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Nektar::StdRegions::StdTriExp Class Reference

#include <StdTriExp.h>

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

 StdTriExp ()
 StdTriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)
 StdTriExp (const StdTriExp &T)
 ~StdTriExp ()
- Public Member Functions inherited from Nektar::StdRegions::StdExpansion2D
 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.
int GetNtrace () const
 Returns the number of trace elements connected to this element.
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 GetForient (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)
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)
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 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_GetForient (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)
void PhysInterpToSimplexEquiSpaced (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function performs an interpolation from the physical space points provided at input into an array of equispaced points which are not the collapsed coordinate. So for a tetrahedron you will only get a tetrahedral number of values.
void GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true)
 This function provides the connectivity of local simplices (triangles or tets) to connect the equispaced data points provided by PhysInterpToSimplexEquiSpaced.
template<class T >
boost::shared_ptr< T > as ()

Protected Member Functions

virtual NekDouble v_Integral (const Array< OneD, const NekDouble > &inarray)
 Integrates the specified function over the domain.
virtual void v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
 Calculate the derivative of the physical points.
virtual void v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 Calculate the derivative of the physical points in a given direction.
virtual void v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray)
virtual void v_StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 Backward tranform for triangular elements.
virtual void v_BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
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)
virtual void v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 Transform a given function from physical quadrature space to coefficient space.
virtual void v_FwdTrans_BndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 Calculate the inner product of inarray with respect to the basis B=base0[p]*base1[pq] and put into outarray.
virtual void v_IProductWRTBase_MatOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
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)
virtual void v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void v_IProductWRTDerivBase_MatOp (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void v_LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
virtual void v_FillMode (const int mode, Array< OneD, NekDouble > &outarray)
virtual int v_GetNverts () const
virtual int v_GetNedges () const
virtual LibUtilities::ShapeType v_DetShapeType () const
virtual int v_NumBndryCoeffs () const
virtual int v_NumDGBndryCoeffs () const
virtual int v_GetEdgeNcoeffs (const int i) const
virtual int v_GetEdgeNumPoints (const int i) const
virtual int v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
virtual LibUtilities::BasisType v_GetEdgeBasisType (const int i) const
virtual void v_GetCoords (Array< OneD, NekDouble > &coords_x, Array< OneD, NekDouble > &coords_y, Array< OneD, NekDouble > &coords_z)
virtual bool v_IsBoundaryInteriorExpansion ()
virtual int v_DetCartesianDirOfEdge (const int edge)
virtual const
LibUtilities::BasisKey 		v_DetEdgeBasisKey (const int edge) const
virtual void v_GetEdgeToElementMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)
virtual int v_GetVertexMap (int localVertexId, bool useCoeffPacking=false)
virtual void v_GetEdgeInteriorMap (const int eid, const Orientation edgeOrient, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray)
virtual void v_GetInteriorMap (Array< OneD, unsigned int > &outarray)
virtual void v_GetBoundaryMap (Array< OneD, unsigned int > &outarray)
virtual DNekMatSharedPtr v_GenMatrix (const StdMatrixKey &mkey)
virtual DNekMatSharedPtr v_CreateStdMatrix (const StdMatrixKey &mkey)
virtual void v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)
virtual void v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void v_GeneralMatrixOp_MatOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
virtual void v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void v_GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true)
- Protected Member Functions inherited from Nektar::StdRegions::StdExpansion2D
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_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)

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 50 of file StdTriExp.h.

Constructor & Destructor Documentation

Nektar::StdRegions::StdTriExp::StdTriExp ( )

Definition at line 45 of file StdTriExp.cpp.

{
}
Nektar::StdRegions::StdTriExp::StdTriExp ( const LibUtilities::BasisKey &  Ba,
const LibUtilities::BasisKey &  Bb 
)

Definition at line 50 of file StdTriExp.cpp.

References ASSERTL0, and Nektar::LibUtilities::BasisKey::GetNumModes().

:
StdExpansion (LibUtilities::StdTriData::getNumberOfCoefficients(
Ba.GetNumModes(),
Bb.GetNumModes()),
2,Ba,Bb),
StdExpansion2D(LibUtilities::StdTriData::getNumberOfCoefficients(
Ba.GetNumModes(),
Bb.GetNumModes()),
Ba,Bb)
{
ASSERTL0(Ba.GetNumModes() <= Bb.GetNumModes(),
"order in 'a' direction is higher than order "
"in 'b' direction");
}
Nektar::StdRegions::StdTriExp::StdTriExp ( const StdTriExp &  T)

Definition at line 67 of file StdTriExp.cpp.

:
StdExpansion(T),
StdExpansion2D(T)
{
}
Nektar::StdRegions::StdTriExp::~StdTriExp ( )

Definition at line 73 of file StdTriExp.cpp.

{
}

Member Function Documentation

void Nektar::StdRegions::StdTriExp::v_BwdTrans ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Backward tranform for triangular elements.

Note
'q' (base[1]) runs fastest in this element.

Implements Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 250 of file StdTriExp.cpp.

References v_BwdTrans_SumFac().

{
v_BwdTrans_SumFac(inarray,outarray);
}
void Nektar::StdRegions::StdTriExp::v_BwdTrans_SumFac ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 258 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion2D::BwdTrans_SumFacKernel(), Nektar::StdRegions::StdExpansion::GetNumPoints(), and Nektar::StdRegions::StdExpansion::m_base.

Referenced by v_BwdTrans().

{
Array<OneD, NekDouble> wsp(m_base[0]->GetNumPoints()*
m_base[1]->GetNumModes());
BwdTrans_SumFacKernel(m_base[0]->GetBdata(),
m_base[1]->GetBdata(),
inarray,outarray,wsp);
}
void Nektar::StdRegions::StdTriExp::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 
)
protectedvirtual

Implements Nektar::StdRegions::StdExpansion2D.

Definition at line 270 of file StdTriExp.cpp.

References ASSERTL1, ASSERTL2, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eOrtho_B, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

{
int i;
int mode;
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
int nmodes0 = m_base[0]->GetNumModes();
int nmodes1 = m_base[1]->GetNumModes();
ASSERTL1(wsp.num_elements() >= nquad0*nmodes1,
"Workspace size is not sufficient");
ASSERTL2((m_base[1]->GetBasisType() != LibUtilities::eOrtho_B)||
(m_base[1]->GetBasisType() != LibUtilities::eModified_B),
"Basis[1] is not of general tensor type");
for (i = mode = 0; i < nmodes0; ++i)
{
Blas::Dgemv('N', nquad1,nmodes1-i,1.0,base1.get()+mode*nquad1,
nquad1,&inarray[0]+mode,1,0.0,&wsp[0]+i*nquad1,1);
mode += nmodes1-i;
}
// fix for modified basis by splitting top vertex mode
if(m_base[0]->GetBasisType() == LibUtilities::eModified_A)
{
Blas::Daxpy(nquad1,inarray[1],base1.get()+nquad1,1,
&wsp[0]+nquad1,1);
}
Blas::Dgemm('N','T', nquad0,nquad1,nmodes0,1.0, base0.get(),nquad0,
&wsp[0], nquad1,0.0, &outarray[0], nquad0);
}
int Nektar::StdRegions::StdTriExp::v_CalcNumberOfCoefficients ( const std::vector< unsigned int > &  nummodes,
int &  modes_offset 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 793 of file StdTriExp.cpp.

