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Nektar::StdRegions::StdExpansion2D Class Referenceabstract

#include <StdExpansion2D.h>

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

 StdExpansion2D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb)
 
 StdExpansion2D ()=default
 
 StdExpansion2D (const StdExpansion2D &T)=default
 
 ~StdExpansion2D () override=default
 
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. More...
 
NekDouble Integral (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &w0, const Array< OneD, const NekDouble > &w1)
 
NekDouble BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
 
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. 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 () const
 
std::shared_ptr< StdExpansion > GetLinStdExp (void) const
 
int GetShapeDimension () const
 
bool IsBoundaryInteriorExpansion () const
 
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 LinearAdvectionMatrixOp (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, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
 This function evaluates the first derivative of the expansion at a single (arbitrary) point of the domain. More...
 
NekDouble PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)
 
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

NekDouble v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals) override
 This function evaluates the expansion at a single (arbitrary) point of the domain. More...
 
NekDouble v_PhysEvaluate (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals) override
 
NekDouble v_PhysEvaluate (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override
 
virtual void v_BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0
 
virtual void v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0
 
void v_LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
 
void v_HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override
 
void v_GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray) override
 
void v_GetElmtTraceToTraceMap (const unsigned int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient, int P, int Q) override
 Determine the mapping to re-orientate the coefficients along the element trace (assumed to align with the standard element) into the orientation of the local trace given by edgeOrient. More...
 
void v_GetTraceToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient=eForwards, int P=-1, int Q=-1) override
 
void v_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat) override
 
- 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_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 LinearAdvectionMatrixOp_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_GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
 
virtual void v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv, NekDouble &deriv2)
 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)
 
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble BaryEvaluate (const NekDouble &coord, const NekDouble *physvals)
 Helper function to pass an unused value by reference into BaryEvaluate. More...
 
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv)
 

Private Member Functions

int v_GetShapeDimension () const final
 

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 44 of file StdExpansion2D.h.

Constructor & Destructor Documentation

◆ StdExpansion2D() [1/3]

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

Definition at line 46 of file StdExpansion2D.cpp.

50{
51}

◆ StdExpansion2D() [2/3]

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

◆ StdExpansion2D() [3/3]

Nektar::StdRegions::StdExpansion2D::StdExpansion2D ( const StdExpansion2D &  T)
default

◆ ~StdExpansion2D()

Nektar::StdRegions::StdExpansion2D::~StdExpansion2D ( )
overridedefault

Member Function Documentation

◆ BaryTensorDeriv()

NekDouble Nektar::StdRegions::StdExpansion2D::BaryTensorDeriv ( const Array< OneD, NekDouble > &  coord,
const Array< OneD, const NekDouble > &  inarray,
std::array< NekDouble, 3 > &  firstOrderDerivs 
)
inline

Definition at line 99 of file StdExpansion2D.h.

103 {
104 const int nq0 = m_base[0]->GetNumPoints();
105 const int nq1 = m_base[1]->GetNumPoints();
106
107 const NekDouble *ptr = &inarray[0];
108 Array<OneD, NekDouble> deriv0(nq1, 0.0);
109 Array<OneD, NekDouble> phys0(nq1, 0.0);
110
111 for (int j = 0; j < nq1; ++j, ptr += nq0)
112 {
113 phys0[j] =
114 StdExpansion::BaryEvaluate<0, true>(coord[0], ptr, deriv0[j]);
115 }
116 firstOrderDerivs[0] =
117 StdExpansion::BaryEvaluate<1, false>(coord[1], &deriv0[0]);
118
119 return StdExpansion::BaryEvaluate<1, true>(coord[1], &phys0[0],
120 firstOrderDerivs[1]);
121 }
Nektar::StdRegions::StdExpansion::m_base
Array< OneD, LibUtilities::BasisSharedPtr > m_base
Definition: StdExpansion.h:1173
Nektar::NekDouble
double NekDouble
Definition: NektarUnivTypeDefs.hpp:43

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

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

◆ BwdTrans_SumFacKernel()

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

Definition at line 188 of file StdExpansion2D.cpp.

