Nektar++
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#include <StdTetExp.h>
Public Member Functions | |
StdTetExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc) | |
StdTetExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc, NekDouble *coeffs, NekDouble *phys) | |
StdTetExp (const StdTetExp &T)=default | |
~StdTetExp () override=default | |
LibUtilities::ShapeType | DetShapeType () const |
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StdExpansion3D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const LibUtilities::BasisKey &Bc) | |
StdExpansion3D ()=default | |
StdExpansion3D (const StdExpansion3D &T)=default | |
~StdExpansion3D () override=default | |
void | PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d1, Array< OneD, NekDouble > &outarray_d2, Array< OneD, NekDouble > &outarray_d3) |
Calculate the 3D derivative in the local tensor/collapsed coordinate at the physical points. More... | |
void | BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2) |
void | IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2) |
int | GetNedges () const |
return the number of edges in 3D expansion More... | |
int | GetEdgeNcoeffs (const int i) const |
This function returns the number of expansion coefficients belonging to the i-th edge. More... | |
void | GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards) |
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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 | |
void | v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_dx, Array< OneD, NekDouble > &out_dy, Array< OneD, NekDouble > &out_dz) 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 |
void | v_StdPhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2) 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 |
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 > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2) override |
void | v_FwdTrans (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 |
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 > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2) 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_GetCoords (Array< OneD, NekDouble > &coords_x, Array< OneD, NekDouble > &coords_y, Array< OneD, NekDouble > &coords_z) 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 |
void | v_GetTraceNumModes (const int fid, int &numModes0, int &numModes1, Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2) override |
int | v_GetNverts () const override |
int | v_GetNedges () const override |
int | v_GetNtraces () const override |
LibUtilities::ShapeType | v_DetShapeType () const override |
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_GetEdgeNcoeffs (const int i) const override |
LibUtilities::PointsKey | v_GetTracePointsKey (const int i, const int j) const override |
int | v_CalcNumberOfCoefficients (const std::vector< unsigned int > &nummodes, int &modes_offset) override |
const LibUtilities::BasisKey | v_GetTraceBasisKey (const int i, const int k, bool UseGLL=false) const override |
bool | v_IsBoundaryInteriorExpansion () 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 fid, Array< OneD, unsigned int > &maparray) override |
void | v_GetElmtTraceToTraceMap (const unsigned int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1) override |
void | v_GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2) override |
void | v_GetTraceInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, const Orientation traceOrient=eDir1FwdDir1_Dir2FwdDir2) override |
DNekMatSharedPtr | v_GenMatrix (const StdMatrixKey &mkey) override |
DNekMatSharedPtr | v_CreateStdMatrix (const StdMatrixKey &mkey) override |
void | v_MultiplyByStdQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) 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_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 > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0 |
virtual void | v_IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &base2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0, bool doCheckCollDir1, bool doCheckCollDir2)=0 |
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 |
NekDouble | v_Integral (const Array< OneD, const NekDouble > &inarray) override |
Integrates the specified function over the domain. More... | |
virtual int | v_GetNedges (void) const |
virtual int | v_GetEdgeNcoeffs (const int i) const |
NekDouble | BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) |
virtual void | v_GetEdgeInteriorToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards) |
void | v_GetTraceToElementMap (const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient, int P, int Q) 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) |
Private Member Functions | |
int | GetMode (const int i, const int j, const int k) |
Compute the mode number in the expansion for a particular tensorial combination. More... | |
Additional Inherited Members | |
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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 StdTetExp.h.
Nektar::StdRegions::StdTetExp::StdTetExp | ( | const LibUtilities::BasisKey & | Ba, |
const LibUtilities::BasisKey & | Bb, | ||
const LibUtilities::BasisKey & | Bc | ||
) |
Definition at line 42 of file StdTetExp.cpp.
References ASSERTL0, and Nektar::LibUtilities::BasisKey::GetNumModes().
Nektar::StdRegions::StdTetExp::StdTetExp | ( | const LibUtilities::BasisKey & | Ba, |
const LibUtilities::BasisKey & | Bb, | ||
const LibUtilities::BasisKey & | Bc, | ||
NekDouble * | coeffs, | ||
NekDouble * | phys | ||
) |
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default |
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overridedefault |
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inline |
Definition at line 56 of file StdTetExp.h.