References Nektar::LibUtilities::StdSegData::getNumberOfCoefficients().

{
int nmodes = LibUtilities::StdTriData::getNumberOfCoefficients(
nummodes[modes_offset],
nummodes[modes_offset+1]);
modes_offset += 2;
return nmodes;
}
DNekMatSharedPtr Nektar::StdRegions::StdTriExp::v_CreateStdMatrix ( const StdMatrixKey &  mkey)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 1275 of file StdTriExp.cpp.

References v_GenMatrix().

{
return v_GenMatrix(mkey);
}
int Nektar::StdRegions::StdTriExp::v_DetCartesianDirOfEdge ( const int  edge)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 846 of file StdTriExp.cpp.

References ASSERTL2.

{
ASSERTL2(edge >= 0 && edge <= 2, "edge id is out of range");
return edge == 0 ? 0 : 1;
}
const LibUtilities::BasisKey Nektar::StdRegions::StdTriExp::v_DetEdgeBasisKey ( const int  edge) const
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 853 of file StdTriExp.cpp.

References ASSERTL0, ASSERTL2, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauMAlpha1Beta0, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetBasis(), Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::NullBasisKey().

{
ASSERTL2(i >= 0 && i <= 2, "edge id is out of range");
if (i == 0)
{
return GetBasis(0)->GetBasisKey();
}
else
{
switch(m_base[1]->GetBasisType())
{
case LibUtilities::eModified_B:
{
switch(m_base[1]->GetPointsType())
{
case LibUtilities::eGaussRadauMAlpha1Beta0:
{
LibUtilities::PointsKey pkey(
m_base[1]->GetBasisKey().GetPointsKey().
GetNumPoints()+1,
LibUtilities::eGaussLobattoLegendre);
return LibUtilities::BasisKey(
LibUtilities::eModified_A,
m_base[1]->GetNumModes(),pkey);
break;
}
default:
ASSERTL0(false,"unexpected points distribution");
break;
}
}
default:
ASSERTL0(false,"Information not available to set edge key");
break;
}
}
return LibUtilities::NullBasisKey;
}
LibUtilities::ShapeType Nektar::StdRegions::StdTriExp::v_DetShapeType ( ) const
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 740 of file StdTriExp.cpp.

References Nektar::LibUtilities::eTriangle.

{
return LibUtilities::eTriangle;
}
void Nektar::StdRegions::StdTriExp::v_FillMode ( const int  mode,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 681 of file StdTriExp.cpp.

References ASSERTL2, Nektar::LibUtilities::eModified_A, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Vmath::Vcopy(), and Vmath::Vmul().

{
int i,m;
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
int order0 = m_base[0]->GetNumModes();
int order1 = m_base[1]->GetNumModes();
int mode0 = 0;
Array<OneD, const NekDouble> base0 = m_base[0]->GetBdata();
Array<OneD, const NekDouble> base1 = m_base[1]->GetBdata();
ASSERTL2(mode <= m_ncoeffs,
"calling argument mode is larger than "
"total expansion order");
m = order1;
for (i = 0; i < order0; ++i, m+=order1-i)
{
if (m > mode)
{
mode0 = i;
break;
}
}
// deal with top vertex mode in modified basis
if (mode == 1 &&
m_base[0]->GetBasisType() == LibUtilities::eModified_A)
{
Vmath::Fill(nquad0*nquad1 , 1.0, outarray, 1);
}
else
{
for (i = 0; i < nquad1; ++i)
{
Vmath::Vcopy(nquad0,(NekDouble *)(base0.get()+mode0*nquad0),
1,&outarray[0]+i*nquad0,1);
}
}
for(i = 0; i < nquad0; ++i)
{
Vmath::Vmul(nquad1,(NekDouble *)(base1.get() + mode*nquad1),
1,&outarray[0]+i,nquad0,&outarray[0]+i,nquad0);
}
}
void Nektar::StdRegions::StdTriExp::v_FwdTrans ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Transform a given function from physical quadrature space to coefficient space.

See Also
StdExpansion::FwdTrans

Implements Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 310 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::eCopy, Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, and v_IProductWRTBase().

{
v_IProductWRTBase(inarray,outarray);
// get Mass matrix inverse
StdMatrixKey masskey(eInvMass,DetShapeType(),*this);
DNekMatSharedPtr matsys = GetStdMatrix(masskey);
// copy inarray in case inarray == outarray
NekVector<NekDouble> in(m_ncoeffs,outarray,eCopy);
NekVector<NekDouble> out(m_ncoeffs,outarray,eWrapper);
out = (*matsys)*in;
}
void Nektar::StdRegions::StdTriExp::v_FwdTrans_BndConstrained ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp.

Definition at line 328 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eForwards, Nektar::StdRegions::eMass, Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::m_stdStaticCondMatrixManager, Nektar::StdRegions::StdExpansion::MassMatrixOp(), sign, v_GetEdgeToElementMap(), v_GetInteriorMap(), v_IProductWRTBase(), v_NumBndryCoeffs(), and Vmath::Vsub().