194{
195 v_BwdTrans_SumFacKernel(base0, base1, inarray, outarray, wsp,
196 doCheckCollDir0, doCheckCollDir1);
197}
Nektar::StdRegions::StdExpansion2D::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 > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0

References v_BwdTrans_SumFacKernel().

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

◆ Integral()

NekDouble Nektar::StdRegions::StdExpansion2D::Integral ( const Array< OneD, const NekDouble > &  inarray,
const Array< OneD, const NekDouble > &  w0,
const Array< OneD, const NekDouble > &  w1 
)

Definition at line 161 of file StdExpansion2D.cpp.

164{
165 int i;
166 NekDouble Int = 0.0;
167 int nquad0 = m_base[0]->GetNumPoints();
168 int nquad1 = m_base[1]->GetNumPoints();
169 Array<OneD, NekDouble> tmp(nquad0 * nquad1);
170
171 // multiply by integration constants
172 for (i = 0; i < nquad1; ++i)
173 {
174 Vmath::Vmul(nquad0, &inarray[0] + i * nquad0, 1, w0.get(), 1,
175 &tmp[0] + i * nquad0, 1);
176 }
177
178 for (i = 0; i < nquad0; ++i)
179 {
180 Vmath::Vmul(nquad1, &tmp[0] + i, nquad0, w1.get(), 1, &tmp[0] + i,
181 nquad0);
182 }
183 Int = Vmath::Vsum(nquad0 * nquad1, tmp, 1);
184
185 return Int;
186}
Vmath::Vmul
void Vmul(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Multiply vector z = x*y.
Definition: Vmath.hpp:72
Vmath::Vsum
T Vsum(int n, const T *x, const int incx)
Subtract return sum(x)
Definition: Vmath.hpp:608

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

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

◆ IProductWRTBase_SumFacKernel()

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

Definition at line 199 of file StdExpansion2D.cpp.

205{
206 v_IProductWRTBase_SumFacKernel(base0, base1, inarray, outarray, wsp,
207 doCheckCollDir0, doCheckCollDir1);
208}
Nektar::StdRegions::StdExpansion2D::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 > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1)=0

References v_IProductWRTBase_SumFacKernel().

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

◆ PhysTensorDeriv()

void Nektar::StdRegions::StdExpansion2D::PhysTensorDeriv ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray_d0,
Array< OneD, NekDouble > &  outarray_d1 
)

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

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

  • \( \frac{d}{d\eta_1} \rightarrow {\bf D^T_0 u } \)
  • \( \frac{d}{d\eta_2} \rightarrow {\bf D_1 u } \)
Parameters
inarrayarray of physical points to be differentiated
outarray_d0the resulting array of derivative in the \(\eta_1\) direction will be stored in outarray_d0 as output of the function
outarray_d1the resulting array of derivative in the \(\eta_2\) direction will be stored in outarray_d1 as output of the function

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

Definition at line 56 of file StdExpansion2D.cpp.

