#include <TriExp.h>
Inheritance diagram for Nektar::LocalRegions::TriExp:
Public Member Functions | |
| TriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb, const SpatialDomains::Geometry2DSharedPtr &geom) | |
| Constructor using BasisKey class for quadrature points and order definition. More... | |
| TriExp (const TriExp &T) | |
| ~TriExp () override=default | |
 Public Member Functions inherited from Nektar::StdRegions::StdTriExp | |
| StdTriExp (const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb) | |
| StdTriExp ()=default | |
| StdTriExp (const StdTriExp &T)=default | |
| ~StdTriExp () override=default | |
| Public Member Functions inherited from Nektar::StdRegions::StdExpansion2D | |
| StdExpansion2D (int numcoeffs, const LibUtilities::BasisKey &Ba, const LibUtilities::BasisKey &Bb) | |
| StdExpansion2D ()=default | |
| StdExpansion2D (const StdExpansion2D &T)=default | |
| ~StdExpansion2D () override=default | |
| void | PhysTensorDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray_d0, Array< OneD, NekDouble > &outarray_d1) |
| Calculate the 2D derivative in the local tensor/collapsed coordinate at the physical points. More... | |
| NekDouble | Integral (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &w0, const Array< OneD, const NekDouble > &w1) |
| NekDouble | BaryTensorDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) |
| void | BwdTrans_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true) |
| void | IProductWRTBase_SumFacKernel (const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true) |
| Public Member Functions inherited from Nektar::StdRegions::StdExpansion | |
| StdExpansion () | |
| Default Constructor. More... | |
| StdExpansion (const int numcoeffs, const int numbases, const LibUtilities::BasisKey &Ba=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bb=LibUtilities::NullBasisKey, const LibUtilities::BasisKey &Bc=LibUtilities::NullBasisKey) | |
| Constructor. More... | |
| StdExpansion (const StdExpansion &T) | |
| Copy Constructor. More... | |
| virtual | ~StdExpansion () |
| Destructor. More... | |
| int | GetNumBases () const |
| This function returns the number of 1D bases used in the expansion. More... | |
| const Array< OneD, const LibUtilities::BasisSharedPtr > & | GetBase () const |
| This function gets the shared point to basis. More... | |
| const LibUtilities::BasisSharedPtr & | GetBasis (int dir) const |
| This function gets the shared point to basis in the dir direction. More... | |
| int | GetNcoeffs (void) const |
| This function returns the total number of coefficients used in the expansion. More... | |
| int | GetTotPoints () const |
| This function returns the total number of quadrature points used in the element. More... | |
| LibUtilities::BasisType | GetBasisType (const int dir) const |
| This function returns the type of basis used in the dir direction. More... | |
| int | GetBasisNumModes (const int dir) const |
| This function returns the number of expansion modes in the dir direction. More... | |
| int | EvalBasisNumModesMax (void) const |
| This function returns the maximum number of expansion modes over all local directions. More... | |
| LibUtilities::PointsType | GetPointsType (const int dir) const |
| This function returns the type of quadrature points used in the dir direction. More... | |
| int | GetNumPoints (const int dir) const |
| This function returns the number of quadrature points in the dir direction. More... | |
| const Array< OneD, const NekDouble > & | GetPoints (const int dir) const |
| This function returns a pointer to the array containing the quadrature points in dir direction. More... | |
| int | GetNverts () const |
| This function returns the number of vertices of the expansion domain. More... | |
| int | GetTraceNcoeffs (const int i) const |
| This function returns the number of expansion coefficients belonging to the i-th trace. More... | |
| int | GetTraceIntNcoeffs (const int i) const |
| int | GetTraceNumPoints (const int i) const |
| This function returns the number of quadrature points belonging to the i-th trace. More... | |
| const LibUtilities::BasisKey | GetTraceBasisKey (const int i, int k=-1, 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) |
| Public Member Functions inherited from Nektar::LocalRegions::Expansion2D | |
| Expansion2D (SpatialDomains::Geometry2DSharedPtr pGeom) | |
| ~Expansion2D () override=default | |
| DNekScalMatSharedPtr | CreateMatrix (const MatrixKey &mkey) |
| void | SetTraceToGeomOrientation (Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, NekDouble > &inout) |
| Array< OneD, unsigned int > | GetTraceInverseBoundaryMap (int eid) |
| void | AddNormTraceInt (const int dir, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &edgeCoeffs, Array< OneD, NekDouble > &outarray) |
| void | AddNormTraceInt (const int dir, Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs) |
| void | AddEdgeBoundaryInt (const int edge, ExpansionSharedPtr &EdgeExp, Array< OneD, NekDouble > &edgePhys, Array< OneD, NekDouble > &outarray, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap) |
| void | AddHDGHelmholtzEdgeTerms (const NekDouble tau, const int edge, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, NekDouble > &edgePhys, const StdRegions::VarCoeffMap &dirForcing, Array< OneD, NekDouble > &outarray) |
| void | AddHDGHelmholtzTraceTerms (const NekDouble tau, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, const StdRegions::VarCoeffMap &dirForcing, Array< OneD, NekDouble > &outarray) |
| SpatialDomains::Geometry2DSharedPtr | GetGeom2D () const |
| void | ReOrientEdgePhysMap (const int nvert, const StdRegions::Orientation orient, const int nq0, Array< OneD, int > &idmap) |
| DNekMatSharedPtr | v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override |
| void | v_GenTraceExp (const int traceid, ExpansionSharedPtr &exp) override |
| Public Member Functions inherited from Nektar::LocalRegions::Expansion | |
| Expansion (SpatialDomains::GeometrySharedPtr pGeom) | |
| Expansion (const Expansion &pSrc) | |
| ~Expansion () override | |
| void | SetTraceExp (const int traceid, ExpansionSharedPtr &f) |
| ExpansionSharedPtr | GetTraceExp (const int traceid) |
| DNekScalMatSharedPtr | GetLocMatrix (const LocalRegions::MatrixKey &mkey) |
| void | DropLocMatrix (const LocalRegions::MatrixKey &mkey) |
| DNekScalMatSharedPtr | GetLocMatrix (const StdRegions::MatrixType mtype, const StdRegions::ConstFactorMap &factors=StdRegions::NullConstFactorMap, const StdRegions::VarCoeffMap &varcoeffs=StdRegions::NullVarCoeffMap) |
| SpatialDomains::GeometrySharedPtr | GetGeom () const |
| void | Reset () |
| IndexMapValuesSharedPtr | CreateIndexMap (const IndexMapKey &ikey) |
| DNekScalBlkMatSharedPtr | CreateStaticCondMatrix (const MatrixKey &mkey) |
| const SpatialDomains::GeomFactorsSharedPtr & | GetMetricInfo () const |
| DNekMatSharedPtr | BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType) |
| DNekMatSharedPtr | BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) |
| void | ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType) |
| void | AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray) |
| void | AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) |
| void | AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) |
| void | DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray) |
| NekDouble | VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec) |
| void | NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors) |
| IndexMapValuesSharedPtr | GetIndexMap (const IndexMapKey &ikey) |
| void | AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray) |
| ExpansionSharedPtr | GetLeftAdjacentElementExp () const |
| ExpansionSharedPtr | GetRightAdjacentElementExp () const |
| int | GetLeftAdjacentElementTrace () const |
| int | GetRightAdjacentElementTrace () const |
| void | SetAdjacentElementExp (int traceid, ExpansionSharedPtr &e) |
| StdRegions::Orientation | GetTraceOrient (int trace) |
| void | SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| void | DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| Divided by the metric jacobi and quadrature weights. More... | |
| void | GetTraceQFactors (const int trace, Array< OneD, NekDouble > &outarray) |
| Extract the metric factors to compute the contravariant fluxes along edge edge and stores them into outarray following the local edge orientation (i.e. anticlockwise convention). More... | |
| void | GetTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient=StdRegions::eNoOrientation) |
| void | GetTracePhysMap (const int edge, Array< OneD, int > &outarray) |
| void | ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1) |
| const NormalVector & | GetTraceNormal (const int id) |
| void | ComputeTraceNormal (const int id) |
| const Array< OneD, const NekDouble > & | GetPhysNormals (void) |
| void | SetPhysNormals (Array< OneD, const NekDouble > &normal) |
| void | SetUpPhysNormals (const int trace) |
| void | AddRobinMassMatrix (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat) |
| void | TraceNormLen (const int traceid, NekDouble &h, NekDouble &p) |
| void | AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs) |
| const Array< OneD, const NekDouble > & | GetElmtBndNormDirElmtLen (const int nbnd) const |
| void | StdDerivBaseOnTraceMat (Array< OneD, DNekMatSharedPtr > &DerivMat) |
Protected Member Functions | |
| 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_PhysDirectionalDeriv (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &direction, Array< OneD, NekDouble > &out) override |
| Physical derivative along a direction vector. More... | |
| 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_IProductWRTDerivBase (const int dir, 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_IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
| void | v_AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray) override |
| void | v_IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
| void | v_IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
| Directinoal Derivative in the modal space in the dir direction of varcoeffs. More... | |
| 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) override |
| void | v_NormVectorIProductWRTBase (const Array< OneD, const Array< OneD, NekDouble > > &Fvec, Array< OneD, NekDouble > &outarray) override |
| StdRegions::StdExpansionSharedPtr | v_GetStdExp (void) const override |
| StdRegions::StdExpansionSharedPtr | v_GetLinStdExp (void) const override |
| void | v_GetCoord (const Array< OneD, const NekDouble > &Lcoords, Array< OneD, NekDouble > &coords) override |
| void | v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override |
| NekDouble | v_StdPhysEvaluate (const Array< OneD, const NekDouble > &Lcoord, const Array< OneD, const NekDouble > &physvals) override |
| NekDouble | v_PhysEvaluate (const Array< OneD, const NekDouble > &coord, const Array< OneD, const NekDouble > &physvals) override |
| This function evaluates the expansion at a single (arbitrary) point of the domain. More... | |
| NekDouble | v_PhysEvalFirstDeriv (const Array< OneD, NekDouble > &coord, const Array< OneD, const NekDouble > &inarray, std::array< NekDouble, 3 > &firstOrderDerivs) override |
| void | v_GetTracePhysVals (const int edge, const StdRegions::StdExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient) override |
| void | v_GetTraceQFactors (const int edge, Array< OneD, NekDouble > &outarray) override |
| void | v_ComputeTraceNormal (const int edge) override |
| void | v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int mode_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType) override |
| StdRegions::Orientation | v_GetTraceOrient (int edge) override |
| void | v_GetTracePhysMap (const int edge, Array< OneD, int > &outarray) override |
| DNekMatSharedPtr | v_GenMatrix (const StdRegions::StdMatrixKey &mkey) override |
