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Public Member Functions | Protected Member Functions | List of all members
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
 
NekDouble BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
 
void IProductWRTBaseKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, NekDouble > &jac, const bool Deformed, bool CollDir0=false, bool CollDir1=false)
 
- Public Member Functions inherited from Nektar::StdRegions::StdExpansion
 StdExpansion ()
 Default Constructor.
 
 StdExpansion (const int numcoeffs, const int numbases, const LibUtilities::BasisKey &Ba=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bb=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bc=LibUtilities::NullBasisKey)
 Constructor.
 
 StdExpansion (const StdExpansion &T)
 Copy Constructor.
 
virtual ~StdExpansion ()
 Destructor.
 
int GetNumBases () const
 This function returns the number of 1D bases used in the expansion.
 
const Array< OneD, const LibUtilities::BasisSharedPtr > & GetBase () const
 This function gets the shared point to basis.
 
const LibUtilities::BasisSharedPtr & GetBasis (int dir) const
 This function gets the shared point to basis in the dir direction.
 
int GetNcoeffs (void) const
 This function returns the total number of coefficients used in the expansion.
 
int GetTotPoints () const
 This function returns the total number of quadrature points used in the element.
 
LibUtilities::BasisType GetBasisType (const int dir) const
 This function returns the type of basis used in the dir direction.
 
int GetBasisNumModes (const int dir) const
 This function returns the number of expansion modes in the dir direction.
 
int EvalBasisNumModesMax (void) const
 This function returns the maximum number of expansion modes over all local directions.
 
LibUtilities::PointsType GetPointsType (const int dir) const
 This function returns the type of quadrature points used in the dir direction.
 
int GetNumPoints (const int dir) const
 This function returns the number of quadrature points in the dir direction.
 
const Array< OneD, const NekDouble > & GetPoints (const int dir) const
 This function returns a pointer to the array containing the quadrature points in dir direction.
 
int GetNverts () const
 This function returns the number of vertices of the expansion domain.
 
int GetTraceNcoeffs (const int i) const
 This function returns the number of expansion coefficients belonging to the i-th trace.
 
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.
 
const LibUtilities::BasisKey GetTraceBasisKey (const int i, int k=-1, bool UseGLL=false) const
 This function returns the basis key belonging to the i-th trace.
 
LibUtilities::PointsKey GetTracePointsKey (const int i, int k=-1) const
 This function returns the basis key belonging to the i-th trace.
 
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.
 
int GetNtraces () const
 Returns the number of trace elements connected to this element.
 
LibUtilities::ShapeType DetShapeType () const
 This function returns the shape of the expansion domain.
 
int GetShapeDimension () const
 
bool IsBoundaryInteriorExpansion () const
 
bool IsNodalNonTensorialExp ()
 
void NodalToModal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
void BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 This function performs the Backward transformation from coefficient space to physical space.
 
void FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
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.
 
void FillMode (const int mode, Array< OneD, NekDouble > &outarray)
 This function fills the array outarray with the mode-th mode of the expansion.
 
void IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 this function calculates the inner product of a given function f with the different modes of the expansion
 
void 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.
 
void SetElmtId (const int id)
 Set the element id of this expansion when used in a list by returning value of m_elmt_id.
 
void GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2=NullNekDouble1DArray, Array< OneD, NekDouble > &coords_3=NullNekDouble1DArray)
 this function returns the physical coordinates of the quadrature points of the expansion
 
Array< OneD, Array< OneD, NekDouble > > GetCoords ()
 
void GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)
 given the coordinates of a point of the element in the local collapsed coordinate system, this function calculates the physical coordinates of the point
 
DNekMatSharedPtr GetStdMatrix (const StdMatrixKey &mkey)
 
DNekBlkMatSharedPtr GetStdStaticCondMatrix (const StdMatrixKey &mkey)
 
Array< OneD, const NekDouble > GetStdFac (const StdFacKey &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 \(\mathbf{M}[i][j] = \int \phi_i(\mathbf{x}) \phi_j(\mathbf{x}) d\mathbf{x}\)
 
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 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)
 
NekDouble PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
 This function evaluates the expansion at a single (arbitrary) point of the domain.
 
NekDouble PhysEvaluate (const Array< OneD, 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.
 
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.
 
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.
 
void ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1, bool Forwards=true)
 
void LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
 Convert local cartesian coordinate xi into local collapsed coordinates eta.
 
void LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)
 Convert local collapsed coordinates eta into local cartesian coordinate xi.
 
void PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData, bool Transpose=false)
 interpolate from one set of quadrature points available from FromExp to the set of quadrature points in the current expansion. If the points are the same this routine will just copy the data
 
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.
 
NekDouble L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
 Function to evaluate the discrete \( L_2\) error, \( | \epsilon |_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol.
 