59{
60 int nquad0 = m_base[0]->GetNumPoints();
61 int nquad1 = m_base[1]->GetNumPoints();
62
63 if (outarray_d0.size() > 0) // calculate du/dx_0
64 {
65 DNekMatSharedPtr D0 = m_base[0]->GetD();
66 if (inarray.data() == outarray_d0.data())
67 {
68 Array<OneD, NekDouble> wsp(nquad0 * nquad1);
69 Vmath::Vcopy(nquad0 * nquad1, inarray.get(), 1, wsp.get(), 1);
70 Blas::Dgemm('N', 'N', nquad0, nquad1, nquad0, 1.0,
71 &(D0->GetPtr())[0], nquad0, &wsp[0], nquad0, 0.0,
72 &outarray_d0[0], nquad0);
73 }
74 else
75 {
76 Blas::Dgemm('N', 'N', nquad0, nquad1, nquad0, 1.0,
77 &(D0->GetPtr())[0], nquad0, &inarray[0], nquad0, 0.0,
78 &outarray_d0[0], nquad0);
79 }
80 }
81
82 if (outarray_d1.size() > 0) // calculate du/dx_1
83 {
84 DNekMatSharedPtr D1 = m_base[1]->GetD();
85 if (inarray.data() == outarray_d1.data())
86 {
87 Array<OneD, NekDouble> wsp(nquad0 * nquad1);
88 Vmath::Vcopy(nquad0 * nquad1, inarray.get(), 1, wsp.get(), 1);
89 Blas::Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0, &wsp[0], nquad0,
90 &(D1->GetPtr())[0], nquad1, 0.0, &outarray_d1[0],
91 nquad0);
92 }
93 else
94 {
95 Blas::Dgemm('N', 'T', nquad0, nquad1, nquad1, 1.0, &inarray[0],
96 nquad0, &(D1->GetPtr())[0], nquad1, 0.0,
97 &outarray_d1[0], nquad0);
98 }
99 }
100}
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:383
Nektar::DNekMatSharedPtr
std::shared_ptr< DNekMat > DNekMatSharedPtr
Definition: NekTypeDefs.hpp:75
Vmath::Vcopy
void Vcopy(int n, const T *x, const int incx, T *y, const int incy)
Definition: Vmath.hpp:825

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

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

◆ v_BwdTrans_SumFacKernel()

virtual void Nektar::StdRegions::StdExpansion2D::v_BwdTrans_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0,
bool  doCheckCollDir1 
)
protectedpure virtual

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

Referenced by BwdTrans_SumFacKernel().

◆ v_GenStdMatBwdDeriv()

void Nektar::StdRegions::StdExpansion2D::v_GenStdMatBwdDeriv ( const int  dir,
DNekMatSharedPtr &  mat 
)
overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 210 of file StdExpansion2D.cpp.

211{
212 ASSERTL1((dir == 0) || (dir == 1), "Invalid direction.");
213
214 int nquad0 = m_base[0]->GetNumPoints();
215 int nquad1 = m_base[1]->GetNumPoints();
216 int nqtot = nquad0 * nquad1;
217 int nmodes0 = m_base[0]->GetNumModes();
218
219 Array<OneD, NekDouble> tmp1(2 * nqtot + m_ncoeffs + nmodes0 * nquad1, 0.0);
220 Array<OneD, NekDouble> tmp3(tmp1 + 2 * nqtot);
221 Array<OneD, NekDouble> tmp4(tmp1 + 2 * nqtot + m_ncoeffs);
222
223 switch (dir)
224 {
225 case 0:
226 for (int i = 0; i < nqtot; i++)
227 {
228 tmp1[i] = 1.0;
229 IProductWRTBase_SumFacKernel(m_base[0]->GetDbdata(),
230 m_base[1]->GetBdata(), tmp1, tmp3,
231 tmp4, false, true);
232 tmp1[i] = 0.0;
233
234 for (int j = 0; j < m_ncoeffs; j++)
235 {
236 (*mat)(j, i) = tmp3[j];
237 }
238 }
239 break;
240 case 1:
241 for (int i = 0; i < nqtot; i++)
242 {
243 tmp1[i] = 1.0;
244 IProductWRTBase_SumFacKernel(m_base[0]->GetBdata(),
245 m_base[1]->GetDbdata(), tmp1, tmp3,
246 tmp4, true, false);
247 tmp1[i] = 0.0;
248
249 for (int j = 0; j < m_ncoeffs; j++)
250 {
251 (*mat)(j, i) = tmp3[j];
252 }
253 }
254 break;
255 default:
256 NEKERROR(ErrorUtil::efatal, "Not a 2D expansion.");
257 break;
258 }
259}
NEKERROR
#define NEKERROR(type, msg)
Assert Level 0 – Fundamental assert which is used whether in FULLDEBUG, DEBUG or OPT compilation mode...
Definition: ErrorUtil.hpp:202
ASSERTL1
#define ASSERTL1(condition, msg)
Assert Level 1 – Debugging which is used whether in FULLDEBUG or DEBUG compilation mode....
Definition: ErrorUtil.hpp:242
Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel
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)
Definition: StdExpansion2D.cpp:199