{
int i,j;
int npoints[2] = {m_base[0]->GetNumPoints(),
m_base[1]->GetNumPoints()};
int nmodes[2] = {m_base[0]->GetNumModes(),
m_base[1]->GetNumModes()};
fill(outarray.get(), outarray.get()+m_ncoeffs, 0.0 );
Array<OneD, NekDouble> physEdge[3];
Array<OneD, NekDouble> coeffEdge[3];
for(i = 0; i < 3; i++)
{
physEdge[i] = Array<OneD, NekDouble>(npoints[i!=0]);
coeffEdge[i] = Array<OneD, NekDouble>(nmodes[i!=0]);
}
for(i = 0; i < npoints[0]; i++)
{
physEdge[0][i] = inarray[i];
}
for(i = 0; i < npoints[1]; i++)
{
physEdge[1][i] = inarray[npoints[0]-1+i*npoints[0]];
physEdge[2][i] = inarray[(npoints[1]-1)*npoints[0]-i*npoints[0]];
}
StdSegExpSharedPtr segexp[2] = {
MemoryManager<StdRegions::StdSegExp>::AllocateSharedPtr(
m_base[0]->GetBasisKey()),
MemoryManager<StdRegions::StdSegExp>::AllocateSharedPtr(
m_base[1]->GetBasisKey())
};
Array<OneD, unsigned int> mapArray;
Array<OneD, int> signArray;
NekDouble sign;
for (i = 0; i < 3; i++)
{
//segexp[i!=0]->v_FwdTrans_BndConstrained(physEdge[i],coeffEdge[i]);
segexp[i!=0]->FwdTrans_BndConstrained(physEdge[i],coeffEdge[i]);
v_GetEdgeToElementMap(i,eForwards,mapArray,signArray);
for (j = 0; j < nmodes[i != 0]; j++)
{
sign = (NekDouble) signArray[j];
outarray[ mapArray[j] ] = sign * coeffEdge[i][j];
}
}
Array<OneD, NekDouble> tmp0(m_ncoeffs);
Array<OneD, NekDouble> tmp1(m_ncoeffs);
StdMatrixKey masskey(eMass,DetShapeType(),*this);
MassMatrixOp(outarray,tmp0,masskey);
v_IProductWRTBase(inarray,tmp1);
Vmath::Vsub(m_ncoeffs, tmp1, 1, tmp0, 1, tmp1, 1);
// get Mass matrix inverse (only of interior DOF)
// use block (1,1) of the static condensed system
// note: this block alreay contains the inverse matrix
DNekMatSharedPtr matsys =
(m_stdStaticCondMatrixManager[masskey])->GetBlock(1,1);
int nBoundaryDofs = v_NumBndryCoeffs();
int nInteriorDofs = m_ncoeffs - nBoundaryDofs;
Array<OneD, NekDouble> rhs (nInteriorDofs);
Array<OneD, NekDouble> result(nInteriorDofs);
v_GetInteriorMap(mapArray);
for (i = 0; i < nInteriorDofs; i++)
{
rhs[i] = tmp1[ mapArray[i] ];
}
Blas::Dgemv('N',nInteriorDofs,nInteriorDofs,
1.0,&(matsys->GetPtr())[0],nInteriorDofs,
rhs.get(),1,
0.0,result.get(),1);
for (i = 0; i < nInteriorDofs; i++)
{
outarray[ mapArray[i] ] = result[i];
}
}
void Nektar::StdRegions::StdTriExp::v_GeneralMatrixOp_MatOp ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const StdMatrixKey &  mkey 
)
protectedvirtual

Reimplemented in Nektar::LocalRegions::TriExp.

Definition at line 1436 of file StdTriExp.cpp.

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

{
DNekMatSharedPtr mat = m_stdMatrixManager[mkey];
if(inarray.get() == outarray.get())
{
Array<OneD,NekDouble> tmp(m_ncoeffs);
Vmath::Vcopy(m_ncoeffs,inarray.get(),1,tmp.get(),1);
Blas::Dgemv('N', m_ncoeffs, m_ncoeffs, 1.0, mat->GetPtr().get(),
m_ncoeffs, tmp.get(), 1, 0.0, outarray.get(), 1);
}
else
{
Blas::Dgemv('N', m_ncoeffs, m_ncoeffs, 1.0, mat->GetPtr().get(),
m_ncoeffs, inarray.get(), 1, 0.0, outarray.get(), 1);
}
}
DNekMatSharedPtr Nektar::StdRegions::StdTriExp::v_GenMatrix ( const StdMatrixKey &  mkey)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, Nektar::StdRegions::StdNodalTriExp, and Nektar::LocalRegions::NodalTriExp.

Definition at line 1211 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::CreateGeneralMatrix(), Nektar::StdRegions::ePhysInterpToEquiSpaced, Nektar::StdRegions::StdMatrixKey::GetMatrixType(), Nektar::LibUtilities::StdSegData::getNumberOfCoefficients(), Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), Nektar::StdRegions::StdExpansion::m_base, Vmath::Smul(), and Vmath::Vcopy().

Referenced by v_CreateStdMatrix().

{
MatrixType mtype = mkey.GetMatrixType();
DNekMatSharedPtr Mat;
switch(mtype)
{
case ePhysInterpToEquiSpaced:
{
int nq0 = m_base[0]->GetNumPoints();
int nq1 = m_base[1]->GetNumPoints();
int nq = max(nq0,nq1);
int neq = LibUtilities::StdTriData::
getNumberOfCoefficients(nq,nq);
Array<OneD, Array<OneD, NekDouble> > coords(neq);
Array<OneD, NekDouble> coll (2);
Array<OneD, DNekMatSharedPtr> I (2);
Array<OneD, NekDouble> tmp (nq0);
Mat = MemoryManager<DNekMat>::AllocateSharedPtr(neq,nq0*nq1);
int cnt = 0;
for(int i = 0; i < nq; ++i)
{
for(int j = 0; j < nq-i; ++j,++cnt)
{
coords[cnt] = Array<OneD, NekDouble>(2);
coords[cnt][0] = -1.0 + 2*j/(NekDouble)(nq-1);
coords[cnt][1] = -1.0 + 2*i/(NekDouble)(nq-1);
}
}
for(int i = 0; i < neq; ++i)
{
LocCoordToLocCollapsed(coords[i],coll);
I[0] = m_base[0]->GetI(coll);
I[1] = m_base[1]->GetI(coll+1);
// interpolate first coordinate direction
for (int j = 0; j < nq1; ++j)
{
NekDouble fac = (I[1]->GetPtr())[j];
Vmath::Smul(nq0, fac, I[0]->GetPtr(), 1, tmp, 1);
Vmath::Vcopy(nq0, &tmp[0], 1,
Mat->GetRawPtr() + j*nq0*neq + i, neq);
}
}
break;
}
default:
{
Mat = StdExpansion::CreateGeneralMatrix(mkey);
break;
}
}
return Mat;
}
void Nektar::StdRegions::StdTriExp::v_GetBoundaryMap ( Array< OneD, unsigned int > &  outarray)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 1174 of file StdTriExp.cpp.

References ASSERTL1, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

{
ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A &&
GetBasisType(1) == LibUtilities::eModified_B,
"Expansion not of expected type");
int i;
int cnt;
int nummodes0, nummodes1;
int value;
if (outarray.num_elements()!=NumBndryCoeffs())
{
outarray = Array<OneD, unsigned int>(NumBndryCoeffs());
}
nummodes0 = m_base[0]->GetNumModes();
nummodes1 = m_base[1]->GetNumModes();
value = 2*nummodes1-1;
for(i = 0; i < value; i++)
{
outarray[i]=i;
}
cnt = value;
for(i = 0; i < nummodes0-2; i++)
{
outarray[cnt++]=value;
value += nummodes1-2-i;
}
}
void Nektar::StdRegions::StdTriExp::v_GetCoords ( Array< OneD, NekDouble > &  coords_x,
Array< OneD, NekDouble > &  coords_y,
Array< OneD, NekDouble > &  coords_z 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp.

Definition at line 820 of file StdTriExp.cpp.