NekDouble H1 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &sol=NullNekDouble1DArray)
 Function to evaluate the discrete \( H^1\) error, \( | \epsilon |^1_{2} = \left [ \int^1_{-1} [u - u_{exact}]^2 + \nabla(u - u_{exact})\cdot\nabla(u - u_{exact})\cdot dx \right]^{1/2} d\xi_1 \) where \( u_{exact}\) is given by the array sol.
 
const 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.
 
void PhysInterpToGLL (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset=-1)
 
void PhysInterpToPoints (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, int npset, MatrixType distrib)
 
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.
 
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.
 
void EquiSpacedToPhys (const int nequi, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
template<class T >
std::shared_ptr< T > as ()
 
void GenStdMatBwdDeriv (const int dir, DNekMatSharedPtr &mat)
 

Protected Member Functions

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.
 
void v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
 Calculate the derivative of the physical points in a given direction.
 
NekDouble v_StdPhysEvaluate (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.
 
NekDouble v_PhysEvaluateInterp (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals) override
 
void v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
 Calculate the inner product of inarray with respect to the basis B=base0*base1 and put into outarray.
 
virtual void v_IProductWRTBaseKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, NekDouble > &jac, const bool Deformed, bool CollDir0=false, bool CollDir1=false)=0
 
void v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
 
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.
 
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
 
void v_PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData, bool Transpose) override
 
void v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1, bool Forwards) override
 
int v_GetShapeDimension () const final
 
bool v_IsCollocatedBasis () const final
 
virtual void v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2, Array< OneD, NekDouble > &out_d3)
 Calculate the derivative of the physical points.
 
virtual void v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0)
 Calculate the derivative of the physical points in a given direction.
 
- Protected Member Functions inherited from Nektar::StdRegions::StdExpansion
DNekMatSharedPtr CreateStdMatrix (const StdMatrixKey &mkey)
 
std::shared_ptr< Array< OneD, const NekDouble > > CreateStdFac (const StdFacKey &mkey)
 
DNekBlkMatSharedPtr CreateStdStaticCondMatrix (const StdMatrixKey &mkey)
 Create the static condensation of a matrix when using a boundary interior decomposition.
 
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)
 
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.
 
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.
 
template<int DIR, bool DERIV = false, bool DERIV2 = false>
NekDouble BaryEvaluate (const NekDouble &coord, const NekDouble *physvals, NekDouble &deriv)
 
virtual int v_GetNverts () const =0
 
virtual int v_GetNtraces () const =0
 
virtual int v_NumBndryCoeffs () const =0
 
virtual int v_NumDGBndryCoeffs () const =0
 
virtual int v_GetTraceNcoeffs (const int i) const =0
 
virtual int v_GetTraceIntNcoeffs (const int i) const =0
 
virtual int v_GetTraceNumPoints (const int i) const =0
 
virtual const LibUtilities::BasisKey v_GetTraceBasisKey (const int i, const int k, bool UseGLL=false) const
 
virtual LibUtilities::PointsKey v_GetTracePointsKey (const int i, const int j) const
 
virtual const LibUtilities::PointsKey v_GetNodalPointsKey () const
 
virtual LibUtilities::ShapeType v_DetShapeType () const =0
 
virtual bool v_IsBoundaryInteriorExpansion () const
 
virtual bool v_IsNodalNonTensorialExp ()
 
virtual void v_NodalToModal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
virtual void v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)=0
 
virtual void v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 Transform a given function from physical quadrature space to coefficient space.
 
virtual void v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
virtual void v_IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
virtual void v_FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
virtual void v_PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &outarray)
 Physical derivative along a direction vector.
 
virtual void v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2, Array< OneD, NekDouble > &out_d3)
 
virtual NekDouble v_PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &physvals)
 
virtual NekDouble v_PhysEvalFirstDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs)
 
virtual NekDouble v_PhysEvalFirstSecondDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs, std::array< NekDouble, 6 > &secondOrderDerivs)
 
virtual NekDouble v_PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode)
 
virtual void v_LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta)
 
virtual void v_LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi)
 
virtual void v_FillMode (const int mode, Array< OneD, NekDouble > &outarray)
 
virtual DNekMatSharedPtr v_GenMatrix (const StdMatrixKey &mkey)
 
virtual DNekMatSharedPtr v_CreateStdMatrix (const StdMatrixKey &mkey)
 
virtual void v_GetCoords (Array< OneD, NekDouble > &coords_0, Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2)
 
virtual void v_GetCoord (const Array< OneD, const NekDouble > &Lcoord, Array< OneD, NekDouble > &coord)
 
virtual int v_GetCoordim () const
 
virtual void v_GetBoundaryMap (Array< OneD, unsigned int > &outarray)
 
virtual void v_GetInteriorMap (Array< OneD, unsigned int > &outarray)
 
virtual int v_GetVertexMap (int localVertexId, bool useCoeffPacking=false)
 
virtual void v_GetTraceInteriorToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eForwards)
 
virtual void v_GetTraceNumModes (const int fid, int &numModes0, int &numModes1, Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2)
 
