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Nektar::StdRegions::StdExpansion3D Class Referenceabstract

#include <StdExpansion3D.h>

Inheritance diagram for Nektar::StdRegions::StdExpansion3D:
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Public Member Functions

 StdExpansion3D ()
 
 StdExpansion3D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc)
 
 StdExpansion3D (const StdExpansion3D &T)
 
virtual ~StdExpansion3D ()
 
void PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d1, Array< OneD, NekDouble > &outarray_d2, Array< OneD, NekDouble > &outarray_d3)
 Calculate the 3D derivative in the local tensor/collapsed coordinate at the physical points. More...
 
void BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)
 
void IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)
 
int GetNedges () const
 return the number of edges in 3D expansion More...
 
int GetEdgeNcoeffs (const int i) const
 This function returns the number of expansion coefficients belonging to the i-th edge. More...
 
void GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards)
 
- Public Member Functions inherited from Nektar::StdRegions::StdExpansion
 StdExpansion ()
 Default Constructor. More...
 
 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. More...
 
 StdExpansion (const StdExpansion &T)
 Copy Constructor. More...
 
virtual ~StdExpansion ()
 Destructor. More...
 
int GetNumBases () const
 This function returns the number of 1D bases used in the expansion. More...
 
const Array< OneD, const LibUtilities::BasisSharedPtr > & GetBase () const
 This function gets the shared point to basis. More...
 
const LibUtilities::BasisSharedPtr & GetBasis (int dir) const
 This function gets the shared point to basis in the dir direction. More...
 
int GetNcoeffs (void) const
 This function returns the total number of coefficients used in the expansion. More...
 
int GetTotPoints () const
 This function returns the total number of quadrature points used in the element. More...
 
LibUtilities::BasisType GetBasisType (const int dir) const
 This function returns the type of basis used in the dir direction. More...
 
int GetBasisNumModes (const int dir) const
 This function returns the number of expansion modes in the dir direction. More...
 
int EvalBasisNumModesMax (void) const
 This function returns the maximum number of expansion modes over all local directions. More...
 
LibUtilities::PointsType GetPointsType (const int dir) const
 This function returns the type of quadrature points used in the dir direction. More...
 
int GetNumPoints (const int dir) const
 This function returns the number of quadrature points in the dir direction. More...
 
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. More...
 
int GetNverts () const
 This function returns the number of vertices of the expansion domain. More...
 
int GetTraceNcoeffs (const int i) const
 This function returns the number of expansion coefficients belonging to the i-th trace. More...
 
int GetTraceIntNcoeffs (const int i) const
 
int GetTraceNumPoints (const int i) const
 This function returns the number of quadrature points belonging to the i-th trace. More...
 
const LibUtilities::BasisKey GetTraceBasisKey (const int i, int k=-1) const
 This function returns the basis key belonging to the i-th trace. More...
 
LibUtilities::PointsKey GetTracePointsKey (const int i, int k=-1) const
 This function returns the basis key belonging to the i-th trace. More...
 
int NumBndryCoeffs (void) const
 
int NumDGBndryCoeffs (void) const
 
const LibUtilities::PointsKey GetNodalPointsKey () const
 This function returns the type of expansion Nodal point type if defined. More...
 
int GetNtraces () const
 Returns the number of trace elements connected to this element. More...
 
LibUtilities::ShapeType DetShapeType () const
 This function returns the shape of the expansion domain. More...
 
std::shared_ptr< StdExpansion > GetStdExp (void) const
 
std::shared_ptr< StdExpansion > GetLinStdExp (void) const
 
int GetShapeDimension () const
 
bool IsBoundaryInteriorExpansion ()
 
bool IsNodalNonTensorialExp ()
 
void BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function performs the Backward transformation from coefficient space to physical space. More...
 
void FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function performs the Forward transformation from physical space to coefficient space. More...
 
void FwdTransBndConstrained (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. More...
 
void FillMode (const int mode, Array< OneD, NekDouble > &outarray)
 This function fills the array outarray with the mode-th mode of the expansion. More...
 
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 More...
 
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)
 
void IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, 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. More...
 
void SetElmtId (const int id)
 Set the element id of this expansion when used in a list by returning value of m_elmt_id. More...
 
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 More...
 
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 More...
 
DNekMatSharedPtr GetStdMatrix (const StdMatrixKey &mkey)
 
DNekBlkMatSharedPtr GetStdStaticCondMatrix (const StdMatrixKey &mkey)
 
void NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
 
void NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, const Array< OneD, 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)
 
void NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble >> &Fvec, Array< OneD, NekDouble > &outarray)
 
DNekScalBlkMatSharedPtr GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
 
void DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
 
int CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
 
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 GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
 
void GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray)
 
void GetElmtTraceToTraceMap (const unsigned int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
 
void GetTraceInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eForwards)
 
void GetTraceNumModes (const int tid, int &numModes0, int &numModes1, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)
 
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 \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\) More...
 
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 ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff)
 
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)
 
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. More...
 
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. More...
 