| DNekMatSharedPtr | v_CreateStdMatrix (const StdRegions::StdMatrixKey &mkey) override |
| DNekScalMatSharedPtr | v_GetLocMatrix (const MatrixKey &mkey) override |
| void | v_DropLocMatrix (const MatrixKey &mkey) override |
| DNekScalBlkMatSharedPtr | v_GetLocStaticCondMatrix (const MatrixKey &mkey) override |
| void | v_DropLocStaticCondMatrix (const MatrixKey &mkey) override |
| void | v_MassMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override |
| void | v_LaplacianMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override |
| void | v_LaplacianMatrixOp (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override |
| void | v_WeakDerivMatrixOp (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override |
| void | v_WeakDirectionalDerivMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override |
| void | v_MassLevelCurvatureMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override |
| void | v_HelmholtzMatrixOp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::StdMatrixKey &mkey) override |
| void | v_LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp) override |
| void | v_ReduceOrderCoeffs (int numMin, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
| void | v_ComputeLaplacianMetric () override |
| void | v_SVVLaplacianFilter (Array< OneD, NekDouble > &array, const StdRegions::StdMatrixKey &mkey) override |
| void | v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors) override |
| : This method gets all of the factors which are required as part of the Gradient Jump Penalty stabilisation and involves the product of the normal and geometric factors along the element trace. More... | |
| Protected Member Functions inherited from Nektar::StdRegions::StdTriExp | |
| 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 |
| Protected Member Functions inherited from Nektar::StdRegions::StdExpansion2D | |
| 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 |
| Protected Member Functions inherited from Nektar::StdRegions::StdExpansion | |
| DNekMatSharedPtr | CreateStdMatrix (const StdMatrixKey &mkey) |
| DNekBlkMatSharedPtr | CreateStdStaticCondMatrix (const StdMatrixKey &mkey) |
| Create the static condensation of a matrix when using a boundary interior decomposition. More... | |
| void | BwdTrans_SumFac (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| void | IProductWRTDerivBase_SumFac (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| void | IProductWRTDirectionalDerivBase_SumFac (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| void | GeneralMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | MassMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | LaplacianMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | LaplacianMatrixOp_MatFree_Kernel (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp) |
| void | LaplacianMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | LaplacianMatrixOp_MatFree (const int k1, const int k2, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | WeakDerivMatrixOp_MatFree (const int i, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | WeakDirectionalDerivMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | MassLevelCurvatureMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | LinearAdvectionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | LinearAdvectionDiffusionReactionMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey, bool addDiffusionTerm=true) |
| void | HelmholtzMatrixOp_MatFree (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| void | HelmholtzMatrixOp_MatFree_GenericImpl (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey) |
| virtual void | v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| virtual 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 Member Functions inherited from Nektar::LocalRegions::Expansion2D | |
| void | v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &incoeffs, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &edgeCoeffs, Array< OneD, NekDouble > &out_d) override |
| void | v_AddEdgeNormBoundaryInt (const int edge, const ExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray) override |
| void | v_AddEdgeNormBoundaryInt (const int edge, const ExpansionSharedPtr &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) override |
| void | v_AddRobinMassMatrix (const int edgeid, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat) override |
| void | v_AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs) override |
| DNekMatSharedPtr | v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) override |
| void | v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1) override |
| void | v_SetUpPhysNormals (const int edge) override |
| NekDouble | v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec) override |
| void | v_TraceNormLen (const int traceid, NekDouble &h, NekDouble &p) override |
| Protected Member Functions inherited from Nektar::LocalRegions::Expansion | |
| void | ComputeLaplacianMetric () |
| void | ComputeQuadratureMetric () |
| void | ComputeGmatcdotMF (const Array< TwoD, const NekDouble > &df, const Array< OneD, const NekDouble > &direction, Array< OneD, Array< OneD, NekDouble > > &dfdir) |
| Array< OneD, NekDouble > | GetMF (const int dir, const int shapedim, const StdRegions::VarCoeffMap &varcoeffs) |
| Array< OneD, NekDouble > | GetMFDiv (const int dir, const StdRegions::VarCoeffMap &varcoeffs) |
| Array< OneD, NekDouble > | GetMFMag (const int dir, const StdRegions::VarCoeffMap &varcoeffs) |
| void | v_MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
| virtual void | v_DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| virtual void | v_ComputeLaplacianMetric () |
| int | v_GetCoordim () const override |
| void | v_GetCoords (Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override |
| virtual DNekScalMatSharedPtr | v_GetLocMatrix (const LocalRegions::MatrixKey &mkey) |
| virtual void | v_DropLocMatrix (const LocalRegions::MatrixKey &mkey) |
| virtual DNekMatSharedPtr | v_BuildTransformationMatrix (const DNekScalMatSharedPtr &r_bnd, const StdRegions::MatrixType matrixType) |
| virtual DNekMatSharedPtr | v_BuildVertexMatrix (const DNekScalMatSharedPtr &r_bnd) |
| virtual void | v_ExtractDataToCoeffs (const NekDouble *data, const std::vector< unsigned int > &nummodes, const int nmodes_offset, NekDouble *coeffs, std::vector< LibUtilities::BasisType > &fromType) |
| virtual void | v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray) |
| virtual void | v_AddEdgeNormBoundaryInt (const int edge, const std::shared_ptr< Expansion > &EdgeExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) |
| virtual void | v_AddFaceNormBoundaryInt (const int face, const std::shared_ptr< Expansion > &FaceExp, const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) |
| virtual void | v_DGDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, ExpansionSharedPtr > &EdgeExp, Array< OneD, Array< OneD, NekDouble > > &coeffs, Array< OneD, NekDouble > &outarray) |
| virtual NekDouble | v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &vec) |
| virtual void | v_NormalTraceDerivFactors (Array< OneD, Array< OneD, NekDouble > > &factors, Array< OneD, Array< OneD, NekDouble > > &d0factors, Array< OneD, Array< OneD, NekDouble > > &d1factors) |
| virtual void | v_AlignVectorToCollapsedDir (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray) |
| virtual StdRegions::Orientation | v_GetTraceOrient (int trace) |
| void | v_SetCoeffsToOrientation (StdRegions::Orientation dir, Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) override |
| virtual void | v_GetTraceQFactors (const int trace, Array< OneD, NekDouble > &outarray) |
| virtual void | v_GetTracePhysVals (const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, StdRegions::Orientation orient) |
| virtual void | v_GetTracePhysMap (const int edge, Array< OneD, int > &outarray) |
| virtual void | v_ReOrientTracePhysMap (const StdRegions::Orientation orient, Array< OneD, int > &idmap, const int nq0, const int nq1=-1) |
| virtual void | v_ComputeTraceNormal (const int id) |
| virtual const Array< OneD, const NekDouble > & | v_GetPhysNormals () |
| virtual void | v_SetPhysNormals (Array< OneD, const NekDouble > &normal) |
| virtual void | v_SetUpPhysNormals (const int id) |
| virtual void | v_AddRobinMassMatrix (const int face, const Array< OneD, const NekDouble > &primCoeffs, DNekMatSharedPtr &inoutmat) |
| virtual void | v_AddRobinTraceContribution (const int traceid, const Array< OneD, const NekDouble > &primCoeffs, const Array< OneD, NekDouble > &incoeffs, Array< OneD, NekDouble > &coeffs) |
| virtual void | v_TraceNormLen (const int traceid, NekDouble &h, NekDouble &p) |
| virtual void | v_GenTraceExp (const int traceid, ExpansionSharedPtr &exp) |
Detailed Description
Constructor & Destructor Documentation
◆ TriExp() [1/2]
| Nektar::LocalRegions::TriExp::TriExp | ( | const LibUtilities::BasisKey & | Ba, |
| const LibUtilities::BasisKey & | Bb, | ||
| const SpatialDomains::Geometry2DSharedPtr & | geom | ||
| ) |
Constructor using BasisKey class for quadrature points and order definition.
Definition at line 45 of file TriExp.cpp.
49 Ba.GetNumModes(), (Bb.GetNumModes())),
50 2, Ba, Bb),
52 Ba.GetNumModes(), (Bb.GetNumModes())),
53 Ba, Bb),
55 m_matrixManager(
57 std::string("TriExpMatrix")),
59 this, std::placeholders::_1),
60 std::string("TriExpStaticCondMatrix"))
61{
62}
DNekScalMatSharedPtr CreateMatrix(const MatrixKey &mkey)
Definition: Expansion2D.cpp:55
Expansion2D(SpatialDomains::Geometry2DSharedPtr pGeom)
Definition: Expansion2D.cpp:50
DNekScalBlkMatSharedPtr CreateStaticCondMatrix(const MatrixKey &mkey)
Definition: Expansion.cpp:272
Expansion(SpatialDomains::GeometrySharedPtr pGeom)
Definition: Expansion.cpp:43
LibUtilities::NekManager< MatrixKey, DNekScalMat, MatrixKey::opLess > m_matrixManager
Definition: TriExp.h:245
LibUtilities::NekManager< MatrixKey, DNekScalBlkMat, MatrixKey::opLess > m_staticCondMatrixManager
Definition: TriExp.h:247
StdExpansion2D()=default
StdTriExp()=default
int getNumberOfCoefficients(int Na, int Nb)
Definition: ShapeType.hpp:109
◆ TriExp() [2/2]
| Nektar::LocalRegions::TriExp::TriExp | ( | const TriExp & | T | ) |
Definition at line 64 of file TriExp.cpp.
◆ ~TriExp()
|
overridedefault |
Member Function Documentation
◆ v_AlignVectorToCollapsedDir()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 463 of file TriExp.cpp.
466{
469 "Invalid direction.");
470
473 int nqtot = nquad0 * nquad1;
476
477 const Array<TwoD, const NekDouble> &df =
479
480 Array<OneD, NekDouble> tmp0(wspsize);
481 Array<OneD, NekDouble> tmp3(wspsize);
482 Array<OneD, NekDouble> gfac0(wspsize);
483 Array<OneD, NekDouble> gfac1(wspsize);
484
485 Array<OneD, NekDouble> tmp1 = outarray[0];
486 Array<OneD, NekDouble> tmp2 = outarray[1];
487
490
491 // set up geometric factor: 2/(1-z1)
492 for (int i = 0; i < nquad1; ++i)
493 {
494 gfac0[i] = 2.0 / (1 - z1[i]);
495 }
496 for (int i = 0; i < nquad0; ++i)
497 {
498 gfac1[i] = 0.5 * (1 + z0[i]);
499 }
500
501 for (int i = 0; i < nquad1; ++i)
502 {
503 Vmath::Smul(nquad0, gfac0[i], &inarray[0] + i * nquad0, 1,
504 &tmp0[0] + i * nquad0, 1);
505 }
506
507 for (int i = 0; i < nquad1; ++i)
508 {
509 Vmath::Vmul(nquad0, &gfac1[0], 1, &tmp0[0] + i * nquad0, 1,
510 &tmp1[0] + i * nquad0, 1);
511 }
512
514 {
515 Vmath::Vmul(nqtot, &df[2 * dir][0], 1, &tmp0[0], 1, &tmp0[0], 1);
516 Vmath::Vmul(nqtot, &df[2 * dir + 1][0], 1, &tmp1[0], 1, &tmp1[0], 1);
517 Vmath::Vmul(nqtot, &df[2 * dir + 1][0], 1, &inarray[0], 1, &tmp2[0], 1);
518 }
519 else
520 {
521 Vmath::Smul(nqtot, df[2 * dir][0], tmp0, 1, tmp0, 1);
522 Vmath::Smul(nqtot, df[2 * dir + 1][0], tmp1, 1, tmp1, 1);
523 Vmath::Smul(nqtot, df[2 * dir + 1][0], inarray, 1, tmp2, 1);
524 }
525 Vmath::Vadd(nqtot, tmp0, 1, tmp1, 1, tmp1, 1);
526}
#define ASSERTL1(condition, msg)
Assert Level 1 – Debugging which is used whether in FULLDEBUG or DEBUG compilation mode....