virtual void v_GetVertexPhysVals (const int vertex, const Array< OneD, const NekDouble > &inarray, NekDouble &outarray)
 
virtual void v_MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
virtual void v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
 
virtual void v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
 
virtual void v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey)
 
virtual void v_ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff)
 
virtual void v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 
virtual void v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
 
virtual void v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
 
virtual void v_WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
 
virtual void v_MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
 
virtual void v_LinearAdvectionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
 
virtual void v_LinearAdvectionDiffusionReactionMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true)
 
virtual void v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
 
virtual void v_LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp)
 
virtual DNekMatSharedPtr v_BuildInverseTransformationMatrix (const DNekScalMatSharedPtr &m_transformationmatrix)
 
virtual void v_GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true)
 

Additional Inherited Members

- Protected Attributes inherited from Nektar::StdRegions::StdExpansion
Array< OneD, LibUtilities::BasisSharedPtr > m_base
 
int m_elmt_id
 
int m_ncoeffs
 
std::vector< Array< OneD, const NekDouble > > m_weights
 
LibUtilities::NekManager< StdMatrixKey, DNekMat, StdMatrixKey::opLess > m_stdMatrixManager
 
LibUtilities::NekManager< StdMatrixKey, DNekBlkMat, StdMatrixKey::opLess > m_stdStaticCondMatrixManager
 
LibUtilities::NekManager< StdFacKey, Array< OneD, const NekDouble > > m_stdFacManager
 

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 54 of file StdExpansion2D.cpp.

58{
59}

◆ 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 56 of file StdExpansion2D.h.

60 {
61 const int nq0 = m_base[0]->GetNumPoints();
62 const int nq1 = m_base[1]->GetNumPoints();
63
64 const NekDouble *ptr = &inarray[0];
65 Array<OneD, NekDouble> deriv0(nq1, 0.0);
66 Array<OneD, NekDouble> phys0(nq1, 0.0);
67
68 for (int j = 0; j < nq1; ++j, ptr += nq0)
69 {
70 phys0[j] =
71 StdExpansion::BaryEvaluate<0, true>(coord[0], ptr, deriv0[j]);
72 }
73 firstOrderDerivs[0] =
74 StdExpansion::BaryEvaluate<1, false>(coord[1], &deriv0[0]);
75
76 return StdExpansion::BaryEvaluate<1, true>(coord[1], &phys0[0],
77 firstOrderDerivs[1]);
78 }
Nektar::StdRegions::StdExpansion::m_base
Array< OneD, LibUtilities::BasisSharedPtr > m_base
Definition StdExpansion.h:1268

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

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

◆ IProductWRTBaseKernel()

void Nektar::StdRegions::StdExpansion2D::IProductWRTBaseKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const Array< OneD, NekDouble > &  jac,
const bool  Deformed,
bool  CollDir0 = false,
bool  CollDir1 = false 
)

Definition at line 253 of file StdExpansion2D.cpp.

259{
260 v_IProductWRTBaseKernel(base0, base1, inarray, outarray, jac, Deformed,
261 CollDir0, CollDir1);
262}
Nektar::StdRegions::StdExpansion2D::v_IProductWRTBaseKernel
virtual void v_IProductWRTBaseKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, NekDouble > &jac, const bool Deformed, bool CollDir0=false, bool CollDir1=false)=0

References v_IProductWRTBaseKernel().

◆ PhysTensorDeriv()

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

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

Calculate the derivative along the tenosr directions. This function was originally in StdEpxansion2D but due to the boost_pp switch statement is currently shape dependent

Definition at line 69 of file StdExpansion2D.cpp.