NekDouble PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode)
 This function evaluates the basis function mode mode at a point coords of the domain. More...
 
void LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
 Convert local cartesian coordinate xi into local collapsed coordinates eta. More...
 
void LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)
 Convert local collapsed coordinates eta into local cartesian coordinate xi. More...
 
virtual int v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset)
 
virtual void v_NormVectorIProductWRTBase (const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
 
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 void v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble >> &Fvec, Array< OneD, NekDouble > &outarray)
 
virtual DNekScalBlkMatSharedPtr v_GetLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
 
virtual void v_DropLocStaticCondMatrix (const LocalRegions::MatrixKey &mkey)
 
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. More...
 
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. More...
 
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. More...
 
const LibUtilities::PointsKeyVector GetPointsKeys () const
 
DNekMatSharedPtr BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)
 
void PhysInterpToSimplexEquiSpaced (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)
 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. More...
 
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. More...
 
void EquiSpacedToCoeffs (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function performs a projection/interpolation from the equispaced points sometimes used in post-processing onto the coefficient space. More...
 
template<class T >
std::shared_ptr< T > as ()
 
void IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true)
 
void GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
 

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. More...
 
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 > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0
 
virtual void v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=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)
 
virtual NekDouble v_Integral (const Array< OneD, const NekDouble > &inarray)
 Integrates the specified function over the domain. More...
 
virtual int v_GetNedges (void) const
 
virtual int v_GetEdgeNcoeffs (const int i) const
 
virtual void v_GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards)
 
virtual void v_GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient, int P, int Q)
 
virtual void v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
 
- 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. More...
 
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 IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
void IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, 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_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
template<int DIR>
NekDouble BaryEvaluate (const NekDouble &coord, const NekDouble *physvals)
 This function performs the barycentric interpolation of the polynomial stored in coord at a point physvals using barycentric interpolation weights in direction. More...
 
template<int DIR>
NekDouble BaryEvaluateBasis (const NekDouble &coord, const int &mode)
 

Private Member Functions

virtual int v_GetShapeDimension () 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
 

Detailed Description

Definition at line 51 of file StdExpansion3D.h.

Constructor & Destructor Documentation

◆ StdExpansion3D() [1/3]

Nektar::StdRegions::StdExpansion3D::StdExpansion3D ( )

Definition at line 49 of file StdExpansion3D.cpp.

50 {
51 }

◆ StdExpansion3D() [2/3]

Nektar::StdRegions::StdExpansion3D::StdExpansion3D ( int  numcoeffs,
const LibUtilities::BasisKey &  Ba,
const LibUtilities::BasisKey &  Bb,
const LibUtilities::BasisKey &  Bc 
)

Definition at line 53 of file StdExpansion3D.cpp.

56  : StdExpansion(numcoeffs, 3, Ba, Bb, Bc)
57 {
58 }
Nektar::StdRegions::StdExpansion::StdExpansion
StdExpansion()
Default Constructor.
Definition: StdExpansion.cpp:45

◆ StdExpansion3D() [3/3]

Nektar::StdRegions::StdExpansion3D::StdExpansion3D ( const StdExpansion3D &  T)

Definition at line 60 of file StdExpansion3D.cpp.

60  : StdExpansion(T)
61 {
62 }

◆ ~StdExpansion3D()

Nektar::StdRegions::StdExpansion3D::~StdExpansion3D ( )
virtual

Definition at line 64 of file StdExpansion3D.cpp.

65 {
66 }

Member Function Documentation

◆ BwdTrans_SumFacKernel()

void Nektar::StdRegions::StdExpansion3D::BwdTrans_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  base2,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0,
bool  doCheckCollDir1,
bool  doCheckCollDir2 
)

Definition at line 109 of file StdExpansion3D.cpp.

116 {
117  v_BwdTrans_SumFacKernel(base0, base1, base2, inarray, outarray, wsp,
118  doCheckCollDir0, doCheckCollDir1, doCheckCollDir2);
119 }
Nektar::StdRegions::StdExpansion3D::v_BwdTrans_SumFacKernel
virtual void v_BwdTrans_SumFacKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0

References v_BwdTrans_SumFacKernel().

Referenced by Nektar::StdRegions::StdHexExp::v_BwdTrans_SumFac(), Nektar::StdRegions::StdPrismExp::v_BwdTrans_SumFac(), Nektar::StdRegions::StdTetExp::v_BwdTrans_SumFac(), v_HelmholtzMatrixOp_MatFree(), and v_LaplacianMatrixOp_MatFree().

◆ GetEdgeInteriorToElementMap()

void Nektar::StdRegions::StdExpansion3D::GetEdgeInteriorToElementMap ( const int  tid,
Array< OneD, unsigned int > &  maparray,
Array< OneD, int > &  signarray,
Orientation  traceOrient = eForwards 
)
inline

Definition at line 145 of file StdExpansion3D.h.

149  {
150  v_GetEdgeInteriorToElementMap(tid, maparray, signarray, traceOrient);
151  }
Nektar::StdRegions::StdExpansion3D::v_GetEdgeInteriorToElementMap
virtual void v_GetEdgeInteriorToElementMap(const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards)
Definition: StdExpansion3D.cpp:414

References v_GetEdgeInteriorToElementMap().