References Nektar::LibUtilities::eTetrahedron.
Referenced by Nektar::StdRegions::StdNodalTetExp::ModalToNodal(), Nektar::StdRegions::StdNodalTetExp::NodalToModal(), Nektar::StdRegions::StdNodalTetExp::NodalToModalTranspose(), Nektar::LocalRegions::TetExp::v_FwdTrans(), Nektar::StdRegions::StdNodalTetExp::v_FwdTrans(), and v_FwdTrans().
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private |
Compute the mode number in the expansion for a particular tensorial combination.
Modes are numbered with the r index travelling fastest, followed by q and then p, and each q-r plane is of size (Q+1)*(Q+2)/2+max(0,R-Q-p)*Q. For example, when P=2, Q=3 and R=4 (nm0=3, nm1 = 4, nm2 = 5) the indexing inside each q-r plane (with r increasing upwards and q to the right) is:
4 3 8 17 2 7 11 16 20 25 1 6 10 13 15 19 22 24 27 0 5 9 12 14 18 21 23 26
Geometrically they can be interpreted as
1 4 8 17 3 11 7 25 16 20 2 10 13 6 24 27 15 19 22 0 9 12 5 23 26 14 18 21
so we have the following breakdown
Vertices V[0,1,2,3] = [0, 14, 5, 1] Edges E[0,1,2,3,4,5,6] =[[23],[18, 21], [9, 12], [2,3,4], [15, 16, 17], [6,7,8]] Faces F[0.1,2,3] = [[26], [24,25], [19, 22, 20], [10, 13, 11] Interior [27] Note that in this element, we must have that \( P \leq Q \leq R\).
Definition at line 1921 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion::m_base.
Referenced by v_GetBoundaryMap(), v_GetEdgeInteriorToElementMap(), v_GetInteriorMap(), v_GetTraceCoeffMap(), v_GetTraceInteriorToElementMap(), and v_GetVertexMap().
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\( u^{\delta} (\xi_{1i}, \xi_{2j}, \xi_{3k}) = \sum_{m(pqr)} \hat u_{pqr} \phi_{pqr} (\xi_{1i}, \xi_{2j}, \xi_{3k})\)
Backward transformation is three dimensional tensorial expansion \( u (\xi_{1i}, \xi_{2j}, \xi_{3k}) = \sum_{p=0}^{Q_x} \psi_p^a (\xi_{1i}) \lbrace { \sum_{q=0}^{Q_y} \psi_{pq}^b (\xi_{2j}) \lbrace { \sum_{r=0}^{Q_z} \hat u_{pqr} \psi_{pqr}^c (\xi_{3k}) \rbrace} \rbrace}. \) And sumfactorizing step of the form is as:\
\( f_{pq} (\xi_{3k}) = \sum_{r=0}^{Q_z} \hat u_{pqr} \psi_{pqr}^c (\xi_{3k}),\\ g_{p} (\xi_{2j}, \xi_{3k}) = \sum_{r=0}^{Q_y} \psi_{pq}^b (\xi_{2j}) f_{pq} (\xi_{3k}),\\ u(\xi_{1i}, \xi_{2j}, \xi_{3k}) = \sum_{p=0}^{Q_x} \psi_{p}^a (\xi_{1i}) g_{p} (\xi_{2j}, \xi_{3k}). \)
Implements Nektar::StdRegions::StdExpansion.
Definition at line 266 of file StdTetExp.cpp.
References ASSERTL1, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::LibUtilities::eOrtho_B, Nektar::LibUtilities::eOrtho_C, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::StdRegions::StdExpansion::m_base, v_BwdTrans_SumFac(), and Vmath::Vcopy().
Referenced by v_FillMode().
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overrideprotectedvirtual |
Sum-factorisation implementation of the BwdTrans operation.
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 293 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion3D::BwdTrans_SumFacKernel(), and Nektar::StdRegions::StdExpansion::m_base.
Referenced by v_BwdTrans(), and Nektar::StdRegions::StdNodalTetExp::v_BwdTrans_SumFac().