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

{
Array<OneD, const NekDouble> z0 = m_base[0]->GetZ();
Array<OneD, const NekDouble> z1 = m_base[1]->GetZ();
int nq0 = GetNumPoints(0);
int nq1 = GetNumPoints(1);
int i,j;
for(i = 0; i < nq1; ++i)
{
for(j = 0; j < nq0; ++j)
{
coords_0[i*nq0+j] = (1+z0[j])*(1-z1[i])/2.0 - 1.0;
}
Vmath::Fill(nq0,z1[i],&coords_1[0] + i*nq0,1);
}
}
LibUtilities::BasisType Nektar::StdRegions::StdTriExp::v_GetEdgeBasisType ( const int  i) const
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 805 of file StdTriExp.cpp.

References ASSERTL2, and Nektar::StdRegions::StdExpansion::GetBasisType().

{
ASSERTL2(i >= 0 && i <= 2, "edge id is out of range");
if (i == 0)
{
return GetBasisType(0);
}
else
{
return GetBasisType(1);
}
}
void Nektar::StdRegions::StdTriExp::v_GetEdgeInteriorMap ( const int  eid,
const Orientation  edgeOrient,
Array< OneD, unsigned int > &  maparray,
Array< OneD, int > &  signarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 1058 of file StdTriExp.cpp.

References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::StdRegions::eForwards, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetEdgeBasisType(), Nektar::StdRegions::StdExpansion::GetEdgeNcoeffs(), and Nektar::StdRegions::StdExpansion::m_base.

{
ASSERTL0(GetEdgeBasisType(eid) == LibUtilities::eModified_A||
GetEdgeBasisType(eid) == LibUtilities::eModified_B,
"Mapping not defined for this type of basis");
int i;
const int nummodes1 = m_base[1]->GetNumModes();
const int nEdgeIntCoeffs = GetEdgeNcoeffs(eid)-2;
if(maparray.num_elements() != nEdgeIntCoeffs)
{
maparray = Array<OneD, unsigned int>(nEdgeIntCoeffs);
}
if(signarray.num_elements() != nEdgeIntCoeffs)
{
signarray = Array<OneD, int>(nEdgeIntCoeffs,1);
}
else
{
fill( signarray.get() , signarray.get()+nEdgeIntCoeffs, 1 );
}
switch(eid)
{
case 0:
{
int cnt = 2*nummodes1 - 1;
for(i = 0; i < nEdgeIntCoeffs; cnt+=nummodes1-2-i, ++i)
{
maparray[i] = cnt;
}
if(edgeOrient==eBackwards)
{
for(i = 1; i < nEdgeIntCoeffs; i+=2)
{
signarray[i] = -1;
}
}
break;
}
case 1:
{
for(i = 0; i < nEdgeIntCoeffs; i++)
{
maparray[i] = nummodes1+1+i;
}
if(edgeOrient==eBackwards)
{
for(i = 1; i < nEdgeIntCoeffs; i+=2)
{
signarray[i] = -1;
}
}
break;
}
case 2:
{
for(i = 0; i < nEdgeIntCoeffs; i++)
{
maparray[i] = 2+i;
}
if(edgeOrient==eForwards)
{
for(i = 1; i < nEdgeIntCoeffs; i+=2)
{
signarray[i] = -1;
}
}
break;
}
default:
{
ASSERTL0(false,"eid must be between 0 and 2");
break;
}
}
}
int Nektar::StdRegions::StdTriExp::v_GetEdgeNcoeffs ( const int  i) const
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 765 of file StdTriExp.cpp.

References ASSERTL2, and Nektar::StdRegions::StdExpansion::GetBasisNumModes().

{
ASSERTL2(i >= 0 && i <= 2, "edge id is out of range");
if (i == 0)
{
return GetBasisNumModes(0);
}
else
{
return GetBasisNumModes(1);
}
}
int Nektar::StdRegions::StdTriExp::v_GetEdgeNumPoints ( const int  i) const
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 779 of file StdTriExp.cpp.

References ASSERTL2, and Nektar::StdRegions::StdExpansion::GetNumPoints().

{
ASSERTL2((i >= 0)&&(i <= 2),"edge id is out of range");
if (i == 0)
{
return GetNumPoints(0);
}
else
{
return GetNumPoints(1);
}
}
void Nektar::StdRegions::StdTriExp::v_GetEdgeToElementMap ( const int  eid,
const Orientation  edgeOrient,
Array< OneD, unsigned int > &  maparray,
Array< OneD, int > &  signarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 901 of file StdTriExp.cpp.

References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::StdRegions::eForwards, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetEdgeBasisType(), Nektar::StdRegions::StdExpansion::GetEdgeNcoeffs(), and Nektar::StdRegions::StdExpansion::m_base.

Referenced by v_FwdTrans_BndConstrained().

{
ASSERTL0(GetEdgeBasisType(eid) == LibUtilities::eModified_A ||
GetEdgeBasisType(eid) == LibUtilities::eModified_B,
"Mapping not defined for this type of basis");
int i;
const int nummodes1 = m_base[1]->GetNumModes();
const int nEdgeCoeffs = GetEdgeNcoeffs(eid);
if(maparray.num_elements() != nEdgeCoeffs)
{
maparray = Array<OneD, unsigned int>(nEdgeCoeffs);
}
if(signarray.num_elements() != nEdgeCoeffs)
{
signarray = Array<OneD, int>(nEdgeCoeffs,1);
}
else
{
fill(signarray.get() , signarray.get()+nEdgeCoeffs, 1);
}
switch(eid)
{
case 0:
{
int cnt = 0;
for(i = 0; i < nEdgeCoeffs; cnt+=nummodes1-i, ++i)
{
maparray[i] = cnt;
}
if(edgeOrient==eBackwards)
{
swap( maparray[0] , maparray[1] );
for(i = 3; i < nEdgeCoeffs; i+=2)
{
signarray[i] = -1;
}
}
break;
}
case 1:
{
maparray[0] = nummodes1;
maparray[1] = 1;
for(i = 2; i < nEdgeCoeffs; i++)
{
maparray[i] = nummodes1-1+i;
}
if(edgeOrient==eBackwards)
{
swap( maparray[0] , maparray[1] );
for(i = 3; i < nEdgeCoeffs; i+=2)
{
signarray[i] = -1;
}
}
break;
}
case 2:
{
for(i = 0; i < nEdgeCoeffs; i++)
{
maparray[i] = i;
}
if(edgeOrient==eForwards)
{
swap( maparray[0] , maparray[1] );
for(i = 3; i < nEdgeCoeffs; i+=2)
{
signarray[i] = -1;
}
}
break;
}
default:
ASSERTL0(false,"eid must be between 0 and 2");
break;
}
}
void Nektar::StdRegions::StdTriExp::v_GetInteriorMap ( Array< OneD, unsigned int > &  outarray)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 1144 of file StdTriExp.cpp.

References ASSERTL1, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().