72{
73 int nquad0 = m_base[0]->GetNumPoints();
74 int nquad1 = m_base[1]->GetNumPoints();
75 bool Deriv0 = (outarray_d0.size() > 0);
76 bool Deriv1 = (outarray_d1.size() > 0);
77 const NekDouble *D0 = m_base[0]->GetD()->GetRawPtr();
78 const NekDouble *D1 = m_base[1]->GetD()->GetRawPtr();
79
80 Array<OneD, const NekDouble> intmp;
81 // copy inarray data if inarray and outarray are the same.
82 if ((inarray.data() == outarray_d0.data()) ||
83 (inarray.data() == outarray_d1.data()))
84 {
85 Array<OneD, NekDouble> wsp(nquad0 * nquad1);
86 CopyArray(inarray, wsp);
87 intmp = wsp;
88 }
89 else
90 {
91 intmp = inarray;
92 }
93
94 // Switch statment using boost_pp and macros. This unfolls into a
95 // nested switch statement which runs from SMIN to SMAX for quadratrure
96 // order. If you want to see it unwrapped compile in verbose mode and add
97 // --preprocess to the c++ command. Default case
98#undef PHYSDERIV_DEF
99#define PHYSDERIV_DEF \
100 PhysDerivTensor2DKernel(nquad0, nquad1, (const vec_t *)intmp.data(), \
101 (const vec_t *)D0, (const vec_t *)D1, \
102 (vec_t *)outarray_d0.data(), \
103 (vec_t *)outarray_d1.data(), Deriv0, Deriv1)
104
105 // Loop case over quarature points
106#undef PHYSDERIV_Q
107#define PHYSDERIV_Q(r, i) \
108 case NQ1(i): \
109 PhysDerivTensor2DKernel(NQ1(i), NQ1(i), (const vec_t *)intmp.data(), \
110 (const vec_t *)D0, (const vec_t *)D1, \
111 (vec_t *)outarray_d0.data(), \
112 (vec_t *)outarray_d1.data(), Deriv0, Deriv1); \
113 break;
114
115 // templated cases on standard quadrature
116 // usage where quad order goes from SMIN to SMAX
117 if (nquad0 == nquad1)
118 {
119 switch (nquad0)
120 {
121 BOOST_PP_FOR((SMIN, SMAX), STDLEV1TEST, STDLEV1UPDATE, PHYSDERIV_Q);
122 default:
123 PHYSDERIV_DEF;
124 break;
125 }
126 }
127 else
128 {
129 PHYSDERIV_DEF;
130 }
131}
PHYSDERIV_Q
#define PHYSDERIV_Q(r, i)
PHYSDERIV_DEF
#define PHYSDERIV_DEF
STDLEV1UPDATE
#define STDLEV1UPDATE(r, state)
Definition SwitchLevel1.h:59
STDLEV1TEST
#define STDLEV1TEST(r, state)
Definition SwitchLevel1.h:51
Nektar::CopyArray
void CopyArray(const Array< OneD, ConstDataType > &source, Array< OneD, DataType > &dest)
Definition BasicUtils/SharedArray.hpp:903

References Nektar::CopyArray(), Nektar::StdRegions::StdExpansion::m_base, PHYSDERIV_DEF, PHYSDERIV_Q, STDLEV1TEST, and STDLEV1UPDATE.

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

◆ v_GenStdMatBwdDeriv()

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

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 264 of file StdExpansion2D.cpp.

265{
266 ASSERTL1((dir == 0) || (dir == 1), "Invalid direction.");
267
268 const int nq0 = m_base[0]->GetNumPoints();
269 const int nq1 = m_base[1]->GetNumPoints();
270 const int nq = nq0 * nq1;
271
272 Array<OneD, NekDouble> in(nq, 0.0);
273 Array<OneD, NekDouble> out(m_ncoeffs);
274 Array<OneD, NekDouble> one(1, 1.0);
275
276 for (int i = 0; i < nq; i++)
277 {
278 int l = i % nq0;
279 int m = (i / nq0);
280
281 // initialise with inverse of weights t
282 in[i] = 1.0 / (m_weights[0][l] * m_weights[1][m]);
283
284 // do standard iproduct
285 if (dir == 0)
286 {
287 v_IProductWRTBaseKernel(m_base[0]->GetDbdata(),
288 m_base[1]->GetBdata(), in, out, one, false,
289 false, m_base[1]->Collocation());
290 }
291 else if (dir == 1)
292 {
293 v_IProductWRTBaseKernel(m_base[0]->GetBdata(),
294 m_base[1]->GetDbdata(), in, out, one, false,
295 m_base[0]->Collocation(), false);
296 }
297 in[i] = 0.0;
298
299 for (int j = 0; j < m_ncoeffs; j++)
300 {
301 (*mat)(j, i) = out[j];
302 }
303 }
304}
ASSERTL1
#define ASSERTL1(condition, msg)
Assert Level 1 – Debugging which is used whether in FULLDEBUG or DEBUG compilation mode....
Definition ErrorUtil.hpp:250
Nektar::StdRegions::StdExpansion::m_weights
std::vector< Array< OneD, const NekDouble > > m_weights
Definition StdExpansion.h:1275

References ASSERTL1, Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::m_weights, and v_IProductWRTBaseKernel().

◆ 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 434 of file StdExpansion2D.cpp.