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

◆ v_GetElmtTraceToTraceMap()

void Nektar::StdRegions::StdExpansion2D::v_GetElmtTraceToTraceMap ( const unsigned int  eid,
Array< OneD, unsigned int > &  maparray,
Array< OneD, int > &  signarray,
Orientation  edgeOrient,
int  P,
int  Q 
)
overrideprotectedvirtual

Determine the mapping to re-orientate the coefficients along the element trace (assumed to align with the standard element) into the orientation of the local trace given by edgeOrient.

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 383 of file StdExpansion2D.cpp.

387{
388 unsigned int i;
389
390 int dir;
391 // determine basis direction for edge.
392 if (DetShapeType() == LibUtilities::eTriangle)
393 {
394 dir = (eid == 0) ? 0 : 1;
395 }
396 else
397 {
398 dir = eid % 2;
399 }
400
401 int numModes = m_base[dir]->GetNumModes();
402
403 // P is the desired length of the map
404 P = (P == -1) ? numModes : P;
405
406 // decalare maparray
407 if (maparray.size() != P)
408 {
409 maparray = Array<OneD, unsigned int>(P);
410 }
411
412 // fill default mapping as increasing index
413 for (i = 0; i < P; ++i)
414 {
415 maparray[i] = i;
416 }
417
418 if (signarray.size() != P)
419 {
420 signarray = Array<OneD, int>(P, 1);
421 }
422 else
423 {
424 std::fill(signarray.get(), signarray.get() + P, 1);
425 }
426
427 // Zero signmap and set maparray to zero if
428 // elemental modes are not as large as trace modes
429 for (i = numModes; i < P; ++i)
430 {
431 signarray[i] = 0.0;
432 maparray[i] = maparray[0];
433 }
434
435 if (edgeOrient == eBackwards)
436 {
437 const LibUtilities::BasisType bType = GetBasisType(dir);
438
439 if ((bType == LibUtilities::eModified_A) ||
440 (bType == LibUtilities::eModified_B))
441 {
442 std::swap(maparray[0], maparray[1]);
443
444 for (i = 3; i < std::min(P, numModes); i += 2)
445 {
446 signarray[i] *= -1;
447 }
448 }
449 else if (bType == LibUtilities::eGLL_Lagrange ||
450 bType == LibUtilities::eGauss_Lagrange)
451 {
452 ASSERTL1(P == numModes, "Different trace space edge dimension "
453 "and element edge dimension not currently "
454 "possible for GLL-Lagrange bases");
455
456 std::reverse(maparray.get(), maparray.get() + P);
457 }
458 else
459 {
460 ASSERTL0(false, "Mapping not defined for this type of basis");
461 }
462 }
463}
ASSERTL0
#define ASSERTL0(condition, msg)
Definition: ErrorUtil.hpp:208
Nektar::StdRegions::StdExpansion::GetBasisType
LibUtilities::BasisType GetBasisType(const int dir) const
This function returns the type of basis used in the dir direction.
Definition: StdExpansion.h:156
Nektar::StdRegions::StdExpansion::DetShapeType
LibUtilities::ShapeType DetShapeType() const
This function returns the shape of the expansion domain.
Definition: StdExpansion.h:367
Nektar::LibUtilities::eModified_B
@ eModified_B
Principle Modified Functions .
Definition: BasisType.h:49
Nektar::LibUtilities::P
@ P
Monomial polynomials .
Definition: BasisType.h:62
Nektar::LibUtilities::eGauss_Lagrange
@ eGauss_Lagrange
Lagrange Polynomials using the Gauss points.
Definition: BasisType.h:57
Nektar::LibUtilities::eGLL_Lagrange
@ eGLL_Lagrange
Lagrange for SEM basis .
Definition: BasisType.h:56
Nektar::LibUtilities::eModified_A
@ eModified_A
Principle Modified Functions .
Definition: BasisType.h:48

References ASSERTL0, ASSERTL1, Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eBackwards, Nektar::LibUtilities::eGauss_Lagrange, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eTriangle, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::P.