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base0 | x-dirn basis matrix |
base1 | y-dirn basis matrix |
base2 | z-dirn basis matrix |
inarray | Input vector of modes. |
outarray | Output vector of physical space data. |
wsp | Workspace of size Q_x*P_z*(P_y+Q_y) |
doCheckCollDir0 | Check for collocation of basis. |
doCheckCollDir1 | Check for collocation of basis. |
doCheckCollDir2 | Check for collocation of basis. |
Implements Nektar::StdRegions::StdExpansion3D.
Definition at line 322 of file StdTetExp.cpp.
References Blas::Daxpy(), Blas::Dgemm(), Blas::Dgemv(), Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1123 of file StdTetExp.cpp.
References Nektar::LibUtilities::StdTetData::getNumberOfCoefficients().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 1877 of file StdTetExp.cpp.
References v_GenMatrix().
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overrideprotectedvirtual |
Implements Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 972 of file StdTetExp.cpp.
References Nektar::LibUtilities::eTetrahedron.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 809 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion::m_ncoeffs, and v_BwdTrans().
Referenced by Nektar::StdRegions::StdNodalTetExp::GenNBasisTransMatrix().
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inarray | array of physical quadrature points to be transformed. |
outarray | updated array of expansion coefficients. |
Implements Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 416 of file StdTetExp.cpp.
References DetShapeType(), Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::StdRegions::StdExpansion::GetStdMatrix(), Nektar::StdRegions::StdExpansion::m_ncoeffs, and v_IProductWRTBase().
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Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 1789 of file StdTetExp.cpp.
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::StdExpansion::CreateGeneralMatrix(), Nektar::StdRegions::eFactorConst, Nektar::StdRegions::ePhysInterpToEquiSpaced, Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdMatrixKey::GetMatrixType(), Nektar::LibUtilities::StdTetData::getNumberOfCoefficients(), Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), Nektar::StdRegions::StdExpansion::m_base, Vmath::Smul(), and Vmath::Vcopy().
Referenced by v_CreateStdMatrix().
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List of all boundary modes in the the expansion.
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1321 of file StdTetExp.cpp.
References ASSERTL1, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), GetMode(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::NumBndryCoeffs(), and Nektar::LibUtilities::P.
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 1161 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion::GetNumPoints(), and Nektar::StdRegions::StdExpansion::m_base.
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Maps interior modes of an edge to the elemental modes.
Reimplemented from Nektar::StdRegions::StdExpansion3D.
Definition at line 1583 of file StdTetExp.cpp.
References ASSERTL0, Nektar::StdRegions::eBackwards, GetMode(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LibUtilities::P, and v_GetEdgeNcoeffs().
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Reimplemented from Nektar::StdRegions::StdExpansion3D.
Definition at line 1082 of file StdTetExp.cpp.
References ASSERTL2, Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::P.
Referenced by v_GetEdgeInteriorToElementMap().
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1468 of file StdTetExp.cpp.
References ASSERTL0, ASSERTL1, Nektar::StdRegions::eDir1BwdDir1_Dir2FwdDir2, Nektar::StdRegions::StdExpansion::m_base, Nektar::LibUtilities::P, and v_IsBoundaryInteriorExpansion().
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Maps interior modes of an edge to the elemental modes. List of all interior modes in the expansion.
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1282 of file StdTetExp.cpp.
References ASSERTL1, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), GetMode(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::NumBndryCoeffs(), and Nektar::LibUtilities::P.
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Reimplemented from Nektar::StdRegions::StdExpansion3D.
Definition at line 962 of file StdTetExp.cpp.
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Implements Nektar::StdRegions::StdExpansion.
Definition at line 967 of file StdTetExp.cpp.
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Implements Nektar::StdRegions::StdExpansion.
Definition at line 957 of file StdTetExp.cpp.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 2236 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion::m_base.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1134 of file StdTetExp.cpp.
References ASSERTL2, Nektar::StdRegions::EvaluateTriFaceBasisKey(), Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::GetNumPoints(), and Nektar::StdRegions::StdExpansion::m_base.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1376 of file StdTetExp.cpp.
References ASSERTL0, GetMode(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::P.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1698 of file StdTetExp.cpp.
References ASSERTL0, GetMode(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LibUtilities::P, and v_GetTraceIntNcoeffs().
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Implements Nektar::StdRegions::StdExpansion.
Definition at line 1043 of file StdTetExp.cpp.