Definition: ErrorUtil.hpp:242
SpatialDomains::GeometrySharedPtr m_geom
Definition: Expansion.h:273
SpatialDomains::GeomFactorsSharedPtr m_metricinfo
Definition: Expansion.h:274
const LibUtilities::PointsKeyVector GetPointsKeys() const
Definition: StdExpansion.h:1115
Array< OneD, LibUtilities::BasisSharedPtr > m_base
Definition: StdExpansion.h:1193
void Vmul(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Multiply vector z = x*y.
Definition: Vmath.hpp:72
void Vadd(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Add vector z = x+y.
Definition: Vmath.hpp:180
void Smul(int n, const T alpha, const T *x, const int incx, T *y, const int incy)
Scalar multiply y = alpha*x.
Definition: Vmath.hpp:100
References ASSERTL1, Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion::m_ncoeffs, Vmath::Smul(), Vmath::Vadd(), and Vmath::Vmul().
Referenced by v_IProductWRTDerivBase_SumFac().
◆ v_ComputeLaplacianMetric()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 1212 of file TriExp.cpp.
1213{
1215 {
1216 ComputeQuadratureMetric();
1217 }
1218
1219 unsigned int i, j;
1222 const unsigned int dim = 2;
1227
1228 Array<OneD, NekDouble> dEta_dXi[2] = {Array<OneD, NekDouble>(nqtot, 1.0),
1229 Array<OneD, NekDouble>(nqtot, 1.0)};
1230
1231 for (i = 0; i < dim; ++i)
1232 {
1233 for (j = i; j < dim; ++j)
1234 {
1235 m_metrics[m[i][j]] = Array<OneD, NekDouble>(nqtot);
1236 }
1237 }
1238
1243 const Array<TwoD, const NekDouble> &df =
1245
1246 for (i = 0; i < nquad1; i++)
1247 {
1248 Blas::Dscal(nquad0, 2.0 / (1 - z1[i]), &dEta_dXi[0][0] + i * nquad0, 1);
1249 Blas::Dscal(nquad0, 2.0 / (1 - z1[i]), &dEta_dXi[1][0] + i * nquad0, 1);
1250 }
1251 for (i = 0; i < nquad0; i++)
1252 {
1253 Blas::Dscal(nquad1, 0.5 * (1 + z0[i]), &dEta_dXi[1][0] + i, nquad0);
1254 }
1255
1256 Array<OneD, NekDouble> tmp(nqtot);
1258 type == SpatialDomains::eMovingRegular))
1259 {
1260 Vmath::Smul(nqtot, df[0][0], &dEta_dXi[0][0], 1, &tmp[0], 1);
1261 Vmath::Svtvp(nqtot, df[1][0], &dEta_dXi[1][0], 1, &tmp[0], 1, &tmp[0],
1262 1);
1263
1264 Vmath::Vmul(nqtot, &tmp[0], 1, &tmp[0], 1,
1266 Vmath::Smul(nqtot, df[1][0], &tmp[0], 1,
1268
1269 Vmath::Smul(nqtot, df[2][0], &dEta_dXi[0][0], 1, &tmp[0], 1);
1270 Vmath::Svtvp(nqtot, df[3][0], &dEta_dXi[1][0], 1, &tmp[0], 1, &tmp[0],
1271 1);
1272
1273 Vmath::Vvtvp(nqtot, &tmp[0], 1, &tmp[0], 1,
1276 Vmath::Svtvp(nqtot, df[3][0], &tmp[0], 1,
1279
1281 {
1282 Vmath::Smul(nqtot, df[4][0], &dEta_dXi[0][0], 1, &tmp[0], 1);
1283 Vmath::Svtvp(nqtot, df[5][0], &dEta_dXi[1][0], 1, &tmp[0], 1,
1284 &tmp[0], 1);
1285
1286 Vmath::Vvtvp(nqtot, &tmp[0], 1, &tmp[0], 1,
1289 Vmath::Svtvp(nqtot, df[5][0], &tmp[0], 1,
1292 }
1293
1294 NekDouble g2 = df[1][0] * df[1][0] + df[3][0] * df[3][0];
1296 {
1297 g2 += df[5][0] * df[5][0];
1298 }
1300 }
1301 else
1302 {
1303
1304 Vmath::Vmul(nqtot, &df[0][0], 1, &dEta_dXi[0][0], 1, &tmp[0], 1);
1305 Vmath::Vvtvp(nqtot, &df[1][0], 1, &dEta_dXi[1][0], 1, &tmp[0], 1,
1306 &tmp[0], 1);
1307
1308 Vmath::Vmul(nqtot, &tmp[0], 1, &tmp[0], 1,
1310 Vmath::Vmul(nqtot, &df[1][0], 1, &tmp[0], 1,
1312 Vmath::Vmul(nqtot, &df[1][0], 1, &df[1][0], 1,
1314
1315 Vmath::Vmul(nqtot, &df[2][0], 1, &dEta_dXi[0][0], 1, &tmp[0], 1);
1316 Vmath::Vvtvp(nqtot, &df[3][0], 1, &dEta_dXi[1][0], 1, &tmp[0], 1,
1317 &tmp[0], 1);
1318
1319 Vmath::Vvtvp(nqtot, &tmp[0], 1, &tmp[0], 1,
1322 Vmath::Vvtvp(nqtot, &df[3][0], 1, &tmp[0], 1,
1325 Vmath::Vvtvp(nqtot, &df[3][0], 1, &df[3][0], 1,
1328
1330 {
1331 Vmath::Vmul(nqtot, &df[4][0], 1, &dEta_dXi[0][0], 1, &tmp[0], 1);
1332 Vmath::Vvtvp(nqtot, &df[5][0], 1, &dEta_dXi[1][0], 1, &tmp[0], 1,
1333 &tmp[0], 1);
1334
1335 Vmath::Vvtvp(nqtot, &tmp[0], 1, &tmp[0], 1,
1338 Vmath::Vvtvp(nqtot, &df[5][0], 1, &tmp[0], 1,
1341 Vmath::Vvtvp(nqtot, &df[5][0], 1, &df[5][0], 1,
1344 }
1345 }
1346
1347 for (unsigned int i = 0; i < dim; ++i)
1348 {
1349 for (unsigned int j = i; j < dim; ++j)
1350 {
1352 }
1353 }
1354}
void ComputeQuadratureMetric()
Definition: Expansion.cpp:458
int GetTotPoints() const
This function returns the total number of quadrature points used in the element.
Definition: StdExpansion.h:134
void MultiplyByQuadratureMetric(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Definition: StdExpansion.h:732
static void Dscal(const int &n, const double &alpha, double *x, const int &incx)
BLAS level 1: x = alpha x.
Definition: Blas.hpp:149
@ eRegular
Geometry is straight-sided with constant geometric factors.
Definition: SpatialDomains.hpp:52
void Svtvp(int n, const T alpha, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Svtvp (scalar times vector plus vector): z = alpha*x + y.
Definition: Vmath.hpp:396
void Vvtvp(int n, const T *w, const int incw, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
vvtvp (vector times vector plus vector): z = w*x + y
Definition: Vmath.hpp:366
void Fill(int n, const T alpha, T *x, const int incx)
Fill a vector with a constant value.
Definition: Vmath.hpp:54
References Nektar::LocalRegions::Expansion::ComputeQuadratureMetric(), Blas::Dscal(), Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian02, Nektar::LocalRegions::eMetricLaplacian11, Nektar::LocalRegions::eMetricLaplacian12, Nektar::LocalRegions::eMetricLaplacian22, Nektar::LocalRegions::eMetricQuadrature, Nektar::SpatialDomains::eMovingRegular, Nektar::SpatialDomains::eRegular, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), Vmath::Smul(), Vmath::Svtvp(), Vmath::Vmul(), and Vmath::Vvtvp().
◆ v_ComputeTraceNormal()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 819 of file TriExp.cpp.
820{
821 int i;
823 GetGeom()->GetMetricInfo();
824
826 for (i = 0; i < ptsKeys.size(); ++i)
827 {
828 // Need at least 2 points for computing normals
830 {
831 LibUtilities::PointsKey pKey(2, ptsKeys[i].GetPointsType());
832 ptsKeys[i] = pKey;
833 }
834 }
835
837 const Array<TwoD, const NekDouble> &df =
838 geomFactors->GetDerivFactors(ptsKeys);
839 const Array<OneD, const NekDouble> &jac = geomFactors->GetJac(ptsKeys);
840
841 // The points of normals should follow trace basis, not local basis.