Referenced by v_GetTraceToElementMap().

◆ v_GetShapeDimension()

int Nektar::StdRegions::StdExpansion2D::v_GetShapeDimension ( ) const
inlinefinalprivatevirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 214 of file StdExpansion2D.h.

215 {
216 return 2;
217 }

◆ v_GetTraceCoeffMap()

void Nektar::StdRegions::StdExpansion2D::v_GetTraceCoeffMap ( const unsigned int  traceid,
Array< OneD, unsigned int > &  maparray 
)
overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

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

Definition at line 370 of file StdExpansion2D.cpp.

373{
374 ASSERTL0(false,
375 "This method must be defined at the individual shape level");
376}

References ASSERTL0.

Referenced by v_GetTraceToElementMap().

◆ v_GetTraceToElementMap()

void Nektar::StdRegions::StdExpansion2D::v_GetTraceToElementMap ( const int  eid,
Array< OneD, unsigned int > &  maparray,
Array< OneD, int > &  signarray,
Orientation  edgeOrient = eForwards,
int  P = -1,
int  Q = -1 
)
overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 465 of file StdExpansion2D.cpp.

470{
471 Array<OneD, unsigned int> map1, map2;
472 v_GetTraceCoeffMap(eid, map1);
473 v_GetElmtTraceToTraceMap(eid, map2, signarray, edgeOrient, P, Q);
474
475 if (maparray.size() != map2.size())
476 {
477 maparray = Array<OneD, unsigned int>(map2.size());
478 }
479
480 for (int i = 0; i < map2.size(); ++i)
481 {
482 maparray[i] = map1[map2[i]];
483 }
484}
Nektar::StdRegions::StdExpansion2D::v_GetTraceCoeffMap
void v_GetTraceCoeffMap(const unsigned int traceid, Array< OneD, unsigned int > &maparray) override
Definition: StdExpansion2D.cpp:370
Nektar::StdRegions::StdExpansion2D::v_GetElmtTraceToTraceMap
void v_GetElmtTraceToTraceMap(const unsigned int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation edgeOrient, int P, int Q) override
Determine the mapping to re-orientate the coefficients along the element trace (assumed to align with...
Definition: StdExpansion2D.cpp:383

References Nektar::LibUtilities::P, v_GetElmtTraceToTraceMap(), and v_GetTraceCoeffMap().

◆ v_HelmholtzMatrixOp_MatFree()

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

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 310 of file StdExpansion2D.cpp.

