Nektar++
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#include <StdNodalTriExp.h>
Public Member Functions | |
StdNodalTriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::PointsType Ntype) | |
StdNodalTriExp ()=default | |
StdNodalTriExp (const StdNodalTriExp &T)=default | |
~StdNodalTriExp () override=default | |
void | v_NodalToModal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | NodalToModalTranspose (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
void | ModalToNodal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
void | GetNodalPoints (Array< OneD, const NekDouble > &x, Array< OneD, const NekDouble > &y) |
DNekMatSharedPtr | GenNBasisTransMatrix () |
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StdTriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb) | |
StdTriExp ()=default | |
StdTriExp (const StdTriExp &T)=default | |
~StdTriExp () override=default | |
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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) |
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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, bool UseGLL=false) 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 | 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. 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... | |
void | PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData) |
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 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 | |
const LibUtilities::PointsKey | v_GetNodalPointsKey () const override |
bool | v_IsNodalNonTensorialExp () override |
void | v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | v_BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
Transform a given function from physical quadrature space to coefficient space. More... | |
void | v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
Calculates the inner product of a given function f with the different modes of the expansion. More... | |
void | v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true) override |
void | v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | v_FillMode (const int mode, Array< OneD, NekDouble > &outarray) override |
int | v_NumBndryCoeffs () const override |
int | v_GetVertexMap (int localVertexId, bool useCoeffPacking=false) override |
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_GetTraceInteriorToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation edgeOrient=eForwards) override |
void | v_GetInteriorMap (Array< OneD, unsigned int > &outarray) override |
void | v_GetBoundaryMap (Array< OneD, unsigned int > &outarray) override |
void | v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
void | v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
void | v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
void | v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
void | v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
DNekMatSharedPtr | v_GenMatrix (const StdMatrixKey &mkey) override |
DNekMatSharedPtr | v_CreateStdMatrix (const StdMatrixKey &mkey) override |
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NekDouble | v_Integral (const Array< OneD, const NekDouble > &inarray) override |
Integrates the specified function over the domain. More... | |
void | v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray) override |
Calculate the derivative of the physical points. More... | |
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. More... | |
void | v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2=NullNekDouble1DArray) override |
void | v_StdPhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
Backward tranform for triangular elements. More... | |
void | v_BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
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) override |
void | v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
Transform a given function from physical quadrature space to coefficient space. More... | |
void | v_FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) 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[p]*base1[pq] and put into outarray. More... | |
void | v_IProductWRTBase_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true) override |
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) override |
void | v_IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | v_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | v_LocCoordToLocCollapsed (const Array< OneD, const NekDouble > &xi, Array< OneD, NekDouble > &eta) override |
void | v_LocCollapsedToLocCoord (const Array< OneD, const NekDouble > &eta, Array< OneD, NekDouble > &xi) override |
void | v_FillMode (const int mode, Array< OneD, NekDouble > &outarray) override |
NekDouble | v_PhysEvaluateBasis (const Array< OneD, const NekDouble > &coords, int mode) final |
NekDouble | v_PhysEvalFirstDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override |
int | v_GetNverts () const final |
int | v_GetNtraces () const final |
LibUtilities::ShapeType | v_DetShapeType () const final |
int | v_NumBndryCoeffs () const override |