438{
439 unsigned int i;
440
441 int dir;
442 // determine basis direction for edge.
443 if (DetShapeType() == LibUtilities::eTriangle)
444 {
445 dir = (eid == 0) ? 0 : 1;
446 }
447 else
448 {
449 dir = eid % 2;
450 }
451
452 int numModes = m_base[dir]->GetNumModes();
453
454 // P is the desired length of the map
455 P = (P == -1) ? numModes : P;
456
457 // decalare maparray
458 if (maparray.size() != P)
459 {
460 maparray = Array<OneD, unsigned int>(P);
461 }
462
463 // fill default mapping as increasing index
464 for (i = 0; i < P; ++i)
465 {
466 maparray[i] = i;
467 }
468
469 if (signarray.size() != P)
470 {
471 signarray = Array<OneD, int>(P, 1);
472 }
473 else
474 {
475 std::fill(signarray.data(), signarray.data() + P, 1);
476 }
477
478 // Zero signmap and set maparray to zero if
479 // elemental modes are not as large as trace modes
480 for (i = numModes; i < P; ++i)
481 {
482 signarray[i] = 0.0;
483 maparray[i] = maparray[0];
484 }
485
486 if (edgeOrient == eBackwards)
487 {
488 const LibUtilities::BasisType bType = GetBasisType(dir);
489
490 if ((bType == LibUtilities::eModified_A) ||
491 (bType == LibUtilities::eModified_B))
492 {
493 std::swap(maparray[0], maparray[1]);
494
495 for (i = 3; i < std::min(P, numModes); i += 2)
496 {
497 signarray[i] *= -1;
498 }
499 }
500 else if (bType == LibUtilities::eGLL_Lagrange ||
501 bType == LibUtilities::eGauss_Lagrange)
502 {
503 ASSERTL1(P == numModes, "Different trace space edge dimension "
504 "and element edge dimension not currently "
505 "possible for GLL-Lagrange bases");
506
507 std::reverse(maparray.data(), maparray.data() + P);
508 }
509 else
510 {
511 ASSERTL0(false, "Mapping not defined for this type of basis");
512 }
513 }
514}
ASSERTL0
#define ASSERTL0(condition, msg)
Definition ErrorUtil.hpp:216
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:200
Nektar::StdRegions::StdExpansion::DetShapeType
LibUtilities::ShapeType DetShapeType() const
This function returns the shape of the expansion domain.
Definition StdExpansion.h:414
Nektar::LibUtilities::eModified_B
@ eModified_B
Principle Modified Functions .
Definition BasisType.h:49
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
inlinefinalprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 210 of file StdExpansion2D.h.

211 {
212 return 2;
213 }

◆ 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 421 of file StdExpansion2D.cpp.

424{
425 ASSERTL0(false,
426 "This method must be defined at the individual shape level");
427}

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 516 of file StdExpansion2D.cpp.

521{
522 Array<OneD, unsigned int> map1, map2;
523 v_GetTraceCoeffMap(eid, map1);
524 v_GetElmtTraceToTraceMap(eid, map2, signarray, edgeOrient, P, Q);
525
526 if (maparray.size() != map2.size())
527 {
528 maparray = Array<OneD, unsigned int>(map2.size());
529 }
530
531 for (int i = 0; i < map2.size(); ++i)
532 {
533 maparray[i] = map1[map2[i]];
534 }
535}
Nektar::StdRegions::StdExpansion2D::v_GetTraceCoeffMap
void v_GetTraceCoeffMap(const unsigned int traceid, Array< OneD, unsigned int > &maparray) override
Definition StdExpansion2D.cpp:421
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:434

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 368 of file StdExpansion2D.cpp.

371{
372 if (mkey.GetNVarCoeff() == 0 &&
373 !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00) &&
374 !mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
375 {
376 using std::max;
377
378 int nquad0 = m_base[0]->GetNumPoints();
379 int nquad1 = m_base[1]->GetNumPoints();
380 int nqtot = nquad0 * nquad1;
381 int nmodes0 = m_base[0]->GetNumModes();
382 int nmodes1 = m_base[1]->GetNumModes();
383 int wspsize =
384 max(max(max(nqtot, m_ncoeffs), nquad1 * nmodes0), nquad0 * nmodes1);
385 NekDouble lambda = mkey.GetConstFactor(StdRegions::eFactorLambda);
386
387 // Allocate temporary storage
388 Array<OneD, NekDouble> wsp0(5 * wspsize); // size wspsize
389 Array<OneD, NekDouble> wsp1(wsp0 + wspsize); // size wspsize
390 Array<OneD, NekDouble> wsp2(wsp0 + 2 * wspsize); // size 3*wspsize
391
392 if (!(m_base[0]->Collocation() && m_base[1]->Collocation()))
393 {
394 // MASS MATRIX OPERATION
395 // The following is being calculated:
396 // wsp0 = B * u_hat = u
397 // wsp1 = W * wsp0
398 // outarray = B^T * wsp1 = B^T * W * B * u_hat = M * u_hat
399 BwdTrans(inarray, wsp0);
400 IProductWRTBase(wsp0, outarray);
401 LaplacianMatrixOp_MatFree_Kernel(wsp0, wsp1, wsp2);
402 }
403 else
404 {
405 MultiplyByQuadratureMetric(inarray, outarray);
406 LaplacianMatrixOp_MatFree_Kernel(inarray, wsp1, wsp2);
407 }
408
409 // outarray = lambda * outarray + wsp1
410 // = (lambda * M + L ) * u_hat
411 Vmath::Svtvp(m_ncoeffs, lambda, &outarray[0], 1, &wsp1[0], 1,
412 &outarray[0], 1);
413 }
414 else
415 {
416 StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl(inarray, outarray,
417 mkey);
418 }
419}
Nektar::StdRegions::StdExpansion::IProductWRTBase
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 expa...
Definition StdExpansion.h:598
Nektar::StdRegions::StdExpansion::BwdTrans
void BwdTrans(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
This function performs the Backward transformation from coefficient space to physical space.
Definition StdExpansion.h:467
Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric
void MultiplyByQuadratureMetric(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Definition StdExpansion.h:814
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:1242
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:1333
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
tinysimd::max
scalarT< T > max(scalarT< T > lhs, scalarT< T > rhs)
Definition scalar.hpp:305