Referenced by v_FwdTrans_BndConstrained().

{
ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A &&
GetBasisType(1) == LibUtilities::eModified_B,
"Expansion not of a proper type");
int i,j;
int cnt = 0;
int nummodes0, nummodes1;
int startvalue;
if(outarray.num_elements()!=GetNcoeffs()-NumBndryCoeffs())
{
outarray = Array<OneD, unsigned int>(GetNcoeffs()-NumBndryCoeffs());
}
nummodes0 = m_base[0]->GetNumModes();
nummodes1 = m_base[1]->GetNumModes();
startvalue = 2*nummodes1;
for(i = 0; i < nummodes0-2; i++)
{
for(j = 0; j < nummodes1-3-i; j++)
{
outarray[cnt++]=startvalue+j;
}
startvalue+=nummodes1-2-i;
}
}
int Nektar::StdRegions::StdTriExp::v_GetNedges ( ) const
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 735 of file StdTriExp.cpp.

{
return 3;
}
int Nektar::StdRegions::StdTriExp::v_GetNverts ( ) const
protectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 730 of file StdTriExp.cpp.

{
return 3;
}
void Nektar::StdRegions::StdTriExp::v_GetSimplexEquiSpacedConnectivity ( Array< OneD, int > &  conn,
bool  standard = true 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1507 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::m_base.

{
int np1 = m_base[0]->GetNumPoints();
int np2 = m_base[1]->GetNumPoints();
int np = max(np1,np2);
conn = Array<OneD, int>(3*(np-1)*(np-1));
int row = 0;
int rowp1 = 0;
int cnt = 0;
for(int i = 0; i < np-1; ++i)
{
rowp1 += np-i;
for(int j = 0; j < np-i-2; ++j)
{
conn[cnt++] = row +j;
conn[cnt++] = row +j+1;
conn[cnt++] = rowp1 +j;
conn[cnt++] = rowp1 +j+1;
conn[cnt++] = rowp1 +j;
conn[cnt++] = row +j+1;
}
conn[cnt++] = row +np-i-2;
conn[cnt++] = row +np-i-1;
conn[cnt++] = rowp1+np-i-2;
row += np-i;
}
}
int Nektar::StdRegions::StdTriExp::v_GetVertexMap ( int  localVertexId,
bool  useCoeffPacking = false 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 994 of file StdTriExp.cpp.

References ASSERTL0, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetEdgeBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

{
ASSERTL0(
GetEdgeBasisType(localVertexId) == LibUtilities::eModified_A ||
GetEdgeBasisType(localVertexId) == LibUtilities::eModified_B,
"Mapping not defined for this type of basis");
int localDOF = 0;
if(useCoeffPacking == true)
{
switch(localVertexId)
{
case 0:
{
localDOF = 0;
break;
}
case 1:
{
localDOF = 1;
break;
}
case 2:
{
localDOF = m_base[1]->GetNumModes();
break;
}
default:
{
ASSERTL0(false,"eid must be between 0 and 2");
break;
}
}
}
else // follow book format for vertex indexing.
{
switch(localVertexId)
{
case 0:
{
localDOF = 0;
break;
}
case 1:
{
localDOF = m_base[1]->GetNumModes();
break;
}
case 2:
{
localDOF = 1;
break;
}
default:
{
ASSERTL0(false,"eid must be between 0 and 2");
break;
}
}
}
return localDOF;
}
void Nektar::StdRegions::StdTriExp::v_HelmholtzMatrixOp ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const StdMatrixKey &  mkey 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 1321 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion2D::v_HelmholtzMatrixOp_MatFree().

{
StdTriExp::v_HelmholtzMatrixOp_MatFree(inarray,outarray,mkey);
}
NekDouble Nektar::StdRegions::StdTriExp::v_Integral ( const Array< OneD, const NekDouble > &  inarray)
protectedvirtual

Integrates the specified function over the domain.

See Also
StdRegions::StdExpansion::Integral.

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp.

Definition at line 80 of file StdTriExp.cpp.

References Nektar::LibUtilities::eGaussRadauMAlpha1Beta0, Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion2D::Integral(), Nektar::StdRegions::StdExpansion::m_base, and Vmath::Smul().

{
int i;
int nquad1 = m_base[1]->GetNumPoints();
Array<OneD, NekDouble> w1_tmp(nquad1);
Array<OneD, const NekDouble> w0 = m_base[0]->GetW();
Array<OneD, const NekDouble> w1 = m_base[1]->GetW();
Array<OneD, const NekDouble> z1 = m_base[1]->GetZ();
switch(m_base[1]->GetPointsType())
{
case LibUtilities::eGaussRadauMAlpha1Beta0: // (0,1) Jacobi Inner product
{
Vmath::Smul(nquad1, 0.5, w1, 1, w1_tmp,1);
break;
}
default:
{
// include jacobian factor on whatever coordinates are defined.
for(i = 0; i < nquad1; ++i)
{
w1_tmp[i] = 0.5*(1-z1[i])*w1[i];
}
break;
}
}
return StdExpansion2D::Integral(inarray,w0,w1_tmp);
}
void Nektar::StdRegions::StdTriExp::v_IProductWRTBase ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Calculate the inner product of inarray with respect to the basis B=base0[p]*base1[pq] and put into outarray.

$ \begin{array}{rcl} I_{pq} = (\phi^A_q \phi^B_{pq}, u) &=& \sum_{i=0}^{nq_0}\sum_{j=0}^{nq_1} \phi^A_p(\eta_{0,i})\phi^B_{pq}(\eta_{1,j}) w^0_i w^1_j u(\xi_{0,i} \xi_{1,j}) \\ & = & \sum_{i=0}^{nq_0} \phi^A_p(\eta_{0,i}) \sum_{j=0}^{nq_1} \phi^B_{pq}(\eta_{1,j}) \tilde{u}_{i,j} \end{array} $

where

$ \tilde{u}_{i,j} = w^0_i w^1_j u(\xi_{0,i},\xi_{1,j}) $

which can be implemented as

$ f_{pj} = \sum_{i=0}^{nq_0} \phi^A_p(\eta_{0,i}) \tilde{u}_{i,j} \rightarrow {\bf B_1 U} $ $ I_{pq} = \sum_{j=0}^{nq_1} \phi^B_{pq}(\eta_{1,j}) f_{pj} \rightarrow {\bf B_2[p*skip] f[skip]} $

Recall: $ \eta_{1} = \frac{2(1+\xi_1)}{(1-\xi_2)}-1, \, \eta_2 = \xi_2$

Note: For the orthgonality of this expansion to be realised the 'q' ordering must run fastest in contrast to the Quad and Hex ordering where 'p' index runs fastest to be consistent with the quadrature ordering.

In the triangular space the i (i.e. $\eta_1$ direction) ordering still runs fastest by convention.

Implements Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 464 of file StdTriExp.cpp.

References v_IProductWRTBase_SumFac().