◆ GetEdgeNcoeffs()

int Nektar::StdRegions::StdExpansion3D::GetEdgeNcoeffs ( const int  i) const
inline

This function returns the number of expansion coefficients belonging to the i-th edge.

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

Parameters
ispecifies which edge
Returns
returns the number of expansion coefficients belonging to the i-th edge

Definition at line 140 of file StdExpansion3D.h.

141  {
142  return v_GetEdgeNcoeffs(i);
143  }
Nektar::StdRegions::StdExpansion3D::v_GetEdgeNcoeffs
virtual int v_GetEdgeNcoeffs(const int i) const
Definition: StdExpansion3D.cpp:407

References v_GetEdgeNcoeffs().

Referenced by Nektar::MultiRegions::PreconditionerLowEnergy::v_BuildPreconditioner(), and Nektar::StdRegions::StdHexExp::v_GetEdgeInteriorToElementMap().

◆ GetNedges()

int Nektar::StdRegions::StdExpansion3D::GetNedges ( ) const
inline

return the number of edges in 3D expansion

Definition at line 125 of file StdExpansion3D.h.

126  {
127  return v_GetNedges();
128  }
Nektar::StdRegions::StdExpansion3D::v_GetNedges
virtual int v_GetNedges(void) const
Definition: StdExpansion3D.cpp:401

References v_GetNedges().

Referenced by Nektar::MultiRegions::PreconditionerLowEnergy::v_BuildPreconditioner().

◆ IProductWRTBase_SumFacKernel()

void Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  base2,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0,
bool  doCheckCollDir1,
bool  doCheckCollDir2 
)

Definition at line 121 of file StdExpansion3D.cpp.

128 {
129  v_IProductWRTBase_SumFacKernel(base0, base1, base2, inarray, outarray, wsp,
130  doCheckCollDir0, doCheckCollDir1,
131  doCheckCollDir2);
132 }
Nektar::StdRegions::StdExpansion3D::v_IProductWRTBase_SumFacKernel
virtual void v_IProductWRTBase_SumFacKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0

References v_IProductWRTBase_SumFacKernel().

Referenced by Nektar::LocalRegions::HexExp::IProductWRTDerivBase_SumFac(), Nektar::LocalRegions::HexExp::IProductWRTDirectionalDerivBase_SumFac(), v_GenStdMatBwdDeriv(), v_HelmholtzMatrixOp_MatFree(), Nektar::StdRegions::StdHexExp::v_IProductWRTBase_SumFac(), Nektar::LocalRegions::HexExp::v_IProductWRTBase_SumFac(), Nektar::LocalRegions::PrismExp::v_IProductWRTBase_SumFac(), Nektar::LocalRegions::PyrExp::v_IProductWRTBase_SumFac(), Nektar::LocalRegions::TetExp::v_IProductWRTBase_SumFac(), Nektar::StdRegions::StdPrismExp::v_IProductWRTBase_SumFac(), Nektar::StdRegions::StdTetExp::v_IProductWRTBase_SumFac(), Nektar::LocalRegions::TetExp::v_IProductWRTDerivBase(), Nektar::LocalRegions::PrismExp::v_IProductWRTDerivBase_SumFac(), Nektar::LocalRegions::PyrExp::v_IProductWRTDerivBase_SumFac(), Nektar::StdRegions::StdHexExp::v_IProductWRTDerivBase_SumFac(), Nektar::StdRegions::StdPrismExp::v_IProductWRTDerivBase_SumFac(), Nektar::StdRegions::StdPyrExp::v_IProductWRTDerivBase_SumFac(), Nektar::StdRegions::StdTetExp::v_IProductWRTDerivBase_SumFac(), Nektar::LocalRegions::HexExp::v_LaplacianMatrixOp_MatFree_Kernel(), and Nektar::LocalRegions::PrismExp::v_LaplacianMatrixOp_MatFree_Kernel().

◆ PhysTensorDeriv()

void Nektar::StdRegions::StdExpansion3D::PhysTensorDeriv ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray_d1,
Array< OneD, NekDouble > &  outarray_d2,
Array< OneD, NekDouble > &  outarray_d3 
)

Calculate the 3D 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:

  • \( \frac{d}{d\eta_1} \rightarrow {\bf D^T_0 u } \)
  • \( \frac{d}{d\eta_2} \rightarrow {\bf D_1 u } \)
  • \( \frac{d}{d\eta_3} \rightarrow {\bf D_2 u } \)
Parameters
inarrayarray of physical points to be differentiated
outarray_d1the resulting array of derivative in the \(\eta_1\) direction will be stored in outarray_d1 as output of the function
outarray_d2the resulting array of derivative in the \(\eta_2\) direction will be stored in outarray_d2 as output of the function
outarray_d3the resulting array of derivative in the \(\eta_3\) direction will be stored in outarray_d3 as output of the function