References Nektar::StdRegions::StdExpansion::BwdTrans(), 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(), Nektar::StdRegions::StdExpansion::IProductWRTBase(), Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_Kernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, tinysimd::max(), Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), and Vmath::Svtvp().

◆ v_IProductWRTBase()

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

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

\( \begin{array}{rcl} I_{pq} = (\phi_p \phi_q, u) & = & \sum_{i=0}^{nq_0} \sum_{j=0}^{nq_1} \phi_p(\xi_{0,i}) \phi_q(\xi_{1,j}) w^0_i w^1_j u(\xi_{0,i} \xi_{1,j}) \\ & = & \sum_{i=0}^{nq_0} \phi_p(\xi_{0,i}) \sum_{j=0}^{nq_1} \phi_q(\xi_{1,j}) \tilde{u}_{i,j} \end{array} \)

where

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

which can be implemented as

\( f_{qi} = \sum_{j=0}^{nq_1} \phi_q(\xi_{1,j}) \tilde{u}_{i,j} = {\bf B_1 U} \) \( I_{pq} = \sum_{i=0}^{nq_0} \phi_p(\xi_{0,i}) f_{qi} = {\bf B_0 F} \)

This is a wrapper function around IProductWRTBaseKernel()

Implements Nektar::StdRegions::StdExpansion.

Reimplemented in Nektar::StdRegions::StdNodalTriExp.

Definition at line 233 of file StdExpansion2D.cpp.

236{
237 const bool CollDir0 = m_base[0]->Collocation();
238 const bool CollDir1 = m_base[1]->Collocation();
239
240 if (CollDir0 && CollDir1)
241 {
242 v_MultiplyByStdQuadratureMetric(inarray, outarray);
243 }
244 else
245 {
246 const Array<OneD, const NekDouble> one(1, 1.0);
247 v_IProductWRTBaseKernel(m_base[0]->GetBdata(), m_base[1]->GetBdata(),
248 inarray, outarray, one, false, CollDir0,
249 CollDir1);
250 }
251}
Nektar::StdRegions::StdExpansion2D::v_MultiplyByStdQuadratureMetric
void v_MultiplyByStdQuadratureMetric(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
Definition StdExpansion2D.cpp:306

References Nektar::StdRegions::StdExpansion::m_base, v_IProductWRTBaseKernel(), and v_MultiplyByStdQuadratureMetric().

Referenced by Nektar::StdRegions::StdTriExp::v_FwdTransBndConstrained().

◆ v_IProductWRTBaseKernel()

virtual void Nektar::StdRegions::StdExpansion2D::v_IProductWRTBaseKernel ( const Array< OneD, const NekDouble > &  base0,
const Array< OneD, const NekDouble > &  base1,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  outarray,
const Array< OneD, NekDouble > &  jac,
const bool  Deformed,
bool  CollDir0 = false,
bool  CollDir1 = false 
)
protectedpure virtual

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

Referenced by IProductWRTBaseKernel(), v_GenStdMatBwdDeriv(), Nektar::LocalRegions::Expansion2D::v_IProductWRTBase(), and v_IProductWRTBase().

◆ v_IsCollocatedBasis()

bool Nektar::StdRegions::StdExpansion2D::v_IsCollocatedBasis ( ) const
inlinefinalprotectedvirtual

Implements Nektar::StdRegions::StdExpansion.

Definition at line 214 of file StdExpansion2D.h.

215 {
216 return ((m_base[0]->Collocation()) && (m_base[1]->Collocation()));
217 }

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

Referenced by Nektar::LocalRegions::Expansion2D::v_IProductWRTBase().

◆ 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 323 of file StdExpansion2D.cpp.