Referenced by v_FwdTrans(), and v_FwdTrans_BndConstrained().

{
StdTriExp::v_IProductWRTBase_SumFac(inarray,outarray);
}
void Nektar::StdRegions::StdTriExp::v_IProductWRTBase_MatOp ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented in Nektar::LocalRegions::TriExp.

Definition at line 471 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eIProductWRTBase, Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::GetTotPoints(), and Nektar::StdRegions::StdExpansion::m_ncoeffs.

{
int nq = GetTotPoints();
StdMatrixKey iprodmatkey(eIProductWRTBase,DetShapeType(),*this);
DNekMatSharedPtr iprodmat = GetStdMatrix(iprodmatkey);
Blas::Dgemv('N',m_ncoeffs,nq,1.0,iprodmat->GetPtr().get(),
m_ncoeffs, inarray.get(), 1, 0.0, outarray.get(), 1);
}
void Nektar::StdRegions::StdTriExp::v_IProductWRTBase_SumFac ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 483 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric().

Referenced by v_IProductWRTBase().

{
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
int order0 = m_base[0]->GetNumModes();
Array<OneD,NekDouble> tmp(nquad0*nquad1+nquad1*order0);
Array<OneD,NekDouble> wsp(tmp+nquad0*nquad1);
// multiply by integration constants
MultiplyByQuadratureMetric(inarray,tmp);
IProductWRTBase_SumFacKernel(
m_base[0]->GetBdata(),
m_base[1]->GetBdata(),
tmp,outarray,wsp);
}
void Nektar::StdRegions::StdTriExp::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 
)
protectedvirtual

Implements Nektar::StdRegions::StdExpansion2D.

Definition at line 503 of file StdTriExp.cpp.

References ASSERTL1, Vmath::Ddot(), Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

{
int i;
int mode;
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
int nmodes0 = m_base[0]->GetNumModes();
int nmodes1 = m_base[1]->GetNumModes();
ASSERTL1(wsp.num_elements() >= nquad1*nmodes0,
"Workspace size is not sufficient");
Blas::Dgemm('T','N',nquad1,nmodes0,nquad0,1.0,inarray.get(),nquad0,
base0.get(),nquad0,0.0,wsp.get(),nquad1);
// Inner product with respect to 'b' direction
for (mode=i=0; i < nmodes0; ++i)
{
Blas::Dgemv('T',nquad1,nmodes1-i,1.0, base1.get()+mode*nquad1,
nquad1,wsp.get()+i*nquad1,1, 0.0,
outarray.get() + mode,1);
mode += nmodes1 - i;
}
// fix for modified basis by splitting top vertex mode
if (m_base[0]->GetBasisType() == LibUtilities::eModified_A)
{
outarray[1] += Blas::Ddot(nquad1,base1.get()+nquad1,1,
wsp.get()+nquad1,1);
}
}
void Nektar::StdRegions::StdTriExp::v_IProductWRTDerivBase ( const int  dir,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 542 of file StdTriExp.cpp.

References v_IProductWRTDerivBase_SumFac().

{
StdTriExp::v_IProductWRTDerivBase_SumFac(dir,inarray,outarray);
}
void Nektar::StdRegions::StdTriExp::v_IProductWRTDerivBase_MatOp ( const int  dir,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented in Nektar::LocalRegions::TriExp.

Definition at line 550 of file StdTriExp.cpp.

References ASSERTL1, Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eIProductWRTDerivBase0, Nektar::StdRegions::eIProductWRTDerivBase1, Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::GetTotPoints(), and Nektar::StdRegions::StdExpansion::m_ncoeffs.

{
int nq = GetTotPoints();
MatrixType mtype = eIProductWRTDerivBase0;
switch(dir)
{
case 0:
{
mtype = eIProductWRTDerivBase0;
break;
}
case 1:
{
mtype = eIProductWRTDerivBase1;
break;
}
default:
{
ASSERTL1(false,"input dir is out of range");
break;
}
}
StdMatrixKey iprodmatkey(mtype,DetShapeType(),*this);
DNekMatSharedPtr iprodmat = GetStdMatrix(iprodmatkey);
Blas::Dgemv('N',m_ncoeffs,nq,1.0,iprodmat->GetPtr().get(),
m_ncoeffs, inarray.get(), 1, 0.0, outarray.get(), 1);
}
void Nektar::StdRegions::StdTriExp::v_IProductWRTDerivBase_SumFac ( const int  dir,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 584 of file StdTriExp.cpp.

References ASSERTL1, Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), Vmath::Smul(), Vmath::Vadd(), and Vmath::Vmul().

Referenced by v_IProductWRTDerivBase().

{
int i;
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
int nqtot = nquad0*nquad1;
int nmodes0 = m_base[0]->GetNumModes();
int wspsize = max(max(nqtot,m_ncoeffs),nquad1*nmodes0);
Array<OneD, NekDouble> gfac0(2*wspsize);
Array<OneD, NekDouble> tmp0 (gfac0+wspsize);
const Array<OneD, const NekDouble>& z1 = m_base[1]->GetZ();
// set up geometric factor: 2/(1-z1)
for(i = 0; i < nquad1; ++i)
{
gfac0[i] = 2.0/(1-z1[i]);
}
for(i = 0; i < nquad1; ++i)
{
Vmath::Smul(nquad0,gfac0[i],&inarray[0]+i*nquad0,1,
&tmp0[0]+i*nquad0,1);
}
MultiplyByQuadratureMetric(tmp0,tmp0);
switch(dir)
{
case 0:
{
IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(),
m_base[1]->GetBdata(),
tmp0,outarray,gfac0);
break;
}
case 1:
{
Array<OneD, NekDouble> tmp3(m_ncoeffs);
const Array<OneD, const NekDouble>& z0 = m_base[0]->GetZ();
for (i = 0; i < nquad0; ++i)
{
gfac0[i] = 0.5*(1+z0[i]);
}
for (i = 0; i < nquad1; ++i)
{
Vmath::Vmul(nquad0,&gfac0[0],1,&tmp0[0]+i*nquad0,1,
&tmp0[0]+i*nquad0,1);
}
IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(),
m_base[1]->GetBdata(),
tmp0,tmp3,gfac0);
MultiplyByQuadratureMetric(inarray,tmp0);
IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
m_base[1]->GetDbdata(),
tmp0,outarray,gfac0);
Vmath::Vadd(m_ncoeffs,&tmp3[0],1,&outarray[0],1,
&outarray[0],1);
break;
}
default:
{
ASSERTL1(false, "input dir is out of range");
break;
}
}
}
bool Nektar::StdRegions::StdTriExp::v_IsBoundaryInteriorExpansion ( )
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 840 of file StdTriExp.cpp.

References Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, and Nektar::StdRegions::StdExpansion::m_base.