842 LibUtilities::BasisKey tobasis = GetTraceBasisKey(edge);
843
844 int nqe = tobasis.GetNumPoints();
846
847 m_traceNormals[edge] = Array<OneD, Array<OneD, NekDouble>>(dim);
848 Array<OneD, Array<OneD, NekDouble>> &normal = m_traceNormals[edge];
849 for (i = 0; i < dim; ++i)
850 {
851 normal[i] = Array<OneD, NekDouble>(nqe);
852 }
853
854 size_t nqb = nqe;
855 size_t nbnd = edge;
856 m_elmtBndNormDirElmtLen[nbnd] = Array<OneD, NekDouble>{nqb, 0.0};
857 Array<OneD, NekDouble> &length = m_elmtBndNormDirElmtLen[nbnd];
858
859 // Regular geometry case
861 (type == SpatialDomains::eMovingRegular))
862 {
863 NekDouble fac;
864 // Set up normals
865 switch (edge)
866 {
867 case 0:
869 {
870 Vmath::Fill(nqe, -df[2 * i + 1][0], normal[i], 1);
871 }
872 break;
873 case 1:
875 {
876 Vmath::Fill(nqe, df[2 * i + 1][0] + df[2 * i][0], normal[i],
877 1);
878 }
879 break;
880 case 2:
882 {
883 Vmath::Fill(nqe, -df[2 * i][0], normal[i], 1);
884 }
885 break;
886 default:
888 }
889
890 // normalise
891 fac = 0.0;
893 {
894 fac += normal[i][0] * normal[i][0];
895 }
896 fac = 1.0 / sqrt(fac);
897
898 Vmath::Fill(nqb, fac, length, 1);
899
901 {
902 Vmath::Smul(nqe, fac, normal[i], 1, normal[i], 1);
903 }
904 }
905 else // Set up deformed normals
906 {
907 int j;
908
909 int nquad0 = ptsKeys[0].GetNumPoints();
910 int nquad1 = ptsKeys[1].GetNumPoints();
911
912 LibUtilities::PointsKey from_key;
913
914 Array<OneD, NekDouble> normals(GetCoordim() * max(nquad0, nquad1), 0.0);
915 Array<OneD, NekDouble> edgejac(GetCoordim() * max(nquad0, nquad1), 0.0);
916
917 // Extract Jacobian along edges and recover local
918 // derivates (dx/dr) for polynomial interpolation by
919 // multiplying m_gmat by jacobian
920 switch (edge)
921 {
922 case 0:
923 for (j = 0; j < nquad0; ++j)
924 {
925 edgejac[j] = jac[j];
927 {
928 normals[i * nquad0 + j] =
929 -df[2 * i + 1][j] * edgejac[j];
930 }
931 }
932 from_key = ptsKeys[0];
933 break;
934 case 1:
935 for (j = 0; j < nquad1; ++j)
936 {
937 edgejac[j] = jac[nquad0 * j + nquad0 - 1];
939 {
940 normals[i * nquad1 + j] =
941 (df[2 * i][nquad0 * j + nquad0 - 1] +
942 df[2 * i + 1][nquad0 * j + nquad0 - 1]) *
943 edgejac[j];
944 }
945 }
946 from_key = ptsKeys[1];
947 break;
948 case 2:
949 for (j = 0; j < nquad1; ++j)
950 {
951 edgejac[j] = jac[nquad0 * j];
953 {
954 normals[i * nquad1 + j] =
955 -df[2 * i][nquad0 * j] * edgejac[j];
956 }
957 }
958 from_key = ptsKeys[1];
959 break;
960 default:
962 }
963
964 int nq = from_key.GetNumPoints();
965 Array<OneD, NekDouble> work(nqe, 0.0);
966
967 // interpolate Jacobian and invert
968 LibUtilities::Interp1D(from_key, jac, tobasis.GetPointsKey(), work);
969 Vmath::Sdiv(nqe, 1.0, &work[0], 1, &work[0], 1);
970
971 // interpolate
973 {
974 LibUtilities::Interp1D(from_key, &normals[i * nq],
975 tobasis.GetPointsKey(), &normal[i][0]);
976 Vmath::Vmul(nqe, work, 1, normal[i], 1, normal[i], 1);
977 }
978
979 // normalise normal vectors
980 Vmath::Zero(nqe, work, 1);
982 {
983 Vmath::Vvtvp(nqe, normal[i], 1, normal[i], 1, work, 1, work, 1);
984 }
985
986 Vmath::Vsqrt(nqe, work, 1, work, 1);
987 Vmath::Sdiv(nqe, 1.0, work, 1, work, 1);
988
989 Vmath::Vcopy(nqb, work, 1, length, 1);
990
992 {
993 Vmath::Vmul(nqe, normal[i], 1, work, 1, normal[i], 1);
994 }
995 }
996
998 {
1000 {
1002 {
1003 Vmath::Reverse(nqe, normal[i], 1, normal[i], 1);
1004 }
1005 }
1006 }
1007}
std::map< int, NormalVector > m_traceNormals
Definition: Expansion.h:276
std::map< int, Array< OneD, NekDouble > > m_elmtBndNormDirElmtLen
the element length in each element boundary(Vertex, edge or face) normal direction calculated based o...
Definition: Expansion.h:286
SpatialDomains::GeometrySharedPtr GetGeom() const
Definition: Expansion.cpp:167
LibUtilities::PointsType GetPointsType(const int dir) const
This function returns the type of quadrature points used in the dir direction.
Definition: StdExpansion.h:205
int GetNumPoints(const int dir) const
This function returns the number of quadrature points in the dir direction.
Definition: StdExpansion.h:218
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.
Definition: StdExpansion.h:301
void Interp1D(const BasisKey &fbasis0, const Array< OneD, const NekDouble > &from, const BasisKey &tbasis0, Array< OneD, NekDouble > &to)
this function interpolates a 1D function evaluated at the quadrature points of the basis fbasis0 to ...
Definition: Interp.cpp:47
std::vector< PointsKey > PointsKeyVector
Definition: Points.h:231
std::shared_ptr< GeomFactors > GeomFactorsSharedPtr
Pointer to a GeomFactors object.
Definition: GeomFactors.h:60
void Vsqrt(int n, const T *x, const int incx, T *y, const int incy)
sqrt y = sqrt(x)
Definition: Vmath.hpp:340
void Sdiv(int n, const T alpha, const T *x, const int incx, T *y, const int incy)
Scalar multiply y = alpha/x.
Definition: Vmath.hpp:154
void Reverse(int n, const T *x, const int incx, T *y, const int incy)
Definition: Vmath.hpp:844
void Vcopy(int n, const T *x, const int incx, T *y, const int incy)
Definition: Vmath.hpp:825
References ASSERTL0, Nektar::StdRegions::eBackwards, Nektar::SpatialDomains::eDeformed, Nektar::SpatialDomains::eMovingRegular, Nektar::SpatialDomains::eRegular, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetCoordim(), Nektar::LocalRegions::Expansion::GetGeom(), Nektar::LibUtilities::BasisKey::GetNumPoints(), Nektar::LibUtilities::PointsKey::GetNumPoints(), Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::LibUtilities::BasisKey::GetPointsKey(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::GetTraceBasisKey(), Nektar::LibUtilities::Interp1D(), Nektar::LocalRegions::Expansion::m_elmtBndNormDirElmtLen, Nektar::LocalRegions::Expansion::m_traceNormals, Vmath::Reverse(), Vmath::Sdiv(), Vmath::Smul(), tinysimd::sqrt(), Vmath::Vcopy(), Vmath::Vmul(), Vmath::Vsqrt(), Vmath::Vvtvp(), and Vmath::Zero().
◆ v_CreateStdMatrix()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 1074 of file TriExp.cpp.
1075{
1076 LibUtilities::BasisKey bkey0 = m_base[0]->GetBasisKey();
1077 LibUtilities::BasisKey bkey1 = m_base[1]->GetBasisKey();
1078 StdRegions::StdTriExpSharedPtr tmp =
1079 MemoryManager<StdTriExp>::AllocateSharedPtr(bkey0, bkey1);
1080
1081 return tmp->GetStdMatrix(mkey);
1082}
static std::shared_ptr< DataType > AllocateSharedPtr(const Args &...args)
Allocate a shared pointer from the memory pool.
Definition: NekMemoryManager.hpp:166
std::shared_ptr< StdTriExp > StdTriExpSharedPtr
Definition: StdTriExp.h:218
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and Nektar::StdRegions::StdExpansion::m_base.
◆ v_DropLocMatrix()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 1089 of file TriExp.cpp.
References m_matrixManager.
◆ v_DropLocStaticCondMatrix()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1099 of file TriExp.cpp.
References m_staticCondMatrixManager.
◆ v_ExtractDataToCoeffs()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 1009 of file TriExp.cpp.
1013{
1014 int data_order0 = nummodes[mode_offset];
1016 int data_order1 = nummodes[mode_offset + 1];
1018 int fillorder1 = min(order1, data_order1);
1019
1021 {
1024 {
1025 int i;
1026 int cnt = 0;
1027 int cnt1 = 0;
1028
1031 "Extraction routine not set up for this basis");
1032
1034 for (i = 0; i < fillorder0; ++i)
1035 {
1036 Vmath::Vcopy(fillorder1 - i, &data[cnt], 1, &coeffs[cnt1], 1);
1037 cnt += data_order1 - i;
1038 cnt1 += order1 - i;
1039 }
1040 }
1041 break;
1042 default:
1044 }
1045}
LibUtilities::BasisType GetBasisType(const int dir) const
This function returns the type of basis used in the dir direction.
Definition: StdExpansion.h:156
References ASSERTL0, ASSERTL1, Nektar::LibUtilities::eModified_A, Nektar::LibUtilities::eModified_B, Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, Nektar::StdRegions::StdExpansion::GetBasisType(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Vmath::Vcopy(), and Vmath::Zero().
◆ v_FwdTrans()
|
overrideprotectedvirtual |
Transform a given function from physical quadrature space to coefficient space.
- See also
- StdExpansion::FwdTrans
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 249 of file TriExp.cpp.
251{
252 IProductWRTBase(inarray, outarray);
253
254 // get Mass matrix inverse
257
258 // copy inarray in case inarray == outarray
261
262 out = (*matsys) * in;
263}
void IProductWRTBase(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
this function calculates the inner product of a given function f with the different modes of the expa...
Definition: StdExpansion.h:537
LibUtilities::ShapeType DetShapeType() const
This function returns the shape of the expansion domain.
Definition: StdExpansion.h:370
std::shared_ptr< DNekScalMat > DNekScalMatSharedPtr
Definition: NekMatrixFwd.hpp:66
References Nektar::StdRegions::StdExpansion::DetShapeType(), Nektar::eCopy, Nektar::StdRegions::eInvMass, Nektar::eWrapper, Nektar::StdRegions::StdExpansion::IProductWRTBase(), m_matrixManager, and Nektar::StdRegions::StdExpansion::m_ncoeffs.
◆ v_FwdTransBndConstrained()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 265 of file TriExp.cpp.
268{
269 int i, j;
272
273 fill(outarray.data(), outarray.data() + m_ncoeffs, 0.0);
274
275 if (nmodes[0] == 1 && nmodes[1] == 1)
276 {
277 outarray[0] = inarray[0];
278 return;
279 }
280
281 Array<OneD, NekDouble> physEdge[3];
282 Array<OneD, NekDouble> coeffEdge[3];
283 for (i = 0; i < 3; i++)
284 {
285 // define physEdge and add 1 so can interpolate grl10 points if
286 // necessary
287 physEdge[i] = Array<OneD, NekDouble>(max(npoints[i != 0], npoints[0]));
288 coeffEdge[i] = Array<OneD, NekDouble>(nmodes[i != 0]);
289 }
290
291 for (i = 0; i < npoints[0]; i++)
292 {
293 physEdge[0][i] = inarray[i];
294 }
295
296 // extract data in cartesian directions
297 for (i = 0; i < npoints[1]; i++)
298 {
299 physEdge[1][i] = inarray[npoints[0] - 1 + i * npoints[0]];
300 physEdge[2][i] = inarray[i * npoints[0]];
301 }
302
303 SegExpSharedPtr segexp[3];
304 segexp[0] = MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
306
308 {
309 for (i = 1; i < 3; i++)
310 {
311 segexp[i] = MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
313 }
314 }
315 else // interploate using edge 0 GLL distribution
316 {
317 for (i = 1; i < 3; i++)
318 {
319 segexp[i] = MemoryManager<LocalRegions::SegExp>::AllocateSharedPtr(
321
323 m_base[0]->GetPointsKey(), physEdge[i]);
324 }
325 npoints[1] = npoints[0];
326 }
327
328 Array<OneD, unsigned int> mapArray;
329 Array<OneD, int> signArray;
331 // define an orientation to get EdgeToElmtMapping from Cartesian data
332 StdRegions::Orientation orient[3] = {
334
335 for (i = 0; i < 3; i++)
336 {
337 segexp[i]->FwdTransBndConstrained(physEdge[i], coeffEdge[i]);
338
339 // this orient goes with the one above and so could
340 // probably set both to eForwards
341 GetTraceToElementMap(i, mapArray, signArray, orient[i]);
342 for (j = 0; j < nmodes[i != 0]; j++)
343 {
345 outarray[mapArray[j]] = sign * coeffEdge[i][j];
346 }
347 }
348
351
352 if (nInteriorDofs > 0)
353 {
354 Array<OneD, NekDouble> tmp0(m_ncoeffs);
355 Array<OneD, NekDouble> tmp1(m_ncoeffs);
356
358 *this);
359 MassMatrixOp(outarray, tmp0, stdmasskey);
360 IProductWRTBase(inarray, tmp1);
361
363
364 // get Mass matrix inverse (only of interior DOF)
365 // use block (1,1) of the static condensed system
366 // note: this block alreay contains the inverse matrix
368 DNekScalMatSharedPtr matsys =
369 (m_staticCondMatrixManager[masskey])->GetBlock(1, 1);
370
371 Array<OneD, NekDouble> rhs(nInteriorDofs);
372 Array<OneD, NekDouble> result(nInteriorDofs);
373
374 GetInteriorMap(mapArray);
375
376 for (i = 0; i < nInteriorDofs; i++)
377 {
378 rhs[i] = tmp1[mapArray[i]];
379 }
380
382 &((matsys->GetOwnedMatrix())->GetPtr())[0], nInteriorDofs,
383 rhs.data(), 1, 0.0, result.data(), 1);
384
385 for (i = 0; i < nInteriorDofs; i++)
386 {
387 outarray[mapArray[i]] = result[i];
388 }
389 }
390}
SpatialDomains::Geometry2DSharedPtr GetGeom2D() const
Definition: Expansion2D.h:164
int NumBndryCoeffs(void) const
Definition: StdExpansion.h:325
void MassMatrixOp(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
Definition: StdExpansion.h:761
void GetTraceToElementMap(const int tid, Array< OneD, unsigned int > &maparray, Array< OneD, int > &signarray, Orientation traceOrient=eForwards, int P=-1, int Q=-1)
Definition: StdExpansion.h:693
void GetInteriorMap(Array< OneD, unsigned int > &outarray)
Definition: StdExpansion.h:683
static void Dgemv(const char &trans, const int &m, const int &n, const double &alpha, const double *a, const int &lda, const double *x, const int &incx, const double &beta, double *y, const int &incy)
BLAS level 2: Matrix vector multiply y = alpha A x plus beta y where A[m x n].
