}
}
else
{
StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(
inarray,outarray,mkey);
}
}
NekDouble Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate ( const Array< OneD, const NekDouble > &  coords,
const Array< OneD, const NekDouble > &  physvals 
)
protectedvirtual

This function evaluates the expansion at a single (arbitrary) point of the domain.

This function is a wrapper around the virtual function v_PhysEvaluate()

Based on the value of the expansion at the quadrature points, this function calculates the value of the expansion at an arbitrary single points (with coordinates $ \mathbf{x_c}$ given by the pointer coords). This operation, equivalent to

\[ u(\mathbf{x_c}) = \sum_p \phi_p(\mathbf{x_c}) \hat{u}_p \]

is evaluated using Lagrangian interpolants through the quadrature points:

\[ u(\mathbf{x_c}) = \sum_p h_p(\mathbf{x_c}) u_p\]

This function requires that the physical value array $\mathbf{u}$ (implemented as the attribute #m_phys) is set.

Parameters
coordsthe coordinates of the single point
Returns
returns the value of the expansion at the single point

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::LocalRegions::QuadExp.

Definition at line 116 of file StdExpansion2D.cpp.

References ASSERTL2, Nektar::NekConstants::kNekZeroTol, Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), and Nektar::StdRegions::StdExpansion::m_base.

Referenced by Nektar::StdRegions::StdNodalTriExp::GenNBasisTransMatrix().

{
Array<OneD, NekDouble> coll(2);
Array<OneD, DNekMatSharedPtr> I(2);
ASSERTL2(coords[0] > -1 - NekConstants::kNekZeroTol, "coord[0] < -1");
ASSERTL2(coords[0] < 1 + NekConstants::kNekZeroTol, "coord[0] > 1");
ASSERTL2(coords[1] > -1 - NekConstants::kNekZeroTol, "coord[1] < -1");
ASSERTL2(coords[1] < 1 + NekConstants::kNekZeroTol, "coord[1] > 1");
LocCoordToLocCollapsed(coords,coll);
I[0] = m_base[0]->GetI(coll);
I[1] = m_base[1]->GetI(coll+1);
return v_PhysEvaluate(I,physvals);
}
NekDouble Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate ( const Array< OneD, DNekMatSharedPtr > &  I,
const Array< OneD, const NekDouble > &  physvals 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 134 of file StdExpansion2D.cpp.

References Vmath::Ddot(), and Nektar::StdRegions::StdExpansion::m_base.

{
NekDouble val;
int i;
int nq0 = m_base[0]->GetNumPoints();
int nq1 = m_base[1]->GetNumPoints();
Array<OneD, NekDouble> wsp1(nq1);
// interpolate first coordinate direction
for (i = 0; i < nq1;++i)
{
wsp1[i] = Blas::Ddot(nq0, &(I[0]->GetPtr())[0], 1,
&physvals[i * nq0], 1);
}
// interpolate in second coordinate direction
val = Blas::Ddot(nq1, I[1]->GetPtr(), 1, wsp1, 1);
return val;
}
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