{
return m_base[0]->GetBasisType() == LibUtilities::eModified_A &&
m_base[1]->GetBasisType() == LibUtilities::eModified_B;
}
void Nektar::StdRegions::StdTriExp::v_LaplacianMatrixOp ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const StdMatrixKey &  mkey 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 1293 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion2D::v_LaplacianMatrixOp_MatFree().

{
StdTriExp::v_LaplacianMatrixOp_MatFree(inarray,outarray,mkey);
}
void Nektar::StdRegions::StdTriExp::v_LaplacianMatrixOp ( const int  k1,
const int  k2,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const StdMatrixKey &  mkey 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 1301 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree().

{
StdExpansion::LaplacianMatrixOp_MatFree(
k1,k2,inarray,outarray,mkey);
}
void Nektar::StdRegions::StdTriExp::v_LocCoordToLocCollapsed ( const Array< OneD, const NekDouble > &  xi,
Array< OneD, NekDouble > &  eta 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 664 of file StdTriExp.cpp.

References Nektar::NekConstants::kNekZeroTol.

{
// set up local coordinate system
if (fabs(xi[1]-1.0) < NekConstants::kNekZeroTol)
{
eta[0] = -1.0;
eta[1] = 1.0;
}
else
{
eta[0] = 2*(1+xi[0])/(1-xi[1])-1.0;
eta[1] = xi[1];
}
}
void Nektar::StdRegions::StdTriExp::v_MassMatrixOp ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const StdMatrixKey &  mkey 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 1285 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::MassMatrixOp_MatFree().

{
StdExpansion::MassMatrixOp_MatFree(inarray,outarray,mkey);
}
void Nektar::StdRegions::StdTriExp::v_MultiplyByStdQuadratureMetric ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1462 of file StdTriExp.cpp.

References ASSERTL0, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eGaussRadauMAlpha1Beta0, Nektar::LibUtilities::ePolyEvenlySpaced, Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::m_base, and Vmath::Vmul().

{
int i;
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
const Array<OneD, const NekDouble>& w0 = m_base[0]->GetW();
const Array<OneD, const NekDouble>& w1 = m_base[1]->GetW();
const Array<OneD, const NekDouble>& z1 = m_base[1]->GetZ();
// multiply by integration constants
for(i = 0; i < nquad1; ++i)
{
Vmath::Vmul(nquad0,inarray.get()+i*nquad0,1,
w0.get(),1, outarray.get()+i*nquad0,1);
}
switch(m_base[1]->GetPointsType())
{
// Legendre inner product
case LibUtilities::ePolyEvenlySpaced:
case LibUtilities::eGaussLobattoLegendre:
for(i = 0; i < nquad1; ++i)
{
Blas::Dscal(nquad0,0.5*(1-z1[i])*w1[i],
outarray.get()+i*nquad0,1);
}
break;
// (1,0) Jacobi Inner product
case LibUtilities::eGaussRadauMAlpha1Beta0:
for(i = 0; i < nquad1; ++i)
{
Blas::Dscal(nquad0,0.5*w1[i],outarray.get()+i*nquad0,1);
}
break;
default:
ASSERTL0(false, "Unsupported quadrature points type.");
break;
}
}
int Nektar::StdRegions::StdTriExp::v_NumBndryCoeffs ( ) const
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 745 of file StdTriExp.cpp.

References ASSERTL1, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetBasisNumModes(), and Nektar::StdRegions::StdExpansion::GetBasisType().

Referenced by v_FwdTrans_BndConstrained().

{
ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A,
"BasisType is not a boundary interior form");
ASSERTL1(GetBasisType(1) == LibUtilities::eModified_B,
"BasisType is not a boundary interior form");
return 3 + (GetBasisNumModes(0)-2) + 2*(GetBasisNumModes(1)-2);
}
int Nektar::StdRegions::StdTriExp::v_NumDGBndryCoeffs ( ) const
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 755 of file StdTriExp.cpp.

References ASSERTL1, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::StdRegions::StdExpansion::GetBasisNumModes(), and Nektar::StdRegions::StdExpansion::GetBasisType().

{
ASSERTL1(GetBasisType(0) == LibUtilities::eModified_A,
"BasisType is not a boundary interior form");
ASSERTL1(GetBasisType(1) == LibUtilities::eModified_B,
"BasisType is not a boundary interior form");
return GetBasisNumModes(0) + 2*GetBasisNumModes(1);
}
void Nektar::StdRegions::StdTriExp::v_PhysDeriv ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  out_d0,
Array< OneD, NekDouble > &  out_d1,
Array< OneD, NekDouble > &  out_d2 = NullNekDouble1DArray 
)
protectedvirtual

Calculate the derivative of the physical points.

$ \frac{\partial u}{\partial x_1} = \left . \frac{2.0}{1-\eta_2} \frac{\partial u}{\partial d\eta_1} \right |_{\eta_2}$

$ \frac{\partial u}{\partial x_2} = \left . \frac{1+\eta_1}{1-\eta_2} \frac{\partial u}{\partial d\eta_1} \right |_{\eta_2} + \left . \frac{\partial u}{\partial d\eta_2} \right |_{\eta_1} $

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp.

Definition at line 128 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion2D::PhysTensorDeriv(), and Vmath::Vvtvp().

Referenced by v_PhysDeriv(), and v_StdPhysDeriv().

{
int i;
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
Array<OneD, NekDouble> wsp(nquad0*nquad1);
const Array<OneD, const NekDouble>& z0 = m_base[0]->GetZ();
const Array<OneD, const NekDouble>& z1 = m_base[1]->GetZ();
// set up geometric factor: 2/(1-z1)
for (i = 0; i < nquad1; ++i)
{
wsp[i] = 2.0/(1-z1[i]);
}
if (out_d0.num_elements() > 0)
{
PhysTensorDeriv(inarray, out_d0, out_d1);
for (i = 0; i < nquad1; ++i)
{
Blas::Dscal(nquad0,wsp[i],&out_d0[0]+i*nquad0,1);
}
// if no d1 required do not need to calculate both deriv
if (out_d1.num_elements() > 0)
{
// set up geometric factor: (1_z0)/(1-z1)
for (i = 0; i < nquad0; ++i)
{
wsp[i] = 0.5*(1+z0[i]);
}
for (i = 0; i < nquad1; ++i)
{
Vmath::Vvtvp(nquad0,&wsp[0],1,&out_d0[0]+i*nquad0,
1,&out_d1[0]+i*nquad0,
1,&out_d1[0]+i*nquad0,1);
}
}
}
else if (out_d1.num_elements() > 0)
{
Array<OneD, NekDouble> diff0(nquad0*nquad1);
PhysTensorDeriv(inarray, diff0, out_d1);
for (i = 0; i < nquad1; ++i)
{
Blas::Dscal(nquad0,wsp[i],&diff0[0]+i*nquad0,1);
}
for (i = 0; i < nquad0; ++i)
{
wsp[i] = 0.5*(1+z0[i]);
}
for (i = 0; i < nquad1; ++i)
{
Vmath::Vvtvp(nquad0,&wsp[0],1,&diff0[0]+i*nquad0,
1,&out_d1[0]+i*nquad0,
1,&out_d1[0]+i*nquad0,1);
}
}
}
void Nektar::StdRegions::StdTriExp::v_PhysDeriv ( const int  dir,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  out_d0 
)
protectedvirtual

Calculate the derivative of the physical points in a given direction.