Definition: Blas.hpp:211
std::shared_ptr< SegExp > SegExpSharedPtr
Definition: SegExp.h:253
void Vsub(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Subtract vector z = x-y.
Definition: Vmath.hpp:220
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::StdRegions::StdExpansion::DetShapeType(), Blas::Dgemv(), Nektar::StdRegions::eForwards, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::StdRegions::eMass, Nektar::LocalRegions::Expansion2D::GetGeom2D(), Nektar::StdRegions::StdExpansion::GetInteriorMap(), Nektar::StdRegions::StdExpansion::GetPointsType(), Nektar::StdRegions::StdExpansion::GetTraceToElementMap(), Nektar::LibUtilities::Interp1D(), Nektar::StdRegions::StdExpansion::IProductWRTBase(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, m_staticCondMatrixManager, Nektar::StdRegions::StdExpansion::MassMatrixOp(), Nektar::StdRegions::StdExpansion::NumBndryCoeffs(), sign, and Vmath::Vsub().
◆ v_GenMatrix()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 1052 of file TriExp.cpp.
1053{
1054 DNekMatSharedPtr returnval;
1055 switch (mkey.GetMatrixType())
1056 {
1064 returnval = Expansion2D::v_GenMatrix(mkey);
1065 break;
1066 default:
1067 returnval = StdTriExp::v_GenMatrix(mkey);
1068 break;
1069 }
1070
1071 return returnval;
1072}
DNekMatSharedPtr v_GenMatrix(const StdRegions::StdMatrixKey &mkey) override
Definition: Expansion2D.cpp:1256
@ eInvLaplacianWithUnityMean
Definition: StdRegions.hpp:96
References Nektar::StdRegions::eHybridDGHelmBndLam, Nektar::StdRegions::eHybridDGHelmholtz, Nektar::StdRegions::eHybridDGLamToQ0, Nektar::StdRegions::eHybridDGLamToQ1, Nektar::StdRegions::eHybridDGLamToQ2, Nektar::StdRegions::eHybridDGLamToU, Nektar::StdRegions::eInvLaplacianWithUnityMean, Nektar::StdRegions::StdMatrixKey::GetMatrixType(), and Nektar::LocalRegions::Expansion2D::v_GenMatrix().
◆ v_GetCoord()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 659 of file TriExp.cpp.
661{
662 int i;
663
664 ASSERTL1(Lcoords[0] >= -1.0 && Lcoords[1] <= 1.0 && Lcoords[1] >= -1.0 &&
665 Lcoords[1] <= 1.0,
666 "Local coordinates are not in region [-1,1]");
667
668 m_geom->FillGeom();
669
671 {
672 coords[i] = m_geom->GetCoord(i, Lcoords);
673 }
674}
References ASSERTL1, and Nektar::LocalRegions::Expansion::m_geom.
◆ v_GetCoords()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 676 of file TriExp.cpp.
679{
680 Expansion::v_GetCoords(coords_0, coords_1, coords_2);
681}
void v_GetCoords(Array< OneD, NekDouble > &coords_1, Array< OneD, NekDouble > &coords_2, Array< OneD, NekDouble > &coords_3) override
Definition: Expansion.cpp:534
References Nektar::LocalRegions::Expansion::v_GetCoords().
◆ v_GetLinStdExp()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 648 of file TriExp.cpp.
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.
◆ v_GetLocMatrix()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 1084 of file TriExp.cpp.
References m_matrixManager.
◆ v_GetLocStaticCondMatrix()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1094 of file TriExp.cpp.
References m_staticCondMatrixManager.
◆ v_GetStdExp()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 641 of file TriExp.cpp.
642{
643
646}
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and Nektar::StdRegions::StdExpansion::m_base.
◆ v_GetTraceOrient()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 1047 of file TriExp.cpp.
References Nektar::LocalRegions::Expansion2D::GetGeom2D().
◆ v_GetTracePhysMap()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 784 of file TriExp.cpp.
785{
788
789 // Get points in Cartesian orientation
790 switch (edge)
791 {
792 case 0:
793 outarray = Array<OneD, int>(nquad0);
794 for (int i = 0; i < nquad0; ++i)
795 {
796 outarray[i] = i;
797 }
798 break;
799 case 1:
800 outarray = Array<OneD, int>(nquad1);
801 for (int i = 0; i < nquad1; ++i)
802 {
803 outarray[i] = (nquad0 - 1) + i * nquad0;
804 }
805 break;
806 case 2:
807 outarray = Array<OneD, int>(nquad1);
808 for (int i = 0; i < nquad1; ++i)
809 {
810 outarray[i] = i * nquad0;
811 }
812 break;
813 default:
815 break;
816 }
817}
References ASSERTL0, and Nektar::StdRegions::StdExpansion::m_base.
◆ v_GetTracePhysVals()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 718 of file TriExp.cpp.
722{
725 int nt = 0;
726 // Extract in Cartesian direction because we have to deal with
727 // e.g. Gauss-Radau points.
728 switch (edge)
729 {
730 case 0:
731 Vmath::Vcopy(nquad0, &(inarray[0]), 1, &(outarray[0]), 1);
732 nt = nquad0;
733 break;
734 case 1:
735 Vmath::Vcopy(nquad1, &(inarray[0]) + (nquad0 - 1), nquad0,
736 &(outarray[0]), 1);
737 nt = nquad1;
738 break;
739 case 2:
740 Vmath::Vcopy(nquad1, &(inarray[0]), nquad0, &(outarray[0]), 1);
741 nt = nquad1;
742 break;
743 default:
745 break;
746 }
747
748 ASSERTL1(EdgeExp->GetBasis(0)->GetPointsType() ==
750 "Edge expansion should be GLL");
751
752 // Interpolate if required
754 EdgeExp->GetBasis(0)->GetPointsKey())
755 {
756 Array<OneD, NekDouble> outtmp(max(nquad0, nquad1));
757
758 Vmath::Vcopy(nt, outarray, 1, outtmp, 1);
759
761 EdgeExp->GetBasis(0)->GetPointsKey(), outarray);
762 }
763
765 {
766 orient = GetTraceOrient(edge);
767 }
768
769 // Reverse data if necessary
771 {
772 Vmath::Reverse(EdgeExp->GetNumPoints(0), &outarray[0], 1, &outarray[0],
773 1);
774 }
775}
StdRegions::Orientation GetTraceOrient(int trace)
Definition: Expansion.h:168
References ASSERTL0, ASSERTL1, Nektar::StdRegions::eBackwards, Nektar::LibUtilities::eGaussLobattoLegendre, Nektar::StdRegions::eNoOrientation, Nektar::LocalRegions::Expansion::GetTraceOrient(), Nektar::LibUtilities::Interp1D(), Nektar::StdRegions::StdExpansion::m_base, Vmath::Reverse(), and Vmath::Vcopy().
◆ v_GetTraceQFactors()
|
overrideprotectedvirtual |
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 777 of file TriExp.cpp.
References ASSERTL0.
◆ v_HelmholtzMatrixOp()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 1148 of file TriExp.cpp.
1151{
1152 TriExp::HelmholtzMatrixOp_MatFree(inarray, outarray, mkey);
1153}
void HelmholtzMatrixOp_MatFree(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
Definition: StdExpansion.h:1304
References Nektar::StdRegions::StdExpansion::HelmholtzMatrixOp_MatFree().
◆ v_Integral()
|
overrideprotectedvirtual |
Integrates the specified function over the domain.
- See also
- StdRegions::StdExpansion::Integral.
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 71 of file TriExp.cpp.
72{
76 NekDouble ival;
77 Array<OneD, NekDouble> tmp(nquad0 * nquad1);
78
79 // multiply inarray with Jacobian
81 {
82 Vmath::Vmul(nquad0 * nquad1, jac, 1, inarray, 1, tmp, 1);
83 }
84 else
85 {
86 Vmath::Smul(nquad0 * nquad1, jac[0], inarray, 1, tmp, 1);
87 }
88
89 // call StdQuadExp version;
90 ival = StdTriExp::v_Integral(tmp);
91 return ival;
92}
References Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Smul(), and Vmath::Vmul().
◆ v_IProductWRTBase()
|
overrideprotectedvirtual |
Calculate the inner product of inarray with respect to the basis B=base0[p]*base1[pq] and put into outarray.
\( \begin{array}{rcl} I_{pq} = (\phi^A_q \phi^B_{pq}, u) &=& \sum_{i=0}^{nq_0}\sum_{j=0}^{nq_1} \phi^A_p(\eta_{0,i})\phi^B_{pq}(\eta_{1,j}) w^0_i w^1_j u(\xi_{0,i} \xi_{1,j}) \\ & = & \sum_{i=0}^{nq_0} \phi^A_p(\eta_{0,i}) \sum_{j=0}^{nq_1} \phi^B_{pq}(\eta_{1,j}) \tilde{u}_{i,j} \end{array} \)
where
\( \tilde{u}_{i,j} = w^0_i w^1_j u(\xi_{0,i},\xi_{1,j}) \)
which can be implemented as
\( f_{pj} = \sum_{i=0}^{nq_0} \phi^A_p(\eta_{0,i}) \tilde{u}_{i,j} \rightarrow {\bf B_1 U} \) \( I_{pq} = \sum_{j=0}^{nq_1} \phi^B_{pq}(\eta_{1,j}) f_{pj} \rightarrow {\bf B_2[p*skip] f[skip]} \)
Recall: \( \eta_{1} = \frac{2(1+\xi_1)}{(1-\xi_2)}-1, \, \eta_2 = \xi_2\)
Note: For the orthgonality of this expansion to be realised the 'q' ordering must run fastest in contrast to the Quad and Hex ordering where 'p' index runs fastest to be consistent with the quadrature ordering.