Recall that: \( \hspace{1cm} \begin{array}{llll} \mbox{Shape} & \mbox{Cartesian coordinate range} & \mbox{Collapsed coord.} & \mbox{Collapsed coordinate definition}\\ \mbox{Hexahedral} & -1 \leq \xi_1,\xi_2, \xi_3 \leq 1 & -1 \leq \eta_1,\eta_2, \eta_3 \leq 1 & \eta_1 = \xi_1, \eta_2 = \xi_2, \eta_3 = \xi_3 \\ \mbox{Tetrahedral} & -1 \leq \xi_1,\xi_2,\xi_3; \xi_1+\xi_2 +\xi_3 \leq -1 & -1 \leq \eta_1,\eta_2, \eta_3 \leq 1 & \eta_1 = \frac{2(1+\xi_1)}{-\xi_2 -\xi_3}-1, \eta_2 = \frac{2(1+\xi_2)}{1 - \xi_3}-1, \eta_3 = \xi_3 \\ \end{array} \)

Definition at line 67 of file StdExpansion3D.cpp.

70 {
71  const int nquad0 = m_base[0]->GetNumPoints();
72  const int nquad1 = m_base[1]->GetNumPoints();
73  const int nquad2 = m_base[2]->GetNumPoints();
74 
75  Array<OneD, NekDouble> wsp(nquad0 * nquad1 * nquad2);
76 
77  // copy inarray to wsp in case inarray is used as outarray
78  Vmath::Vcopy(nquad0 * nquad1 * nquad2, &inarray[0], 1, &wsp[0], 1);
79 
80  if (out_dx.size() > 0)
81  {
82  NekDouble *D0 = &((m_base[0]->GetD())->GetPtr())[0];
83 
84  Blas::Dgemm('N', 'N', nquad0, nquad1 * nquad2, nquad0, 1.0, D0, nquad0,
85  &wsp[0], nquad0, 0.0, &out_dx[0], nquad0);
86  }
87 
88  if (out_dy.size() > 0)
89  {
90  NekDouble *D1 = &((m_base[1]->GetD())->GetPtr())[0];
91  for (int j = 0; j < nquad2; ++j)
92  {
93  Blas::Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0,
94  &wsp[j * nquad0 * nquad1], nquad0, D1, nquad1, 0.0,
95  &out_dy[j * nquad0 * nquad1], nquad0);
96  }
97  }
98 
99  if (out_dz.size() > 0)
100  {
101  NekDouble *D2 = &((m_base[2]->GetD())->GetPtr())[0];
102 
103  Blas::Dgemm('N', 'T', nquad0 * nquad1, nquad2, nquad2, 1.0, &wsp[0],
104  nquad0 * nquad1, D2, nquad2, 0.0, &out_dz[0],
105  nquad0 * nquad1);
106  }
107 }
Nektar::StdRegions::StdExpansion::m_base
Array< OneD, LibUtilities::BasisSharedPtr > m_base
Definition: StdExpansion.h:1145
Blas::Dgemm
static void Dgemm(const char &transa, const char &transb, const int &m, const int &n, const int &k, const double &alpha, const double *a, const int &lda, const double *b, const int &ldb, const double &beta, double *c, const int &ldc)
BLAS level 3: Matrix-matrix multiply C = A x B where op(A)[m x k], op(B)[k x n], C[m x n] DGEMM perfo...
Definition: Blas.hpp:368
Nektar::NekDouble
double NekDouble
Definition: NektarUnivTypeDefs.hpp:43
Vmath::Vcopy
void Vcopy(int n, const T *x, const int incx, T *y, const int incy)
Definition: Vmath.cpp:1255

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

Referenced by Nektar::StdRegions::StdHexExp::v_PhysDeriv(), Nektar::StdRegions::StdPrismExp::v_PhysDeriv(), Nektar::StdRegions::StdPyrExp::v_PhysDeriv(), and Nektar::StdRegions::StdTetExp::v_PhysDeriv().

◆ v_BwdTrans_SumFacKernel()

virtual void Nektar::StdRegions::StdExpansion3D::v_BwdTrans_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  base2,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0,
bool  doCheckCollDir1,
bool  doCheckCollDir2 
)
protectedpure virtual

Implemented in Nektar::StdRegions::StdTetExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdPrismExp, and Nektar::StdRegions::StdHexExp.

Referenced by BwdTrans_SumFacKernel().

◆ v_GenStdMatBwdDeriv()

void Nektar::StdRegions::StdExpansion3D::v_GenStdMatBwdDeriv ( const int  dir,
DNekMatSharedPtr &  mat 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 134 of file StdExpansion3D.cpp.