See Also
StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp.

Definition at line 198 of file StdTriExp.cpp.

References ASSERTL1, Nektar::NullNekDouble1DArray, and v_PhysDeriv().

{
switch(dir)
{
case 0:
{
v_PhysDeriv(inarray, outarray, NullNekDouble1DArray);
break;
}
case 1:
{
v_PhysDeriv(inarray, NullNekDouble1DArray, outarray);
break;
}
default:
{
ASSERTL1(false,"input dir is out of range");
break;
}
}
}
void Nektar::StdRegions::StdTriExp::v_ReduceOrderCoeffs ( int  numMin,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp.

Definition at line 1379 of file StdTriExp.cpp.

References Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.

{
int n_coeffs = inarray.num_elements();
int nquad0 = m_base[0]->GetNumPoints();
int nquad1 = m_base[1]->GetNumPoints();
Array<OneD, NekDouble> coeff(n_coeffs);
Array<OneD, NekDouble> coeff_tmp(n_coeffs,0.0);
Array<OneD, NekDouble> tmp;
Array<OneD, NekDouble> tmp2;
int nqtot = nquad0*nquad1;
Array<OneD, NekDouble> phys_tmp(nqtot,0.0);
int nmodes0 = m_base[0]->GetNumModes();
int nmodes1 = m_base[1]->GetNumModes();
int numMin2 = nmodes0;
int i;
const LibUtilities::PointsKey Pkey0(
nmodes0, LibUtilities::eGaussLobattoLegendre);
const LibUtilities::PointsKey Pkey1(
nmodes1, LibUtilities::eGaussLobattoLegendre);
LibUtilities::BasisKey b0(m_base[0]->GetBasisType(),nmodes0,Pkey0);
LibUtilities::BasisKey b1(m_base[1]->GetBasisType(),nmodes1,Pkey1);
LibUtilities::BasisKey bortho0(LibUtilities::eOrtho_A,nmodes0,Pkey0);
LibUtilities::BasisKey bortho1(LibUtilities::eOrtho_B,nmodes1,Pkey1);
StdRegions::StdTriExpSharedPtr m_OrthoTriExp;
StdRegions::StdTriExpSharedPtr m_TriExp;
m_TriExp = MemoryManager<StdRegions::StdTriExp>
::AllocateSharedPtr(b0, b1);
m_OrthoTriExp = MemoryManager<StdRegions::StdTriExp>
::AllocateSharedPtr(bortho0, bortho1);
m_TriExp ->BwdTrans(inarray,phys_tmp);
m_OrthoTriExp->FwdTrans(phys_tmp, coeff);
for (i = 0; i < n_coeffs; i++)
{
if (i == numMin)
{
coeff[i] = 0.0;
numMin += numMin2 - 1;
numMin2 -= 1.0;
}
}
m_OrthoTriExp->BwdTrans(coeff,phys_tmp);
m_TriExp ->FwdTrans(phys_tmp, outarray);
}
void Nektar::StdRegions::StdTriExp::v_StdPhysDeriv ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  out_d0,
Array< OneD, NekDouble > &  out_d1,
Array< OneD, NekDouble > &  out_d2 = NullNekDouble1DArray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 223 of file StdTriExp.cpp.

References v_PhysDeriv().

{
StdTriExp::v_PhysDeriv(inarray, out_d0, out_d1);
}
void Nektar::StdRegions::StdTriExp::v_StdPhysDeriv ( const int  dir,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 232 of file StdTriExp.cpp.

References v_PhysDeriv().

{
StdTriExp::v_PhysDeriv(dir,inarray,outarray);
}
void Nektar::StdRegions::StdTriExp::v_SVVLaplacianFilter ( Array< OneD, NekDouble > &  array,
const StdMatrixKey &  mkey 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1330 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::eFactorSVVDiffCoeff, Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetPointsType(), and Nektar::StdRegions::StdExpansion::m_base.

{
int qa = m_base[0]->GetNumPoints();
int qb = m_base[1]->GetNumPoints();
int nmodes_a = m_base[0]->GetNumModes();
int nmodes_b = m_base[1]->GetNumModes();
// Declare orthogonal basis.
LibUtilities::PointsKey pa(qa,m_base[0]->GetPointsType());
LibUtilities::PointsKey pb(qb,m_base[1]->GetPointsType());
LibUtilities::BasisKey Ba(LibUtilities::eOrtho_A,nmodes_a,pa);
LibUtilities::BasisKey Bb(LibUtilities::eOrtho_B,nmodes_b,pb);
StdTriExp OrthoExp(Ba,Bb);
Array<OneD, NekDouble> orthocoeffs(OrthoExp.GetNcoeffs());
int j, k , cnt = 0;
int cutoff = (int) (mkey.GetConstFactor(eFactorSVVCutoffRatio)*min(nmodes_a,nmodes_b));
NekDouble SvvDiffCoeff = mkey.GetConstFactor(eFactorSVVDiffCoeff);
NekDouble epsilon = 1.0;
int nmodes = min(nmodes_a,nmodes_b);
//To avoid the fac[j] from blowing up
//NekDouble epsilon = 0.001;
// project onto physical space.
OrthoExp.FwdTrans(array,orthocoeffs);
//cout << "nmodes_a = " << nmodes_a << " and nmodes_b = " << nmodes_b << "and and orthocoeffs is of size " << sizeof(orthocoeffs) << endl;
// apply SVV filter (JEL)
for(j = 0; j < nmodes_a; ++j)
{
for(k = 0; k < nmodes_b-j; ++k)
{
if(j + k >= cutoff)
{
orthocoeffs[cnt] *= (1.0+SvvDiffCoeff*exp(-(j+k-nmodes)*(j+k-nmodes)/((NekDouble)((j+k-cutoff+epsilon)*(j+k-cutoff+epsilon)))));
}
cnt++;
}
}
// backward transform to physical space
OrthoExp.BwdTrans(orthocoeffs,array);
}
void Nektar::StdRegions::StdTriExp::v_WeakDerivMatrixOp ( const int  i,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const StdMatrixKey &  mkey 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TriExp, and Nektar::StdRegions::StdNodalTriExp.

Definition at line 1312 of file StdTriExp.cpp.

References Nektar::StdRegions::StdExpansion::WeakDerivMatrixOp_MatFree().

{
StdExpansion::WeakDerivMatrixOp_MatFree(i,inarray,outarray,mkey);
}
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