In the triangular space the i (i.e. \(\eta_1\) direction) ordering still runs fastest by convention.
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 392 of file TriExp.cpp.
394{
395 IProductWRTBase_SumFac(inarray, outarray);
396}
void IProductWRTBase_SumFac(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool multiplybyweights=true)
Definition: StdExpansion.h:1178
References Nektar::StdRegions::StdExpansion::IProductWRTBase_SumFac().
◆ v_IProductWRTBase_SumFac()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 405 of file TriExp.cpp.
408{
412
413 if (multiplybyweights)
414 {
415 Array<OneD, NekDouble> tmp(nquad0 * nquad1 + nquad1 * order0);
416 Array<OneD, NekDouble> wsp(tmp + nquad0 * nquad1);
417
418 MultiplyByQuadratureMetric(inarray, tmp);
420 m_base[1]->GetBdata(), tmp, outarray, wsp);
421 }
422 else
423 {
424 Array<OneD, NekDouble> wsp(+nquad1 * order0);
425
427 m_base[1]->GetBdata(), inarray, outarray,
428 wsp);
429 }
430}
void IProductWRTBase_SumFacKernel(const Array< OneD, const NekDouble > &base0, const Array< OneD, const NekDouble > &base1, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wsp, bool doCheckCollDir0=true, bool doCheckCollDir1=true)
Definition: StdExpansion2D.cpp:192
References Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, and Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric().
◆ v_IProductWRTDerivBase()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 398 of file TriExp.cpp.
401{
402 IProductWRTDerivBase_SumFac(dir, inarray, outarray);
403}
void IProductWRTDerivBase_SumFac(const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Definition: StdExpansion.h:1229
References Nektar::StdRegions::StdExpansion::IProductWRTDerivBase_SumFac().
◆ v_IProductWRTDerivBase_SumFac()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 432 of file TriExp.cpp.
435{
438 int nqtot = nquad0 * nquad1;
441
442 Array<OneD, NekDouble> tmp0(4 * wspsize);
443 Array<OneD, NekDouble> tmp1(tmp0 + wspsize);
444 Array<OneD, NekDouble> tmp2(tmp0 + 2 * wspsize);
445 Array<OneD, NekDouble> tmp3(tmp0 + 3 * wspsize);
446
447 Array<OneD, Array<OneD, NekDouble>> tmp2D{2};
448 tmp2D[0] = tmp1;
449 tmp2D[1] = tmp2;
450
451 TriExp::v_AlignVectorToCollapsedDir(dir, inarray, tmp2D);
452
453 MultiplyByQuadratureMetric(tmp1, tmp1);
454 MultiplyByQuadratureMetric(tmp2, tmp2);
455
457 tmp1, tmp3, tmp0);
459 tmp2, outarray, tmp0);
461}
void v_AlignVectorToCollapsedDir(const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray) override
Definition: TriExp.cpp:463
References Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), v_AlignVectorToCollapsedDir(), and Vmath::Vadd().
◆ v_IProductWRTDirectionalDerivBase()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 528 of file TriExp.cpp.
532{
533 IProductWRTDirectionalDerivBase_SumFac(direction, inarray, outarray);
534}
void IProductWRTDirectionalDerivBase_SumFac(const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
Definition: StdExpansion.h:1236
References Nektar::StdRegions::StdExpansion::IProductWRTDirectionalDerivBase_SumFac().
◆ v_IProductWRTDirectionalDerivBase_SumFac()
|
overrideprotectedvirtual |
Directinoal Derivative in the modal space in the dir direction of varcoeffs.
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 540 of file TriExp.cpp.
544{
545 int i;
546 int shapedim = 2;
549 int nqtot = nquad0 * nquad1;
552
553 const Array<TwoD, const NekDouble> &df =
555
556 Array<OneD, NekDouble> tmp0(6 * wspsize);
557 Array<OneD, NekDouble> tmp1(tmp0 + wspsize);
558 Array<OneD, NekDouble> tmp2(tmp0 + 2 * wspsize);
559 Array<OneD, NekDouble> tmp3(tmp0 + 3 * wspsize);
560 Array<OneD, NekDouble> gfac0(tmp0 + 4 * wspsize);
561 Array<OneD, NekDouble> gfac1(tmp0 + 5 * wspsize);
562
565
566 // set up geometric factor: 2/(1-z1)
567 for (i = 0; i < nquad1; ++i)
568 {
569 gfac0[i] = 2.0 / (1 - z1[i]);
570 }
571 for (i = 0; i < nquad0; ++i)
572 {
573 gfac1[i] = 0.5 * (1 + z0[i]);
574 }
575 for (i = 0; i < nquad1; ++i)
576 {
577 Vmath::Smul(nquad0, gfac0[i], &inarray[0] + i * nquad0, 1,
578 &tmp0[0] + i * nquad0, 1);
579 }
580 for (i = 0; i < nquad1; ++i)
581 {
582 Vmath::Vmul(nquad0, &gfac1[0], 1, &tmp0[0] + i * nquad0, 1,
583 &tmp1[0] + i * nquad0, 1);
584 }
585
586 // Compute gmat \cdot e^j
587 Array<OneD, Array<OneD, NekDouble>> dfdir(shapedim);
588 Expansion::ComputeGmatcdotMF(df, direction, dfdir);
589
590 Vmath::Vmul(nqtot, &dfdir[0][0], 1, &tmp0[0], 1, &tmp0[0], 1);
591 Vmath::Vmul(nqtot, &dfdir[1][0], 1, &tmp1[0], 1, &tmp1[0], 1);
592 Vmath::Vmul(nqtot, &dfdir[1][0], 1, &inarray[0], 1, &tmp2[0], 1);
593
594 Vmath::Vadd(nqtot, &tmp0[0], 1, &tmp1[0], 1, &tmp1[0], 1);
595
596 MultiplyByQuadratureMetric(tmp1, tmp1);
597 MultiplyByQuadratureMetric(tmp2, tmp2);
598
600 tmp1, tmp3, tmp0);
602 tmp2, outarray, tmp0);
604}
void ComputeGmatcdotMF(const Array< TwoD, const NekDouble > &df, const Array< OneD, const NekDouble > &direction, Array< OneD, Array< OneD, NekDouble > > &dfdir)
Definition: Expansion.cpp:607
References Nektar::LocalRegions::Expansion::ComputeGmatcdotMF(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Nektar::StdRegions::StdExpansion::m_ncoeffs, Nektar::StdRegions::StdExpansion::MultiplyByQuadratureMetric(), Vmath::Smul(), Vmath::Vadd(), and Vmath::Vmul().
◆ v_LaplacianMatrixOp() [1/2]
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 1111 of file TriExp.cpp.
1114{
1115 TriExp::LaplacianMatrixOp_MatFree(inarray, outarray, mkey);
1116}
void LaplacianMatrixOp_MatFree(const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdMatrixKey &mkey)
Definition: StdExpansion.h:1261
References Nektar::StdRegions::StdExpansion::LaplacianMatrixOp_MatFree().
◆ v_LaplacianMatrixOp() [2/2]
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 1118 of file TriExp.cpp.
1122{
1123 StdExpansion::LaplacianMatrixOp_MatFree(k1, k2, inarray, outarray, mkey);
1124}
◆ v_LaplacianMatrixOp_MatFree_Kernel()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1155 of file TriExp.cpp.
1158{
1160 {
1161 ComputeLaplacianMetric();
1162 }
1163
1166 int nqtot = nquad0 * nquad1;
1169 int wspsize =
1170 max(max(max(nqtot, m_ncoeffs), nquad1 * nmodes0), nquad0 * nmodes1);
1171
1173
1178 const Array<OneD, const NekDouble> &metric00 =
1180 const Array<OneD, const NekDouble> &metric01 =
1182 const Array<OneD, const NekDouble> &metric11 =
1184
1185 // Allocate temporary storage
1186 Array<OneD, NekDouble> wsp0(wsp);
1187 Array<OneD, NekDouble> wsp1(wsp + wspsize);
1188 Array<OneD, NekDouble> wsp2(wsp + 2 * wspsize);
1189
1190 StdExpansion2D::PhysTensorDeriv(inarray, wsp1, wsp2);
1191
1192 // wsp0 = k = g0 * wsp1 + g1 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
1193 // wsp2 = l = g1 * wsp1 + g2 * wsp2 = g0 * du_dxi1 + g1 * du_dxi2
1194 // where g0, g1 and g2 are the metric terms set up in the GeomFactors class
1195 // especially for this purpose
1196 Vmath::Vvtvvtp(nqtot, &metric00[0], 1, &wsp1[0], 1, &metric01[0], 1,
1197 &wsp2[0], 1, &wsp0[0], 1);
1198 Vmath::Vvtvvtp(nqtot, &metric01[0], 1, &wsp1[0], 1, &metric11[0], 1,
1199 &wsp2[0], 1, &wsp2[0], 1);
1200
1201 // outarray = m = (D_xi1 * B)^T * k
1202 // wsp1 = n = (D_xi2 * B)^T * l
1203 IProductWRTBase_SumFacKernel(dbase0, base1, wsp0, outarray, wsp1);
1204 IProductWRTBase_SumFacKernel(base0, dbase1, wsp2, wsp1, wsp0);
1205
1206 // outarray = outarray + wsp1
1207 // = L * u_hat
1209 1);
1210}
void ComputeLaplacianMetric()
Definition: Expansion.cpp:453
void Vvtvvtp(int n, const T *v, int incv, const T *w, int incw, const T *x, int incx, const T *y, int incy, T *z, int incz)
vvtvvtp (vector times vector plus vector times vector):
Definition: Vmath.hpp:439
References ASSERTL1, Nektar::LocalRegions::Expansion::ComputeLaplacianMetric(), Nektar::LocalRegions::eMetricLaplacian00, Nektar::LocalRegions::eMetricLaplacian01, Nektar::LocalRegions::eMetricLaplacian11, Nektar::StdRegions::StdExpansion2D::IProductWRTBase_SumFacKernel(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metrics, Nektar::StdRegions::StdExpansion::m_ncoeffs, Vmath::Vadd(), and Vmath::Vvtvvtp().
◆ v_MassLevelCurvatureMatrixOp()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1141 of file TriExp.cpp.
1144{
1145 StdExpansion::MassLevelCurvatureMatrixOp_MatFree(inarray, outarray, mkey);
1146}
◆ v_MassMatrixOp()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 1104 of file TriExp.cpp.
1107{
1108 StdExpansion::MassMatrixOp_MatFree(inarray, outarray, mkey);
1109}
◆ v_NormalTraceDerivFactors()
|
overrideprotectedvirtual |
: This method gets all of the factors which are required as part of the Gradient Jump Penalty stabilisation and involves the product of the normal and geometric factors along the element trace.
Reimplemented from Nektar::LocalRegions::Expansion.