135 {
136  ASSERTL1((dir == 0) || (dir == 1) || (dir == 2), "Invalid direction.");
137 
138  const int nq0 = m_base[0]->GetNumPoints();
139  const int nq1 = m_base[1]->GetNumPoints();
140  const int nq2 = m_base[2]->GetNumPoints();
141  const int nq = nq0 * nq1 * nq2;
142  const int nm0 = m_base[0]->GetNumModes();
143  const int nm1 = m_base[1]->GetNumModes();
144 
145  Array<OneD, NekDouble> alloc(4 * nq + m_ncoeffs + nm0 * nq2 * (nq1 + nm1),
146  0.0);
147  Array<OneD, NekDouble> tmp1(alloc); // Quad metric
148  Array<OneD, NekDouble> tmp2(alloc + nq); // Dir1 metric
149  Array<OneD, NekDouble> tmp3(alloc + 2 * nq); // Dir2 metric
150  Array<OneD, NekDouble> tmp4(alloc + 3 * nq); // Dir3 metric
151  Array<OneD, NekDouble> tmp5(alloc + 4 * nq); // iprod tmp
152  Array<OneD, NekDouble> wsp(tmp5 + m_ncoeffs); // Wsp
153  switch (dir)
154  {
155  case 0:
156  for (int i = 0; i < nq; i++)
157  {
158  tmp2[i] = 1.0;
159  IProductWRTBase_SumFacKernel(
160  m_base[0]->GetDbdata(), m_base[1]->GetBdata(),
161  m_base[2]->GetBdata(), tmp2, tmp5, wsp, false, true, true);
162 
163  tmp2[i] = 0.0;
164 
165  for (int j = 0; j < m_ncoeffs; j++)
166  {
167  (*mat)(j, i) = tmp5[j];
168  }
169  }
170  break;
171  case 1:
172  for (int i = 0; i < nq; i++)
173  {
174  tmp2[i] = 1.0;
175  IProductWRTBase_SumFacKernel(
176  m_base[0]->GetBdata(), m_base[1]->GetDbdata(),
177  m_base[2]->GetBdata(), tmp2, tmp5, wsp, true, false, true);
178 
179  tmp2[i] = 0.0;
180 
181  for (int j = 0; j < m_ncoeffs; j++)
182  {
183  (*mat)(j, i) = tmp5[j];
184  }
185  }
186  break;
187  case 2:
188  for (int i = 0; i < nq; i++)
189  {
190  tmp2[i] = 1.0;
191  IProductWRTBase_SumFacKernel(
192  m_base[0]->GetBdata(), m_base[1]->GetBdata(),
193  m_base[2]->GetDbdata(), tmp2, tmp5, wsp, true, true, false);
194  tmp2[i] = 0.0;
195 
196  for (int j = 0; j < m_ncoeffs; j++)
197  {
198  (*mat)(j, i) = tmp5[j];
199  }
200  }
201  break;
202  default:
203  NEKERROR(ErrorUtil::efatal, "Not a 2D expansion.");
204  break;
205  }
206 }
NEKERROR
#define NEKERROR(type, msg)
Assert Level 0 – Fundamental assert which is used whether in FULLDEBUG, DEBUG or OPT compilation mode...
Definition: ErrorUtil.hpp:209
ASSERTL1
#define ASSERTL1(condition, msg)
Assert Level 1 – Debugging which is used whether in FULLDEBUG or DEBUG compilation mode....
Definition: ErrorUtil.hpp:249
Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel
void IProductWRTBase_SumFacKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)
Definition: StdExpansion3D.cpp:121

References ASSERTL1, Nektar::ErrorUtil::efatal, IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, and NEKERROR.

◆ v_GetCoordim()

virtual int Nektar::StdRegions::StdExpansion3D::v_GetCoordim ( void  )
inlineprivatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::TetExp, Nektar::LocalRegions::PyrExp, and Nektar::LocalRegions::PrismExp.

Definition at line 229 of file StdExpansion3D.h.

230  {
231  return 3;
232  }

◆ v_GetEdgeInteriorToElementMap()

void Nektar::StdRegions::StdExpansion3D::v_GetEdgeInteriorToElementMap ( const int  tid,
Array< OneD, unsigned int > &  maparray,
Array< OneD, int > &  signarray,
Orientation  traceOrient = eForwards 
)
protectedvirtual

Reimplemented in Nektar::StdRegions::StdTetExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdPrismExp, and Nektar::StdRegions::StdHexExp.

Definition at line 414 of file StdExpansion3D.cpp.

417 {
418  boost::ignore_unused(tid, maparray, signarray, traceOrient);
419  NEKERROR(ErrorUtil::efatal, "Method does not exist for this shape");
420 }

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetEdgeInteriorToElementMap().

◆ v_GetEdgeNcoeffs()

int Nektar::StdRegions::StdExpansion3D::v_GetEdgeNcoeffs ( const int  i) const
protectedvirtual

Reimplemented in Nektar::StdRegions::StdTetExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdPrismExp, and Nektar::StdRegions::StdHexExp.

Definition at line 407 of file StdExpansion3D.cpp.

408 {
409  boost::ignore_unused(i);
410  NEKERROR(ErrorUtil::efatal, "This function is not valid or not defined");
411  return 0;
412 }

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetEdgeNcoeffs().

◆ v_GetNedges()

int Nektar::StdRegions::StdExpansion3D::v_GetNedges ( void  ) const
protectedvirtual

Reimplemented in Nektar::StdRegions::StdTetExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdPrismExp, and Nektar::StdRegions::StdHexExp.

Definition at line 401 of file StdExpansion3D.cpp.

402 {
403  NEKERROR(ErrorUtil::efatal, "This function is not valid or not defined");
404  return 0;
405 }

References Nektar::ErrorUtil::efatal, and NEKERROR.

Referenced by GetNedges().