313{
314 if (mkey.GetNVarCoeff() == 0 &&
315 !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00) &&
316 !mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
317 {
318 using std::max;
319
320 int nquad0 = m_base[0]->GetNumPoints();
321 int nquad1 = m_base[1]->GetNumPoints();
322 int nqtot = nquad0 * nquad1;
323 int nmodes0 = m_base[0]->GetNumModes();
324 int nmodes1 = m_base[1]->GetNumModes();
325 int wspsize =
326 max(max(max(nqtot, m_ncoeffs), nquad1 * nmodes0), nquad0 * nmodes1);
327 NekDouble lambda = mkey.GetConstFactor(StdRegions::eFactorLambda);
328
329 const Array<OneD, const NekDouble> &base0 = m_base[0]->GetBdata();
330 const Array<OneD, const NekDouble> &base1 = m_base[1]->GetBdata();
331
332 // Allocate temporary storage
333 Array<OneD, NekDouble> wsp0(5 * wspsize); // size wspsize
334 Array<OneD, NekDouble> wsp1(wsp0 + wspsize); // size wspsize
335 Array<OneD, NekDouble> wsp2(wsp0 + 2 * wspsize); // size 3*wspsize
336
337 if (!(m_base[0]->Collocation() && m_base[1]->Collocation()))
338 {
339 // MASS MATRIX OPERATION
340 // The following is being calculated:
341 // wsp0 = B * u_hat = u
342 // wsp1 = W * wsp0
343 // outarray = B^T * wsp1 = B^T * W * B * u_hat = M * u_hat
344 BwdTrans_SumFacKernel(base0, base1, inarray, wsp0, wsp2, true,
345 true);
346 MultiplyByQuadratureMetric(wsp0, wsp1);
347 IProductWRTBase_SumFacKernel(base0, base1, wsp1, outarray, wsp2,
348 true, true);
349
350 LaplacianMatrixOp_MatFree_Kernel(wsp0, wsp1, wsp2);
351 }
352 else
353 {
354 MultiplyByQuadratureMetric(inarray, outarray);
355 LaplacianMatrixOp_MatFree_Kernel(inarray, wsp1, wsp2);
356 }
357
358 // outarray = lambda * outarray + wsp1
359 // = (lambda * M + L ) * u_hat
360 Vmath::Svtvp(m_ncoeffs, lambda, &outarray[0], 1, &wsp1[0], 1,
361 &outarray[0], 1);
362 }
363 else
364 {
365 StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(inarray, outarray,
366 mkey);
367 }
368}
Nektar::StdRegions::StdExpansion2D::BwdTrans_SumFacKernel
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)
Definition: StdExpansion2D.cpp:188
Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric
void MultiplyByQuadratureMetric(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Definition: StdExpansion.h:723
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:986
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:1248
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.hpp:396

References BwdTrans_SumFacKernel(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::eFactorCoeffD00, Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdMatrixKey::GetNVarCoeff(), Nektar::StdRegions::StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(), IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_Kernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), and Vmath::Svtvp().

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

◆ v_IProductWRTBase_SumFacKernel()

virtual void Nektar::StdRegions::StdExpansion2D::v_IProductWRTBase_SumFacKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
Array< OneD, NekDouble > &  wsp,
bool  doCheckCollDir0,
bool  doCheckCollDir1 
)
protectedpure virtual

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

Referenced by IProductWRTBase_SumFacKernel().

◆ v_LaplacianMatrixOp_MatFree()

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

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 261 of file StdExpansion2D.cpp.

264{
265 if (mkey.GetNVarCoeff() == 0 &&
266 !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00) &&
267 !mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
268 {
269 using std::max;
270
271 // This implementation is only valid when there are no
272 // coefficients associated to the Laplacian operator
273 int nquad0 = m_base[0]->GetNumPoints();
274 int nquad1 = m_base[1]->GetNumPoints();
275 int nqtot = nquad0 * nquad1;
276 int nmodes0 = m_base[0]->GetNumModes();
277 int nmodes1 = m_base[1]->GetNumModes();
278 int wspsize =
279 max(max(max(nqtot, m_ncoeffs), nquad1 * nmodes0), nquad0 * nmodes1);
280
281 const Array<OneD, const NekDouble> &base0 = m_base[0]->GetBdata();
282 const Array<OneD, const NekDouble> &base1 = m_base[1]->GetBdata();
283
284 // Allocate temporary storage
285 Array<OneD, NekDouble> wsp0(4 * wspsize); // size wspsize
286 Array<OneD, NekDouble> wsp1(wsp0 + wspsize); // size 3*wspsize
287
288 if (!(m_base[0]->Collocation() && m_base[1]->Collocation()))
289 {
290 // LAPLACIAN MATRIX OPERATION
291 // wsp0 = u = B * u_hat
292 // wsp1 = du_dxi1 = D_xi1 * wsp0 = D_xi1 * u
293 // wsp2 = du_dxi2 = D_xi2 * wsp0 = D_xi2 * u
294 BwdTrans_SumFacKernel(base0, base1, inarray, wsp0, wsp1, true,
295 true);
296 LaplacianMatrixOp_MatFree_Kernel(wsp0, outarray, wsp1);
297 }
298 else
299 {
300 LaplacianMatrixOp_MatFree_Kernel(inarray, outarray, wsp1);
301 }
302 }
303 else
304 {
305 StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(inarray, outarray,
306 mkey);
307 }
308}
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:780