Definition at line 1456 of file TriExp.cpp.
1460{
1463
1464 const Array<TwoD, const NekDouble> &df =
1466
1467 if (d0factors.size() != 3)
1468 {
1469 d0factors = Array<OneD, Array<OneD, NekDouble>>(3);
1470 d1factors = Array<OneD, Array<OneD, NekDouble>>(3);
1471 }
1472
1473 if (d0factors[0].size() != nquad0)
1474 {
1475 d0factors[0] = Array<OneD, NekDouble>(nquad0);
1476 d1factors[0] = Array<OneD, NekDouble>(nquad0);
1477 }
1478
1479 if (d0factors[1].size() != nquad1)
1480 {
1481 d0factors[1] = Array<OneD, NekDouble>(nquad1);
1482 d0factors[2] = Array<OneD, NekDouble>(nquad1);
1483 d1factors[1] = Array<OneD, NekDouble>(nquad1);
1484 d1factors[2] = Array<OneD, NekDouble>(nquad1);
1485 }
1486
1487 // Outwards normals
1488 const Array<OneD, const Array<OneD, NekDouble>> &normal_0 =
1489 GetTraceNormal(0);
1490 const Array<OneD, const Array<OneD, NekDouble>> &normal_1 =
1491 GetTraceNormal(1);
1492 const Array<OneD, const Array<OneD, NekDouble>> &normal_2 =
1493 GetTraceNormal(2);
1494
1495 int ncoords = normal_0.size();
1496
1498 {
1499
1500 // d xi_2/dx n_x
1501 for (int i = 0; i < nquad0; ++i)
1502 {
1503 d1factors[0][i] = df[1][i] * normal_0[0][i];
1504 }
1505
1506 // d xi_1/dx n_x
1507 for (int i = 0; i < nquad1; ++i)
1508 {
1509 d0factors[1][i] = df[0][(i + 1) * nquad0 - 1] * normal_1[0][i];
1510 d0factors[2][i] = df[0][i * nquad0] * normal_2[0][i];
1511 }
1512
1513 for (int n = 1; n < ncoords; ++n)
1514 {
1515 // d xi_2/dy n_y
1516 // needs checking for 3D coords
1517 for (int i = 0; i < nquad0; ++i)
1518 {
1519 d1factors[0][i] += df[2 * n + 1][i] * normal_0[n][i];
1520 }
1521
1522 // d xi_1/dy n_y
1523 // needs checking for 3D coords
1524 for (int i = 0; i < nquad1; ++i)
1525 {
1526 d0factors[1][i] +=
1527 df[2 * n][(i + 1) * nquad0 - 1] * normal_1[n][i];
1528 d0factors[2][i] += df[2 * n][i * nquad0] * normal_2[n][i];
1529 }
1530 }
1531
1532 // d0 factors
1533 // d xi_1/dx n_x
1534 for (int i = 0; i < nquad0; ++i)
1535 {
1536 d0factors[0][i] = df[0][i] * normal_0[0][i];
1537 }
1538
1539 // d xi_2/dx n_x
1540 for (int i = 0; i < nquad1; ++i)
1541 {
1542 d1factors[1][i] = df[1][(i + 1) * nquad0 - 1] * normal_1[0][i];
1543 d1factors[2][i] = df[1][i * nquad0] * normal_2[0][i];
1544 }
1545
1546 for (int n = 1; n < ncoords; ++n)
1547 {
1548 // d xi_1/dy n_y
1549 // needs checking for 3D coords
1550 for (int i = 0; i < nquad0; ++i)
1551 {
1552 d0factors[0][i] += df[2 * n][i] * normal_0[n][i];
1553 }
1554
1555 // d xi_2/dy n_y
1556 // needs checking for 3D coords
1557 for (int i = 0; i < nquad1; ++i)
1558 {
1559 d1factors[1][i] +=
1560 df[2 * n + 1][(i + 1) * nquad0 - 1] * normal_1[n][i];
1561 d1factors[2][i] += df[2 * n + 1][i * nquad0] * normal_2[n][i];
1562 }
1563 }
1564 }
1565 else
1566 {
1567 // d xi_2/dx n_x
1568 for (int i = 0; i < nquad0; ++i)
1569 {
1570 d1factors[0][i] = df[1][0] * normal_0[0][i];
1571 }
1572
1573 // d xi_1/dx n_x
1574 for (int i = 0; i < nquad1; ++i)
1575 {
1576 d0factors[1][i] = df[0][0] * normal_1[0][i];
1577 d0factors[2][i] = df[0][0] * normal_2[0][i];
1578 }
1579
1580 for (int n = 1; n < ncoords; ++n)
1581 {
1582 // d xi_2/dy n_y
1583 // needs checking for 3D coords
1584 for (int i = 0; i < nquad0; ++i)
1585 {
1586 d1factors[0][i] += df[2 * n + 1][0] * normal_0[n][i];
1587 }
1588
1589 // d xi_1/dy n_y
1590 // needs checking for 3D coords
1591 for (int i = 0; i < nquad1; ++i)
1592 {
1593 d0factors[1][i] += df[2 * n][0] * normal_1[n][i];
1594 d0factors[2][i] += df[2 * n][0] * normal_2[n][i];
1595 }
1596 }
1597
1598 // d1factors
1599 // d xi_1/dx n_x
1600 for (int i = 0; i < nquad0; ++i)
1601 {
1602 d0factors[0][i] = df[0][0] * normal_0[0][i];
1603 }
1604
1605 // d xi_2/dx n_x
1606 for (int i = 0; i < nquad1; ++i)
1607 {
1608 d1factors[1][i] = df[1][0] * normal_1[0][i];
1609 d1factors[2][i] = df[1][0] * normal_2[0][i];
1610 }
1611
1612 for (int n = 1; n < ncoords; ++n)
1613 {
1614 // d xi_1/dy n_y
1615 // needs checking for 3D coords
1616 for (int i = 0; i < nquad0; ++i)
1617 {
1618 d0factors[0][i] += df[2 * n][0] * normal_0[n][i];
1619 }
1620
1621 // d xi_2/dy n_y
1622 // needs checking for 3D coords
1623 for (int i = 0; i < nquad1; ++i)
1624 {
1625 d1factors[1][i] += df[2 * n + 1][0] * normal_1[n][i];
1626 d1factors[2][i] += df[2 * n + 1][0] * normal_2[n][i];
1627 }
1628 }
1629 }
1630}
const NormalVector & GetTraceNormal(const int id)
Definition: Expansion.cpp:251
References Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetNumPoints(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::LocalRegions::Expansion::GetTraceNormal(), and Nektar::LocalRegions::Expansion::m_metricinfo.
◆ v_NormVectorIProductWRTBase() [1/2]
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 634 of file TriExp.cpp.
637{
638 NormVectorIProductWRTBase(Fvec[0], Fvec[1], Fvec[2], outarray);
639}
void NormVectorIProductWRTBase(const Array< OneD, const NekDouble > &Fx, Array< OneD, NekDouble > &outarray)
Definition: StdExpansion.h:622
References Nektar::StdRegions::StdExpansion::NormVectorIProductWRTBase().
◆ v_NormVectorIProductWRTBase() [2/2]
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 606 of file TriExp.cpp.
610{
612 Array<OneD, NekDouble> Fn(nq);
613
614 const Array<OneD, const Array<OneD, NekDouble>> &normals =
615 GetLeftAdjacentElementExp()->GetTraceNormal(
616 GetLeftAdjacentElementTrace());
617
619 {
620 Vmath::Vvtvvtp(nq, &normals[0][0], 1, &Fx[0], 1, &normals[1][0], 1,
621 &Fy[0], 1, &Fn[0], 1);
622 Vmath::Vvtvp(nq, &normals[2][0], 1, &Fz[0], 1, &Fn[0], 1, &Fn[0], 1);
623 }
624 else
625 {
626 Vmath::Svtsvtp(nq, normals[0][0], &Fx[0], 1, normals[1][0], &Fy[0], 1,
627 &Fn[0], 1);
628 Vmath::Svtvp(nq, normals[2][0], &Fz[0], 1, &Fn[0], 1, &Fn[0], 1);
629 }
630
631 IProductWRTBase(Fn, outarray);
632}
ExpansionSharedPtr GetLeftAdjacentElementExp() const
Definition: Expansion.h:441
int GetLeftAdjacentElementTrace() const
Definition: Expansion.h:454
void Svtsvtp(int n, const T alpha, const T *x, int incx, const T beta, const T *y, int incy, T *z, int incz)
Svtsvtp (scalar times vector plus scalar times vector):
Definition: Vmath.hpp:473
References Nektar::SpatialDomains::eDeformed, Nektar::LocalRegions::Expansion::GetLeftAdjacentElementExp(), Nektar::LocalRegions::Expansion::GetLeftAdjacentElementTrace(), Nektar::StdRegions::StdExpansion::IProductWRTBase(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Svtsvtp(), Vmath::Svtvp(), Vmath::Vvtvp(), and Vmath::Vvtvvtp().
◆ v_PhysDeriv() [1/2]
|
overrideprotectedvirtual |
Calculate the derivative of the physical points.
\( \frac{\partial u}{\partial x_1} = \left . \frac{2.0}{1-\eta_2} \frac{\partial u}{\partial d\eta_1} \right |_{\eta_2}\)
\( \frac{\partial u}{\partial x_2} = \left . \frac{1+\eta_1}{1-\eta_2} \frac{\partial u}{\partial d\eta_1} \right |_{\eta_2} + \left . \frac{\partial u}{\partial d\eta_2} \right |_{\eta_1} \)
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 94 of file TriExp.cpp.
98{
101 int nqtot = nquad0 * nquad1;
102 const Array<TwoD, const NekDouble> &df =
104
105 Array<OneD, NekDouble> diff0(2 * nqtot);
106 Array<OneD, NekDouble> diff1(diff0 + nqtot);
107
108 StdTriExp::v_PhysDeriv(inarray, diff0, diff1);
109
111 {
112 if (out_d0.size())
113 {
114 Vmath::Vmul(nqtot, df[0], 1, diff0, 1, out_d0, 1);
115 Vmath::Vvtvp(nqtot, df[1], 1, diff1, 1, out_d0, 1, out_d0, 1);
116 }
117
118 if (out_d1.size())
119 {
120 Vmath::Vmul(nqtot, df[2], 1, diff0, 1, out_d1, 1);
121 Vmath::Vvtvp(nqtot, df[3], 1, diff1, 1, out_d1, 1, out_d1, 1);
122 }
123
124 if (out_d2.size())
125 {
126 Vmath::Vmul(nqtot, df[4], 1, diff0, 1, out_d2, 1);
127 Vmath::Vvtvp(nqtot, df[5], 1, diff1, 1, out_d2, 1, out_d2, 1);
128 }
129 }
130 else // regular geometry
131 {
132 if (out_d0.size())
133 {
134 Vmath::Smul(nqtot, df[0][0], diff0, 1, out_d0, 1);
135 Blas::Daxpy(nqtot, df[1][0], diff1, 1, out_d0, 1);
136 }
137
138 if (out_d1.size())
139 {
140 Vmath::Smul(nqtot, df[2][0], diff0, 1, out_d1, 1);
141 Blas::Daxpy(nqtot, df[3][0], diff1, 1, out_d1, 1);
142 }
143
144 if (out_d2.size())
145 {
146 Vmath::Smul(nqtot, df[4][0], diff0, 1, out_d2, 1);
147 Blas::Daxpy(nqtot, df[5][0], diff1, 1, out_d2, 1);
148 }
149 }
150}
static void Daxpy(const int &n, const double &alpha, const double *x, const int &incx, const double *y, const int &incy)
BLAS level 1: y = alpha x plus y.