int | v_NumDGBndryCoeffs () const override |
int | v_GetTraceNcoeffs (const int i) const override |
int | v_GetTraceIntNcoeffs (const int i) const override |
int | v_GetTraceNumPoints (const int i) const override |
int | v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset) override |
void | v_GetCoords (Array< OneD, NekDouble > &coords_x, Array< OneD, NekDouble > &coords_y, Array< OneD, NekDouble > &coords_z) override |
bool | v_IsBoundaryInteriorExpansion () const override |
const LibUtilities::BasisKey | v_GetTraceBasisKey (const int i, const int j, bool UseGLL=false) const override |
int | v_GetVertexMap (int localVertexId, bool useCoeffPacking=false) override |
void | v_GetInteriorMap (Array< OneD, unsigned int > &outarray) override |
void | v_GetBoundaryMap (Array< OneD, unsigned int > &outarray) override |
void | v_GetTraceCoeffMap (const unsigned int traceid, Array< OneD, unsigned int > &maparray) override |
void | v_GetTraceInteriorToElementMap (const int eid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation edgeOrient=eForwards) override |
DNekMatSharedPtr | v_GenMatrix (const StdMatrixKey &mkey) override |
DNekMatSharedPtr | v_CreateStdMatrix (const StdMatrixKey &mkey) override |
void | v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
void | v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
void | v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdMatrixKey &mkey) override |
void | v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
void | v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
void | v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) override |
void | v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
void | v_GetSimplexEquiSpacedConnectivity (Array< OneD, int > &conn, bool standard=true) override |
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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_PhysEvaluateInterp (const Array< OneD, DNekMatSharedPtr > &I, const Array< OneD, const NekDouble > &physvals) 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 |
void | v_PhysInterp (std::shared_ptr< StdExpansion > fromExp, const Array< OneD, const NekDouble > &fromData, Array< OneD, NekDouble > &toData) override |
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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 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) |
Protected Attributes | |
LibUtilities::PointsKey | m_nodalPointsKey |
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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 |
Definition at line 43 of file StdNodalTriExp.h.
Nektar::StdRegions::StdNodalTriExp::StdNodalTriExp | ( | const LibUtilities::BasisKey & | Ba, |
const LibUtilities::BasisKey & | Bb, | ||
const LibUtilities::PointsType | Ntype | ||
) |
Definition at line 42 of file StdNodalTriExp.cpp.
References ASSERTL0, and Nektar::StdRegions::StdExpansion::m_base.
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default |
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default |
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overridedefault |
DNekMatSharedPtr Nektar::StdRegions::StdNodalTriExp::GenNBasisTransMatrix | ( | ) |
Definition at line 114 of file StdNodalTriExp.cpp.
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), GetNodalPoints(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdTriExp::v_FillMode(), and Nektar::StdRegions::StdExpansion2D::v_PhysEvaluate().
Referenced by v_GenMatrix().
void Nektar::StdRegions::StdNodalTriExp::GetNodalPoints | ( | Array< OneD, const NekDouble > & | x, |
Array< OneD, const NekDouble > & | y | ||
) |
Definition at line 108 of file StdNodalTriExp.cpp.
References m_nodalPointsKey, and Nektar::LibUtilities::PointsManager().
Referenced by GenNBasisTransMatrix().
void Nektar::StdRegions::StdNodalTriExp::ModalToNodal | ( | const Array< OneD, const NekDouble > & | inarray, |
Array< OneD, NekDouble > & | outarray | ||
) |
Definition at line 95 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eNBasisTrans, Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, m_nodalPointsKey, Nektar::StdRegions::NullConstFactorMap, and Nektar::StdRegions::NullVarCoeffMap.
Referenced by Nektar::GlobalMapping::UpdateGeometry(), and Nektar::LocalRegions::NodalTriExp::v_ExtractDataToCoeffs().
void Nektar::StdRegions::StdNodalTriExp::NodalToModalTranspose | ( | const Array< OneD, const NekDouble > & | inarray, |
Array< OneD, NekDouble > & | outarray | ||
) |
Definition at line 81 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::eCopy, Nektar::StdRegions::eInvNBasisTrans, Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, m_nodalPointsKey, Nektar::StdRegions::NullConstFactorMap, Nektar::StdRegions::NullVarCoeffMap, and Nektar::Transpose().
Referenced by Nektar::LocalRegions::NodalTriExp::v_IProductWRTBase_SumFac(), v_IProductWRTBase_SumFac(), Nektar::LocalRegions::NodalTriExp::v_IProductWRTDerivBase_SumFac(), and v_IProductWRTDerivBase_SumFac().
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overrideprotectedvirtual |
Implements Nektar::StdRegions::StdExpansion.
Definition at line 149 of file StdNodalTriExp.cpp.