326{
327 if (mkey.GetNVarCoeff() == 0 &&
328 !mkey.ConstFactorExists(StdRegions::eFactorCoeffD00) &&
329 !mkey.ConstFactorExists(StdRegions::eFactorSVVCutoffRatio))
330 {
331 using std::max;
332
333 // This implementation is only valid when there are no
334 // coefficients associated to the Laplacian operator
335 int nquad0 = m_base[0]->GetNumPoints();
336 int nquad1 = m_base[1]->GetNumPoints();
337 int nqtot = nquad0 * nquad1;
338 int nmodes0 = m_base[0]->GetNumModes();
339 int nmodes1 = m_base[1]->GetNumModes();
340 int wspsize =
341 max(max(max(nqtot, m_ncoeffs), nquad1 * nmodes0), nquad0 * nmodes1);
342
343 // Allocate temporary storage
344 Array<OneD, NekDouble> wsp0(4 * wspsize); // size wspsize
345 Array<OneD, NekDouble> wsp1(wsp0 + wspsize); // size 3*wspsize
346
347 if (!(m_base[0]->Collocation() && m_base[1]->Collocation()))
348 {
349 // LAPLACIAN MATRIX OPERATION
350 // wsp0 = u = B * u_hat
351 // wsp1 = du_dxi1 = D_xi1 * wsp0 = D_xi1 * u
352 // wsp2 = du_dxi2 = D_xi2 * wsp0 = D_xi2 * u
353 BwdTrans(inarray, wsp0);
354 LaplacianMatrixOp_MatFree_Kernel(wsp0, outarray, wsp1);
355 }
356 else
357 {
358 LaplacianMatrixOp_MatFree_Kernel(inarray, outarray, wsp1);
359 }
360 }
361 else
362 {
363 StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl(inarray, outarray,
364 mkey);
365 }
366}
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:1037

References Nektar::StdRegions::StdExpansion::BwdTrans(), 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, Nektar::StdRegions::StdExpansion::m_ncoeffs, and tinysimd::max().

◆ v_MultiplyByStdQuadratureMetric()

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

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 306 of file StdExpansion2D.cpp.

309{
310 int nquad0 = m_base[0]->GetNumPoints();
311 int nquad1 = m_base[1]->GetNumPoints();
312
313 int cnt = 0;
314 for (int i = 0; i < nquad1; ++i)
315 {
316 for (int j = 0; j < nquad0; ++j, ++cnt)
317 {
318 outarray[cnt] = inarray[cnt] * m_weights[0][j] * m_weights[1][i];
319 }
320 }
321}

References Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::m_weights.

Referenced by Nektar::LocalRegions::Expansion2D::v_IProductWRTBase(), and v_IProductWRTBase().

◆ v_PhysDeriv() [1/3]

void Nektar::StdRegions::StdExpansion::v_PhysDeriv ( const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  out_d1,
Array< OneD, NekDouble > &  out_d2,
Array< OneD, NekDouble > &  out_d3 
)
protectedvirtual

Calculate the derivative of the physical points.

See also
StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1636 of file StdExpansion.cpp.

1471{
1472 v_StdPhysDeriv(inarray, out_d1, out_d2, out_d3);
1473}
Nektar::StdRegions::StdExpansion::v_StdPhysDeriv
virtual void v_StdPhysDeriv(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2, Array< OneD, NekDouble > &out_d3)
Definition StdExpansion.cpp:1503

◆ v_PhysDeriv() [2/3]

void Nektar::StdRegions::StdExpansion::v_PhysDeriv ( const int  dir,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  out_d0 
)
protectedvirtual

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

See also
StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 1641 of file StdExpansion.cpp.

1485{
1486 NEKERROR(ErrorUtil::efatal, "This function is only valid for "
1487 "specific element types");
1488}
NEKERROR
#define NEKERROR(type, msg)
Assert Level 0 – Fundamental assert which is used whether in FULLDEBUG, DEBUG or OPT compilation mode...
Definition ErrorUtil.hpp:210

◆ v_PhysDeriv() [3/3]

void Nektar::StdRegions::StdExpansion2D::v_PhysDeriv ( const int  dir,
const Array< OneD, const NekDouble > &  inarray,
Array< OneD, NekDouble > &  out_d0 
)
overrideprotectedvirtual

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

See also
StdRegions::StdExpansion::PhysDeriv

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 133 of file StdExpansion2D.cpp.

136{
137 switch (dir)
138 {
139 case 0:
140 {
141 v_PhysDeriv(inarray, outarray, NullNekDouble1DArray,
142 NullNekDouble1DArray);
143 break;
144 }
145 case 1:
146 {
147 v_PhysDeriv(inarray, NullNekDouble1DArray, outarray,
148 NullNekDouble1DArray);
149 break;
150 }
151 default:
152 {
153 ASSERTL1(false, "input dir is out of range");
154 break;
155 }
156 }
157}
Nektar::StdRegions::StdExpansion2D::v_PhysDeriv
void v_PhysDeriv(const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override
Calculate the derivative of the physical points in a given direction.
Definition StdExpansion2D.cpp:133
Nektar::NullNekDouble1DArray
static Array< OneD, NekDouble > NullNekDouble1DArray
Definition BasicUtils/SharedArray.hpp:928

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

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

◆ v_PhysEvaluateInterp()

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

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 183 of file StdExpansion2D.cpp.