References ASSERTL2, and Nektar::StdRegions::StdExpansion::m_base.
Referenced by v_GetTraceInteriorToElementMap().
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Implements Nektar::StdRegions::StdExpansion.
Definition at line 1017 of file StdTetExp.cpp.
References ASSERTL2, Nektar::StdRegions::StdExpansion::GetBasisNumModes(), and Nektar::LibUtilities::P.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 923 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion::m_base.
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Implements Nektar::StdRegions::StdExpansion.
Definition at line 1064 of file StdTetExp.cpp.
References ASSERTL2, and Nektar::StdRegions::StdExpansion::m_base.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1103 of file StdTetExp.cpp.
References ASSERTL2, and Nektar::StdRegions::StdExpansion::m_base.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1201 of file StdTetExp.cpp.
References ASSERTL0, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), and GetMode().
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overrideprotectedvirtual |
\( \begin{array}{rcl} I_{pqr} = (\phi_{pqr}, u)_{\delta} & = &
\sum_{i=0}^{nq_0} \sum_{j=0}^{nq_1} \sum_{k=0}^{nq_2} \psi_{p}^{a}
(\eta_{1i}) \psi_{pq}^{b} (\eta_{2j}) \psi_{pqr}^{c} (\eta_{3k})
w_i w_j w_k u(\eta_{1,i} \eta_{2,j} \eta_{3,k}) J_{i,j,k}\\ & = &
\sum_{i=0}^{nq_0} \psi_p^a(\eta_{1,i}) \sum_{j=0}^{nq_1}
\psi_{pq}^b(\eta_{2,j}) \sum_{k=0}^{nq_2} \psi_{pqr}^c
u(\eta_{1i},\eta_{2j},\eta_{3k}) J_{i,j,k} \end{array} \)
where
\( \phi_{pqr} (\xi_1 , \xi_2 , \xi_3) = \psi_p^a (\eta_1) \psi_{pq}^b (\eta_2) \psi_{pqr}^c (\eta_3) \)
which can be implemented as
\(f_{pqr} (\xi_{3k}) =
\sum_{k=0}^{nq_3} \psi_{pqr}^c u(\eta_{1i},\eta_{2j},\eta_{3k})
J_{i,j,k} = {\bf B_3 U} \)
\( g_{pq} (\xi_{3k}) = \sum_{j=0}^{nq_1} \psi_{pq}^b (\xi_{2j})
f_{pqr} (\xi_{3k}) = {\bf B_2 F} \)
\( (\phi_{pqr}, u)_{\delta} = \sum_{k=0}^{nq_0} \psi_{p}^a
(\xi_{3k}) g_{pq} (\xi_{3k}) = {\bf B_1 G} \)
inarray | Function evaluated at physical collocation points. |
outarray | Inner product with respect to each basis function over the element. |
Implements Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 466 of file StdTetExp.cpp.
References ASSERTL1, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::LibUtilities::eOrtho_B, Nektar::LibUtilities::eOrtho_C, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), and v_IProductWRTBase_SumFac().
Referenced by v_FwdTrans().
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overrideprotectedvirtual |
inarray | Function evaluated at physical collocation points. |
outarray | Inner product with respect to each basis function over the element. |
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 493 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric().
Referenced by v_IProductWRTBase(), and Nektar::StdRegions::StdNodalTetExp::v_IProductWRTBase_SumFac().
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overrideprotectedvirtual |
Implements Nektar::StdRegions::StdExpansion3D.
Definition at line 523 of file StdTetExp.cpp.
References Blas::Ddot(), Blas::Dgemm(), Blas::Dgemv(), Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 605 of file StdTetExp.cpp.
References v_IProductWRTDerivBase_SumFac().
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inarray | Function evaluated at physical collocation points. |
outarray | Inner product with respect to each basis function over the element. |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 618 of file StdTetExp.cpp.
References ASSERTL1, Nektar::StdRegions::StdExpansion3D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), Vmath::Smul(), Vmath::Vadd(), and Vmath::Vmul().
Referenced by v_IProductWRTDerivBase(), and Nektar::StdRegions::StdNodalTetExp::v_IProductWRTDerivBase_SumFac().
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1191 of file StdTetExp.cpp.
References Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.
Referenced by v_GetElmtTraceToTraceMap().