References v_BwdTrans_SumFac().
Referenced by v_FillMode().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 155 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdTriExp::v_BwdTrans_SumFac(), and v_NodalToModal().
Referenced by v_BwdTrans().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 386 of file StdNodalTriExp.cpp.
References v_GenMatrix().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 219 of file StdNodalTriExp.cpp.
References ASSERTL2, Nektar::StdRegions::StdExpansion::m_ncoeffs, v_BwdTrans(), and Vmath::Zero().
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overrideprotectedvirtual |
Transform a given function from physical quadrature space to coefficient space.
Implements Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 164 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::eCopy, Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, m_nodalPointsKey, Nektar::StdRegions::NullConstFactorMap, Nektar::StdRegions::NullVarCoeffMap, and v_IProductWRTBase().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 369 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::CreateGeneralMatrix(), Nektar::StdRegions::eNBasisTrans, GenNBasisTransMatrix(), and Nektar::StdRegions::StdMatrixKey::GetMatrixType().
Referenced by v_CreateStdMatrix().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 351 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::NumBndryCoeffs().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 337 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::GetNcoeffs(), and Nektar::StdRegions::StdExpansion::NumBndryCoeffs().
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inlineoverrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 72 of file StdNodalTriExp.h.
References m_nodalPointsKey.
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 298 of file StdNodalTriExp.cpp.
References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::StdRegions::eForwards, and Nektar::StdRegions::StdExpansion::GetTraceNcoeffs().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion2D.
Definition at line 251 of file StdNodalTriExp.cpp.
References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::StdRegions::eForwards, Nektar::StdRegions::StdExpansion::GetTraceNcoeffs(), and Nektar::LibUtilities::P.
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 243 of file StdNodalTriExp.cpp.
References ASSERTL0.
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 425 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::HelmholtzMatrixOp_MatFree_GenericImpl().
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overrideprotectedvirtual |
Calculates the inner product of a given function f with the different modes of the expansion.
Implements Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 185 of file StdNodalTriExp.cpp.
References v_IProductWRTBase_SumFac().
Referenced by v_FwdTrans().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 192 of file StdNodalTriExp.cpp.
References NodalToModalTranspose(), and Nektar::StdRegions::StdTriExp::v_IProductWRTBase_SumFac().
Referenced by v_IProductWRTBase().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 200 of file StdNodalTriExp.cpp.
References v_IProductWRTDerivBase_SumFac().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 207 of file StdNodalTriExp.cpp.
References NodalToModalTranspose(), and Nektar::StdRegions::StdTriExp::v_IProductWRTDerivBase_SumFac().
Referenced by v_IProductWRTDerivBase().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 58 of file StdNodalTriExp.cpp.
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 402 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree_GenericImpl().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 410 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 395 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::MassMatrixOp_MatFree().
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overridevirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 67 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::StdRegions::eInvNBasisTrans, Nektar::eWrapper, Nektar::LibUtilities::PointsKey::GetPointsType(), Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, m_nodalPointsKey, Nektar::StdRegions::NullConstFactorMap, and Nektar::StdRegions::NullVarCoeffMap.
Referenced by v_BwdTrans_SumFac().
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overrideprotectedvirtual |
Implements Nektar::StdRegions::StdExpansion.
Definition at line 234 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::GetBasisNumModes().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::NodalTriExp.
Definition at line 418 of file StdNodalTriExp.cpp.
References Nektar::StdRegions::StdExpansion::WeakDerivMatrixOp_MatFree().
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protected |
Definition at line 70 of file StdNodalTriExp.h.
Referenced by GetNodalPoints(), ModalToNodal(), NodalToModalTranspose(), Nektar::LocalRegions::NodalTriExp::v_CreateStdMatrix(), Nektar::LocalRegions::NodalTriExp::v_FwdTrans(), v_FwdTrans(), Nektar::LocalRegions::NodalTriExp::v_GetLinStdExp(), v_GetNodalPointsKey(), Nektar::LocalRegions::NodalTriExp::v_GetStdExp(), and v_NodalToModal().