◆ v_GetShapeDimension()

virtual int Nektar::StdRegions::StdExpansion3D::v_GetShapeDimension ( ) const
inlineprivatevirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 224 of file StdExpansion3D.h.

225  {
226  return 3;
227  }

◆ v_GetTraceToElementMap()

void Nektar::StdRegions::StdExpansion3D::v_GetTraceToElementMap ( const int  tid,
Array< OneD, unsigned int > &  maparray,
Array< OneD, int > &  signarray,
Orientation  traceOrient,
int  P,
int  Q 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 422 of file StdExpansion3D.cpp.

427 {
428  Array<OneD, unsigned int> map1, map2;
429  GetTraceCoeffMap(tid, map1);
430  GetElmtTraceToTraceMap(tid, map2, signarray, traceOrient, P, Q);
431 
432  if (maparray.size() != map2.size())
433  {
434  maparray = Array<OneD, unsigned int>(map2.size());
435  }
436 
437  for (int i = 0; i < map2.size(); ++i)
438  {
439  maparray[i] = map1[map2[i]];
440  }
441 }
Nektar::StdRegions::StdExpansion::GetElmtTraceToTraceMap
void GetElmtTraceToTraceMap(const unsigned int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
Definition: StdExpansion.h:707
Nektar::StdRegions::StdExpansion::GetTraceCoeffMap
void GetTraceCoeffMap(const unsigned int traceid, Array< OneD, unsigned int > &maparray)
Definition: StdExpansion.h:701

References Nektar::StdRegions::StdExpansion::GetElmtTraceToTraceMap(), Nektar::StdRegions::StdExpansion::GetTraceCoeffMap(), and Nektar::LibUtilities::P.

◆ v_HelmholtzMatrixOp_MatFree()

void Nektar::StdRegions::StdExpansion3D::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 329 of file StdExpansion3D.cpp.

332 {
333  if (mkey.GetNVarCoeff() == 0 &&
334  !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00))
335  {
336  using std::max;
337 
338  int nquad0 = m_base[0]->GetNumPoints();
339  int nquad1 = m_base[1]->GetNumPoints();
340  int nquad2 = m_base[2]->GetNumPoints();
341  int nmodes0 = m_base[0]->GetNumModes();
342  int nmodes1 = m_base[1]->GetNumModes();
343  int nmodes2 = m_base[2]->GetNumModes();
344  int wspsize = max(nquad0 * nmodes2 * (nmodes1 + nquad1),
345  nquad0 * nquad1 * (nquad2 + nmodes0) +
346  nmodes0 * nmodes1 * nquad2);
347 
348  NekDouble lambda = mkey.GetConstFactor(StdRegions::eFactorLambda);
349 
350  const Array<OneD, const NekDouble> &base0 = m_base[0]->GetBdata();
351  const Array<OneD, const NekDouble> &base1 = m_base[1]->GetBdata();
352  const Array<OneD, const NekDouble> &base2 = m_base[2]->GetBdata();
353  Array<OneD, NekDouble> wsp0(8 * wspsize);
354  Array<OneD, NekDouble> wsp1(wsp0 + 1 * wspsize);
355  Array<OneD, NekDouble> wsp2(wsp0 + 2 * wspsize);
356 
357  if (!(m_base[0]->Collocation() && m_base[1]->Collocation() &&
358  m_base[2]->Collocation()))
359  {
360  // MASS MATRIX OPERATION
361  // The following is being calculated:
362  // wsp0 = B * u_hat = u
363  // wsp1 = W * wsp0
364  // outarray = B^T * wsp1 = B^T * W * B * u_hat = M * u_hat
365  BwdTrans_SumFacKernel(base0, base1, base2, inarray, wsp0, wsp2,
366  true, true, true);
367  MultiplyByQuadratureMetric(wsp0, wsp1);
368  IProductWRTBase_SumFacKernel(base0, base1, base2, wsp1, outarray,
369  wsp2, true, true, true);
370  LaplacianMatrixOp_MatFree_Kernel(wsp0, wsp1, wsp2);
371  }
372  else
373  {
374  // specialised implementation for the classical spectral
375  // element method
376  MultiplyByQuadratureMetric(inarray, outarray);
377  LaplacianMatrixOp_MatFree_Kernel(inarray, wsp1, wsp2);
378  }
379 
380  // outarray = lambda * outarray + wsp1
381  // = (lambda * M + L ) * u_hat
382  Vmath::Svtvp(m_ncoeffs, lambda, &outarray[0], 1, &wsp1[0], 1,
383  &outarray[0], 1);
384  }
385  else
386  {
387  StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(inarray, outarray,
388  mkey);
389  }
390 }
Nektar::StdRegions::StdExpansion3D::BwdTrans_SumFacKernel
void BwdTrans_SumFacKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)
Definition: StdExpansion3D.cpp:109
Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric
void MultiplyByQuadratureMetric(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Definition: StdExpansion.h:731
Nektar::StdRegions::StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl
void HelmholtzMatrixOp_MatFree_GenericImpl(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
Definition: StdExpansion.cpp:927
Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_Kernel
void LaplacianMatrixOp_MatFree_Kernel(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)
Definition: StdExpansion.h:1224
Vmath::Svtvp
void Svtvp(int n, const T alpha, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
svtvp (scalar times vector plus vector): z = alpha*x + y
Definition: Vmath.cpp:622

References BwdTrans_SumFacKernel(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::eFactorCoeffD00, Nektar::StdRegions::eFactorLambda, 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::StdHexExp::v_HelmholtzMatrixOp(), Nektar::LocalRegions::HexExp::v_HelmholtzMatrixOp(), Nektar::LocalRegions::PrismExp::v_HelmholtzMatrixOp(), and Nektar::LocalRegions::TetExp::v_HelmholtzMatrixOp().