186{
187 NekDouble val;
188 int i;
189 int nq0 = m_base[0]->GetNumPoints();
190 int nq1 = m_base[1]->GetNumPoints();
191 Array<OneD, NekDouble> wsp1(nq1);
192
193 // interpolate first coordinate direction
194 for (i = 0; i < nq1; ++i)
195 {
196 wsp1[i] =
197 Vmath::Dot(nq0, &(I[0]->GetPtr())[0], 1, &physvals[i * nq0], 1);
198 }
199
200 // interpolate in second coordinate direction
201 val = Vmath::Dot(nq1, I[1]->GetPtr(), 1, wsp1, 1);
202
203 return val;
204}
Vmath::Dot
T Dot(int n, const T *w, const T *x)
dot product
Definition Vmath.hpp:761

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

◆ v_PhysInterp()

void Nektar::StdRegions::StdExpansion2D::v_PhysInterp ( std::shared_ptr< StdExpansion >  fromExp,
const Array< OneD, const NekDouble > &  fromData,
Array< OneD, NekDouble > &  toData,
bool  Transpose 
)
overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 537 of file StdExpansion2D.cpp.

541{
542 if (Transpose)
543 {
544 LibUtilities::Interp2D(fromExp->GetBasis(0)->GetPointsKey(),
545 fromExp->GetBasis(1)->GetPointsKey(), fromData,
546 m_base[1]->GetPointsKey(),
547 m_base[0]->GetPointsKey(), toData);
548 }
549 else
550 {
551 LibUtilities::Interp2D(fromExp->GetBasis(0)->GetPointsKey(),
552 fromExp->GetBasis(1)->GetPointsKey(), fromData,
553 m_base[0]->GetPointsKey(),
554 m_base[1]->GetPointsKey(), toData);
555 }
556}
Nektar::LibUtilities::Interp2D
void Interp2D(const BasisKey &fbasis0, const BasisKey &fbasis1, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, const BasisKey &tbasis1, Array< OneD, NekDouble > &to)
this function interpolates a 2D function evaluated at the quadrature points of the 2D basis,...
Definition Interp.cpp:101
Nektar::Transpose
NekMatrix< InnerMatrixType, BlockMatrixTag > Transpose(NekMatrix< InnerMatrixType, BlockMatrixTag > &rhs)
Definition BlockMatrix.hpp:235

References Nektar::LibUtilities::Interp2D(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::Transpose().

◆ v_ReOrientTracePhysMap()

void Nektar::StdRegions::StdExpansion2D::v_ReOrientTracePhysMap ( const StdRegions::Orientation  orient,
Array< OneD, int > &  idmap,
const int  nq0,
const int  nq1,
bool  Forwards 
)
overrideprotectedvirtual

Reimplemented from Nektar::StdRegions::StdExpansion.

Definition at line 558 of file StdExpansion2D.cpp.

562{
563 if (idmap.size() != nq0)
564 {
565 idmap = Array<OneD, int>(nq0);
566 }
567 switch (orient)
568 {
569 case StdRegions::eForwards:
570 // Fwd
571 for (int i = 0; i < nq0; ++i)
572 {
573 idmap[i] = i;
574 }
575 break;
576 case StdRegions::eBackwards:
577 {
578 // Bwd
579 for (int i = 0; i < nq0; ++i)
580 {
581 idmap[i] = nq0 - 1 - i;
582 }
583 }
584 break;
585 default:
586 ASSERTL0(false, "Unknown orientation");
587 break;
588 }
589}

References ASSERTL0, Nektar::StdRegions::eBackwards, and Nektar::StdRegions::eForwards.

◆ v_StdPhysEvaluate()

NekDouble Nektar::StdRegions::StdExpansion2D::v_StdPhysEvaluate ( 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.

Definition at line 159 of file StdExpansion2D.cpp.

162{
163 ASSERTL2(coords[0] > -1 - NekConstants::kNekZeroTol, "coord[0] < -1");
164 ASSERTL2(coords[0] < 1 + NekConstants::kNekZeroTol, "coord[0] > 1");
165 ASSERTL2(coords[1] > -1 - NekConstants::kNekZeroTol, "coord[1] < -1");
166 ASSERTL2(coords[1] < 1 + NekConstants::kNekZeroTol, "coord[1] > 1");
167
168 Array<OneD, NekDouble> coll(2);
169 LocCoordToLocCollapsed(coords, coll);
170
171 const int nq0 = m_base[0]->GetNumPoints();
172 const int nq1 = m_base[1]->GetNumPoints();
173
174 Array<OneD, NekDouble> wsp(nq1);
175 for (int i = 0; i < nq1; ++i)
176 {
177 wsp[i] = StdExpansion::BaryEvaluate<0>(coll[0], &physvals[0] + i * nq0);
178 }
179
180 return StdExpansion::BaryEvaluate<1>(coll[1], &wsp[0]);
181}
ASSERTL2
#define ASSERTL2(condition, msg)
Assert Level 2 – Debugging which is used FULLDEBUG compilation mode. This level assert is designed to...
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:1081
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.

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