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

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

◆ v_PhysEvaluate() [1/3]

NekDouble Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate ( const Array< OneD, const NekDouble > &  coords,
const Array< OneD, const NekDouble > &  physvals 
)
overrideprotectedvirtual

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

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

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

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

is evaluated using Lagrangian interpolants through the quadrature points:

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

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

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

Reimplemented from Nektar::StdRegions::StdExpansion.

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

Definition at line 102 of file StdExpansion2D.cpp.

105{
106 ASSERTL2(coords[0] > -1 - NekConstants::kNekZeroTol, "coord[0] < -1");
107 ASSERTL2(coords[0] < 1 + NekConstants::kNekZeroTol, "coord[0] > 1");
108 ASSERTL2(coords[1] > -1 - NekConstants::kNekZeroTol, "coord[1] < -1");
109 ASSERTL2(coords[1] < 1 + NekConstants::kNekZeroTol, "coord[1] > 1");
110
111 Array<OneD, NekDouble> coll(2);
112 LocCoordToLocCollapsed(coords, coll);
113
114 const int nq0 = m_base[0]->GetNumPoints();
115 const int nq1 = m_base[1]->GetNumPoints();
116
117 Array<OneD, NekDouble> wsp(nq1);
118 for (int i = 0; i < nq1; ++i)
119 {
120 wsp[i] = StdExpansion::BaryEvaluate<0>(coll[0], &physvals[0] + i * nq0);
121 }
122
123 return StdExpansion::BaryEvaluate<1>(coll[1], &wsp[0]);
124}
ASSERTL2
#define ASSERTL2(condition, msg)
Assert Level 2 – Debugging which is used FULLDEBUG compilation mode. This level assert is designed to...
Definition: ErrorUtil.hpp:265
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:1002
Nektar::NekConstants::kNekZeroTol
static const NekDouble kNekZeroTol
Definition: NektarUnivConsts.hpp:49

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

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

◆ v_PhysEvaluate() [2/3]

NekDouble Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate ( const Array< OneD, DNekMatSharedPtr > &  I,
const Array< OneD, const NekDouble > &  physvals 
)
overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 126 of file StdExpansion2D.cpp.

129{
130 NekDouble val;
131 int i;
132 int nq0 = m_base[0]->GetNumPoints();
133 int nq1 = m_base[1]->GetNumPoints();
134 Array<OneD, NekDouble> wsp1(nq1);
135
136 // interpolate first coordinate direction
137 for (i = 0; i < nq1; ++i)
138 {
139 wsp1[i] =
140 Blas::Ddot(nq0, &(I[0]->GetPtr())[0], 1, &physvals[i * nq0], 1);
141 }
142
143 // interpolate in second coordinate direction
144 val = Blas::Ddot(nq1, I[1]->GetPtr(), 1, wsp1, 1);
145
146 return val;
147}
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:163

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

◆ v_PhysEvaluate() [3/3]

NekDouble Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate ( const Array< OneD, NekDouble > &  coord,
const Array< OneD, const NekDouble > &  inarray,
std::array< NekDouble, 3 > &  firstOrderDerivs 
)
overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::LocalRegions::NodalTriExp, Nektar::LocalRegions::QuadExp, Nektar::LocalRegions::TriExp, Nektar::StdRegions::StdQuadExp, and Nektar::StdRegions::StdTriExp.

Definition at line 149 of file StdExpansion2D.cpp.

153{
154 return 0;
155}
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