◆ v_Integral()

NekDouble Nektar::StdRegions::StdExpansion3D::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::TetExp, Nektar::LocalRegions::PyrExp, Nektar::LocalRegions::PrismExp, and Nektar::LocalRegions::HexExp.

Definition at line 392 of file StdExpansion3D.cpp.

394 {
395  const int nqtot = GetTotPoints();
396  Array<OneD, NekDouble> tmp(GetTotPoints());
397  v_MultiplyByStdQuadratureMetric(inarray, tmp);
398  return Vmath::Vsum(nqtot, tmp, 1);
399 }
Nektar::StdRegions::StdExpansion::GetTotPoints
int GetTotPoints() const
This function returns the total number of quadrature points used in the element.
Definition: StdExpansion.h:140
Nektar::StdRegions::StdExpansion::v_MultiplyByStdQuadratureMetric
virtual void v_MultiplyByStdQuadratureMetric(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Definition: StdExpansion.cpp:1428
Vmath::Vsum
T Vsum(int n, const T *x, const int incx)
Subtract return sum(x)
Definition: Vmath.cpp:895

References Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::v_MultiplyByStdQuadratureMetric(), and Vmath::Vsum().

◆ v_IProductWRTBase_SumFacKernel()

virtual void Nektar::StdRegions::StdExpansion3D::v_IProductWRTBase_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  base2,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0,
bool  doCheckCollDir1,
bool  doCheckCollDir2 
)
protectedpure virtual

Implemented in Nektar::StdRegions::StdTetExp, Nektar::StdRegions::StdPyrExp, Nektar::StdRegions::StdPrismExp, and Nektar::StdRegions::StdHexExp.

Referenced by IProductWRTBase_SumFacKernel().

◆ v_LaplacianMatrixOp_MatFree()

void Nektar::StdRegions::StdExpansion3D::v_LaplacianMatrixOp_MatFree ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const StdRegions::StdMatrixKey &  mkey 
)
protectedvirtual
Parameters
inarrayInput coefficients.
outputOutput coefficients.
mkeyMatrix key

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 286 of file StdExpansion3D.cpp.

289 {
290  if (mkey.GetNVarCoeff() == 0 &&
291  !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00) &&
292  !mkey.ConstFactorExists(eFactorSVVCutoffRatio))
293  {
294  // This implementation is only valid when there are no
295  // coefficients associated to the Laplacian operator
296  int nqtot = GetTotPoints();
297 
298  const Array<OneD, const NekDouble> &base0 = m_base[0]->GetBdata();
299  const Array<OneD, const NekDouble> &base1 = m_base[1]->GetBdata();
300  const Array<OneD, const NekDouble> &base2 = m_base[2]->GetBdata();
301 
302  // Allocate temporary storage
303  Array<OneD, NekDouble> wsp0(7 * nqtot);
304  Array<OneD, NekDouble> wsp1(wsp0 + nqtot);
305 
306  if (!(m_base[0]->Collocation() && m_base[1]->Collocation() &&
307  m_base[2]->Collocation()))
308  {
309  // LAPLACIAN MATRIX OPERATION
310  // wsp0 = u = B * u_hat
311  // wsp1 = du_dxi1 = D_xi1 * wsp0 = D_xi1 * u
312  // wsp2 = du_dxi2 = D_xi2 * wsp0 = D_xi2 * u
313  BwdTrans_SumFacKernel(base0, base1, base2, inarray, wsp0, wsp1,
314  true, true, true);
315  LaplacianMatrixOp_MatFree_Kernel(wsp0, outarray, wsp1);
316  }
317  else
318  {
319  LaplacianMatrixOp_MatFree_Kernel(inarray, outarray, wsp1);
320  }
321  }
322  else
323  {
324  StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(inarray, outarray,
325  mkey);
326  }
327 }
Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl
void LaplacianMatrixOp_MatFree_GenericImpl(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
Definition: StdExpansion.cpp:773

References BwdTrans_SumFacKernel(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::eFactorCoeffD00, Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::StdMatrixKey::GetNVarCoeff(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_Kernel(), and Nektar::StdRegions::StdExpansion::m_base.

Referenced by Nektar::StdRegions::StdHexExp::v_LaplacianMatrixOp(), Nektar::LocalRegions::HexExp::v_LaplacianMatrixOp(), and Nektar::LocalRegions::TetExp::v_LaplacianMatrixOp().

◆ v_PhysEvaluate() [1/2]

NekDouble Nektar::StdRegions::StdExpansion3D::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.