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 801 of file StdTetExp.cpp.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 769 of file StdTetExp.cpp.
References Nektar::NekConstants::kNekZeroTol.
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1953 of file StdTetExp.cpp.
References Blas::Dscal(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::m_base, and Vmath::Vmul().
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overrideprotectedvirtual |
Implements Nektar::StdRegions::StdExpansion.
Definition at line 977 of file StdTetExp.cpp.
References ASSERTL1, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::LibUtilities::StdTetData::getNumberOfBndCoefficients(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::P.
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Implements Nektar::StdRegions::StdExpansion.
Definition at line 996 of file StdTetExp.cpp.
References ASSERTL1, Nektar::LibUtilities::eGLL_Lagrange, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eModified_C, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::LibUtilities::P.
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Calculate the derivative of the physical points.
The derivative is evaluated at the nodal physical points. Derivatives with respect to the local Cartesian coordinates
\(\begin{Bmatrix} \frac {\partial} {\partial \xi_1} \\ \frac {\partial} {\partial \xi_2} \\ \frac {\partial} {\partial \xi_3} \end{Bmatrix} = \begin{Bmatrix} \frac 4 {(1-\eta_2)(1-\eta_3)} \frac \partial {\partial \eta_1} \ \ \frac {2(1+\eta_1)} {(1-\eta_2)(1-\eta_3)} \frac \partial {\partial \eta_1} + \frac 2 {1-\eta_3} \frac \partial {\partial \eta_3} \\ \frac {2(1 + \eta_1)} {2(1 - \eta_2)(1-\eta_3)} \frac \partial {\partial \eta_1} + \frac {1 + \eta_2} {1 - \eta_3} \frac \partial {\partial \eta_2} + \frac \partial {\partial \eta_3} \end{Bmatrix}\)
Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 83 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion::m_base, Nektar::NullNekDouble1DArray, Nektar::StdRegions::StdExpansion3D::PhysTensorDeriv(), Vmath::Sadd(), Vmath::Smul(), Vmath::Vadd(), and Vmath::Vmul().
Referenced by v_PhysDeriv(), and v_StdPhysDeriv().
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dir | Direction in which to compute derivative. Valid values are 0, 1, 2. |
inarray | Input array. |
outarray | Output array. |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 194 of file StdTetExp.cpp.
References ASSERTL1, Nektar::NullNekDouble1DArray, and v_PhysDeriv().
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Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 858 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion3D::BaryTensorDeriv(), Nektar::StdRegions::StdExpansion::GetBase(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), Nektar::StdRegions::StdExpansion::PhysDeriv(), and Nektar::StdRegions::StdExpansion::PhysEvaluate().
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 816 of file StdTetExp.cpp.
References Nektar::LibUtilities::eModified_A, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::LocCoordToLocCollapsed(), Nektar::StdRegions::StdExpansion::m_base, and tinysimd::sqrt().
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 2176 of file StdTetExp.cpp.
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, Nektar::LibUtilities::eOrtho_C, Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Vmath::Vcopy(), and Vmath::Zero().
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 226 of file StdTetExp.cpp.
References v_PhysDeriv().
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Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 234 of file StdTetExp.cpp.
References v_PhysDeriv().
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Reimplemented from Nektar::StdRegions::StdExpansion.
Reimplemented in Nektar::LocalRegions::TetExp.
Definition at line 2034 of file StdTetExp.cpp.
References Nektar::StdRegions::StdExpansion::BwdTrans(), Nektar::StdRegions::StdMatrixKey::ConstFactorExists(), Nektar::StdRegions::eFactorSVVCutoffRatio, Nektar::StdRegions::eFactorSVVDGKerDiffCoeff, Nektar::StdRegions::eFactorSVVDiffCoeff, Nektar::StdRegions::eFactorSVVPowerKerDiffCoeff, Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, Nektar::LibUtilities::eOrtho_C, Nektar::StdRegions::StdExpansion::FwdTrans(), Nektar::StdRegions::StdMatrixKey::GetConstFactor(), Nektar::StdRegions::StdExpansion::GetNcoeffs(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::kSVVDGFilter, Nektar::StdRegions::kSVVDGFiltermodesmax, Nektar::StdRegions::kSVVDGFiltermodesmin, and Nektar::StdRegions::StdExpansion::m_base.