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 #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::TetExp, Nektar::LocalRegions::HexExp, Nektar::LocalRegions::PyrExp, and Nektar::LocalRegions::PrismExp.

Definition at line 208 of file StdExpansion3D.cpp.

211 {
212  Array<OneD, NekDouble> eta(3);
213 
214  WARNINGL2(coords[0] >= -1 - NekConstants::kNekZeroTol, "coord[0] < -1");
215  WARNINGL2(coords[0] <= 1 + NekConstants::kNekZeroTol, "coord[0] > 1");
216  WARNINGL2(coords[1] >= -1 - NekConstants::kNekZeroTol, "coord[1] < -1");
217  WARNINGL2(coords[1] <= 1 + NekConstants::kNekZeroTol, "coord[1] > 1");
218  WARNINGL2(coords[2] >= -1 - NekConstants::kNekZeroTol, "coord[2] < -1");
219  WARNINGL2(coords[2] <= 1 + NekConstants::kNekZeroTol, "coord[2] > 1");
220 
221  // Obtain local collapsed corodinate from Cartesian coordinate.
222  LocCoordToLocCollapsed(coords, eta);
223 
224  const int nq0 = m_base[0]->GetNumPoints();
225  const int nq1 = m_base[1]->GetNumPoints();
226  const int nq2 = m_base[2]->GetNumPoints();
227 
228  Array<OneD, NekDouble> wsp1(nq1 * nq2), wsp2(nq2);
229 
230  // Construct the 2D square...
231  const NekDouble *ptr = &physvals[0];
232  for (int i = 0; i < nq1 * nq2; ++i, ptr += nq0)
233  {
234  wsp1[i] = StdExpansion::BaryEvaluate<0>(eta[0], ptr);
235  }
236 
237  for (int i = 0; i < nq2; ++i)
238  {
239  wsp2[i] = StdExpansion::BaryEvaluate<1>(eta[1], &wsp1[i * nq1]);
240  }
241 
242  return StdExpansion::BaryEvaluate<2>(eta[2], &wsp2[0]);
243 }
WARNINGL2
#define WARNINGL2(condition, msg)
Definition: ErrorUtil.hpp:273
Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed
void LocCoordToLocCollapsed(const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
Convert local cartesian coordinate xi into local collapsed coordinates eta.
Definition: StdExpansion.h:974
Nektar::NekConstants::kNekZeroTol
static const NekDouble kNekZeroTol
Definition: NektarUnivConsts.hpp:51

References Nektar::NekConstants::kNekZeroTol, Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), Nektar::StdRegions::StdExpansion::m_base, and WARNINGL2.

Referenced by Nektar::StdRegions::StdNodalPrismExp::GenNBasisTransMatrix(), and Nektar::StdRegions::StdNodalTetExp::GenNBasisTransMatrix().

◆ v_PhysEvaluate() [2/2]

NekDouble Nektar::StdRegions::StdExpansion3D::v_PhysEvaluate ( const Array< OneD, DNekMatSharedPtr > &  I,
const Array< OneD, const NekDouble > &  physvals 
)
protectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 245 of file StdExpansion3D.cpp.

248 {
249  NekDouble value;
250 
251  int Qx = m_base[0]->GetNumPoints();
252  int Qy = m_base[1]->GetNumPoints();
253  int Qz = m_base[2]->GetNumPoints();
254 
255  Array<OneD, NekDouble> sumFactorization_qr =
256  Array<OneD, NekDouble>(Qy * Qz);
257  Array<OneD, NekDouble> sumFactorization_r = Array<OneD, NekDouble>(Qz);
258 
259  // Lagrangian interpolation matrix
260  NekDouble *interpolatingNodes = 0;
261 
262  // Interpolate first coordinate direction
263  interpolatingNodes = &I[0]->GetPtr()[0];
264 
265  Blas::Dgemv('T', Qx, Qy * Qz, 1.0, &physvals[0], Qx, &interpolatingNodes[0],
266  1, 0.0, &sumFactorization_qr[0], 1);
267 
268  // Interpolate in second coordinate direction
269  interpolatingNodes = &I[1]->GetPtr()[0];
270 
271  Blas::Dgemv('T', Qy, Qz, 1.0, &sumFactorization_qr[0], Qy,
272  &interpolatingNodes[0], 1, 0.0, &sumFactorization_r[0], 1);
273 
274  // Interpolate in third coordinate direction
275  interpolatingNodes = &I[2]->GetPtr()[0];
276  value = Blas::Ddot(Qz, interpolatingNodes, 1, &sumFactorization_r[0], 1);
277 
278  return value;
279 }
Blas::Dgemv
static void Dgemv(const char &trans, const int &m, const int &n, const double &alpha, const double *a, const int &lda, const double *x, const int &incx, const double &beta, double *y, const int &incy)
BLAS level 2: Matrix vector multiply y = A x where A[m x n].
Definition: Blas.hpp:246
Blas::Ddot
static double Ddot(const int &n, const double *x, const int &incx, const double *y, const int &incy)
BLAS level 1: output = .
Definition: Blas.hpp:182

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

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