Definition: Blas.hpp:135
References Blas::Daxpy(), Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Smul(), Vmath::Vmul(), and Vmath::Vvtvp().
◆ v_PhysDeriv() [2/2]
|
overrideprotectedvirtual |
Calculate the derivative of the physical points in a given direction.
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 152 of file TriExp.cpp.
155{
156 switch (dir)
157 {
158 case 0:
159 {
161 NullNekDouble1DArray);
162 }
163 break;
164 case 1:
165 {
167 NullNekDouble1DArray);
168 }
169 break;
170 case 2:
171 {
173 outarray);
174 }
175 break;
176 default:
177 {
179 }
180 break;
181 }
182}
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)
Definition: StdExpansion.h:858
static Array< OneD, NekDouble > NullNekDouble1DArray
Definition: BasicUtils/SharedArray.hpp:919
References ASSERTL1, Nektar::NullNekDouble1DArray, and Nektar::StdRegions::StdExpansion::PhysDeriv().
◆ v_PhysDirectionalDeriv()
|
overrideprotectedvirtual |
Physical derivative along a direction vector.
D_v = D^v_xi * du/d_xi + D^v_eta * du/d_eta
D_v = D^v_xi * du/d_xi + D^v_eta * du/d_eta
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 184 of file TriExp.cpp.
187{
188 if (!out.size())
189 {
190 return;
191 }
192
195 int nqtot = nquad0 * nquad1;
196
197 const Array<TwoD, const NekDouble> &df =
199
200 Array<OneD, NekDouble> diff0(2 * nqtot);
201 Array<OneD, NekDouble> diff1(diff0 + nqtot);
202
203 // diff0 = du/d_xi, diff1 = du/d_eta
204 StdTriExp::v_PhysDeriv(inarray, diff0, diff1);
205
207 {
208 Array<OneD, Array<OneD, NekDouble>> tangmat(2);
209
210 // D^v_xi = v_x*d_xi/dx + v_y*d_xi/dy + v_z*d_xi/dz
211 // D^v_eta = v_x*d_eta/dx + v_y*d_eta/dy + v_z*d_eta/dz
212 for (int i = 0; i < 2; ++i)
213 {
214 tangmat[i] = Array<OneD, NekDouble>(nqtot, 0.0);
216 {
217 Vmath::Vvtvp(nqtot, &df[2 * k + i][0], 1, &direction[k * nqtot],
218 1, &tangmat[i][0], 1, &tangmat[i][0], 1);
219 }
220 }
221
222 /// D_v = D^v_xi * du/d_xi + D^v_eta * du/d_eta
223 Vmath::Vmul(nqtot, &tangmat[0][0], 1, &diff0[0], 1, &out[0], 1);
224 Vmath::Vvtvp(nqtot, &tangmat[1][0], 1, &diff1[0], 1, &out[0], 1,
225 &out[0], 1);
226 }
227 else
228 {
229 Array<OneD, Array<OneD, NekDouble>> tangmat(2);
230
231 for (int i = 0; i < 2; ++i)
232 {
233 tangmat[i] = Array<OneD, NekDouble>(nqtot, 0.0);
235 {
236 Vmath::Svtvp(nqtot, df[2 * k + i][0], &direction[k * nqtot], 1,
237 &tangmat[i][0], 1, &tangmat[i][0], 1);
238 }
239 }
240
241 /// D_v = D^v_xi * du/d_xi + D^v_eta * du/d_eta
242 Vmath::Vmul(nqtot, &tangmat[0][0], 1, &diff0[0], 1, &out[0], 1);
243
244 Vmath::Vvtvp(nqtot, &tangmat[1][0], 1, &diff1[0], 1, &out[0], 1,
245 &out[0], 1);
246 }
247}
References Nektar::SpatialDomains::eDeformed, Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::m_base, Nektar::LocalRegions::Expansion::m_geom, Nektar::LocalRegions::Expansion::m_metricinfo, Vmath::Svtvp(), Vmath::Vmul(), and Vmath::Vvtvp().
◆ v_PhysEvalFirstDeriv()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 707 of file TriExp.cpp.
711{
712 Array<OneD, NekDouble> Lcoord(2);
714 m_geom->GetLocCoords(coord, Lcoord);
715 return StdTriExp::v_PhysEvalFirstDeriv(Lcoord, inarray, firstOrderDerivs);
716}
References ASSERTL0, and Nektar::LocalRegions::Expansion::m_geom.
◆ v_PhysEvaluate()
|
overrideprotectedvirtual |
This function evaluates the expansion at a single (arbitrary) point of the domain.
This function is a wrapper around the virtual function v_PhysEvaluate()
Based on the value of the expansion at the quadrature points, this function calculates the value of the expansion at an arbitrary single points (with coordinates \( \mathbf{x_c}\) given by the pointer coords). This operation, equivalent to
\[ u(\mathbf{x_c}) = \sum_p \phi_p(\mathbf{x_c}) \hat{u}_p \]
is evaluated using Lagrangian interpolants through the quadrature points:
\[ u(\mathbf{x_c}) = \sum_p h_p(\mathbf{x_c}) u_p\]
This function requires that the physical value array \(\mathbf{u}\) (implemented as the attribute #m_phys) is set.
- Parameters
-
coords the coordinates of the single point
- Returns
- returns the value of the expansion at the single point
Reimplemented from Nektar::StdRegions::StdExpansion2D.
Definition at line 696 of file TriExp.cpp.
698{
699 Array<OneD, NekDouble> Lcoord = Array<OneD, NekDouble>(2);
700
702 m_geom->GetLocCoords(coord, Lcoord);
703
704 return StdExpansion2D::v_PhysEvaluate(Lcoord, physvals);
705}
References ASSERTL0, and Nektar::LocalRegions::Expansion::m_geom.
◆ v_ReduceOrderCoeffs()
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overrideprotectedvirtual |
Function is used to compute exactly the advective numerical flux on theinterface of two elements with different expansions, hence an appropriate number of Gauss points has to be used. The number of Gauss points has to be equal to the number used by the highest polynomial degree of the two adjacent elements. Furthermore, this function is used to compute the sensor value in each element.
- Parameters
-
numMin Is the reduced polynomial order inarray Input array of coefficients dumpVar Output array of reduced coefficients.
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 1368 of file TriExp.cpp.
1371{
1372 int n_coeffs = inarray.size();
1375 int nqtot = nquad0 * nquad1;
1378 int numMin2 = nmodes0, i;
1379
1380 Array<OneD, NekDouble> coeff(n_coeffs, 0.0);
1381 Array<OneD, NekDouble> phys_tmp(nqtot, 0.0);
1382 Array<OneD, NekDouble> tmp, tmp2;
1383
1386
1389 LibUtilities::BasisKey bortho0(LibUtilities::eOrtho_A, nmodes0, Pkey0);
1390 LibUtilities::BasisKey bortho1(LibUtilities::eOrtho_B, nmodes1, Pkey1);
1391
1392 // Check if it is also possible to use the same InterCoeff routine
1393 // which is also used for Quadrilateral and Hexagonal shaped
1394 // elements
1395
1396 // For now, set up the used basis on the standard element to
1397 // calculate the phys values, set up the orthogonal basis to do a
1398 // forward transform, to obtain the coefficients in orthogonal
1399 // coefficient space
1400 StdRegions::StdTriExpSharedPtr m_OrthoTriExp;
1401 StdRegions::StdTriExpSharedPtr m_TriExp;
1402
1403 m_TriExp = MemoryManager<StdRegions::StdTriExp>::AllocateSharedPtr(b0, b1);
1404 m_OrthoTriExp = MemoryManager<StdRegions::StdTriExp>::AllocateSharedPtr(
1405 bortho0, bortho1);
1406
1407 m_TriExp->BwdTrans(inarray, phys_tmp);
1408 m_OrthoTriExp->FwdTrans(phys_tmp, coeff);
1409
1410 for (i = 0; i < n_coeffs; i++)
1411 {
1412 if (i == numMin)
1413 {
1414 coeff[i] = 0.0;
1415 numMin += numMin2 - 1;
1416 numMin2 -= 1.0;
1417 }
1418 }
1419
1420 m_OrthoTriExp->BwdTrans(coeff, phys_tmp);
1421 m_TriExp->FwdTrans(phys_tmp, outarray);
1422}
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::LibUtilities::eOrtho_A, Nektar::LibUtilities::eOrtho_B, Nektar::StdRegions::StdExpansion::GetBasisType(), and Nektar::StdRegions::StdExpansion::m_base.
◆ v_StdPhysEvaluate()
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overrideprotectedvirtual |
Given the local cartesian coordinate Lcoord evaluate the value of physvals at this point by calling through to the StdExpansion method
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 688 of file TriExp.cpp.
691{
692 // Evaluate point in local (eta) coordinates.
693 return StdExpansion2D::v_PhysEvaluate(Lcoord, physvals);
694}
◆ v_SVVLaplacianFilter()
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 1424 of file TriExp.cpp.
1426{
1428
1429 // Calculate sqrt of the Jacobian
1431 Array<OneD, NekDouble> sqrt_jac(nq);
1433 {
1434 Vmath::Vsqrt(nq, jac, 1, sqrt_jac, 1);
1435 }
1436 else
1437 {
1439 }
1440
1441 // Multiply array by sqrt(Jac)
1442 Vmath::Vmul(nq, sqrt_jac, 1, array, 1, array, 1);
1443
1444 // Apply std region filter
1445 StdTriExp::v_SVVLaplacianFilter(array, mkey);
1446
1447 // Divide by sqrt(Jac)
1448 Vmath::Vdiv(nq, array, 1, sqrt_jac, 1, array, 1);
1449}
void Vdiv(int n, const T *x, const int incx, const T *y, const int incy, T *z, const int incz)
Multiply vector z = x/y.
Definition: Vmath.hpp:126
References Nektar::SpatialDomains::eDeformed, Vmath::Fill(), Nektar::StdRegions::StdExpansion::GetPointsKeys(), Nektar::StdRegions::StdExpansion::GetTotPoints(), Nektar::LocalRegions::Expansion::m_metricinfo, tinysimd::sqrt(), Vmath::Vdiv(), Vmath::Vmul(), and Vmath::Vsqrt().
◆ v_WeakDerivMatrixOp()
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overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdTriExp.
Definition at line 1126 of file TriExp.cpp.
1130{
1131 StdExpansion::WeakDerivMatrixOp_MatFree(i, inarray, outarray, mkey);
1132}
◆ v_WeakDirectionalDerivMatrixOp()
|
overrideprotectedvirtual |
Reimplemented from Nektar::StdRegions::StdExpansion.
Definition at line 1134 of file TriExp.cpp.
1137{
1138 StdExpansion::WeakDirectionalDerivMatrixOp_MatFree(inarray, outarray, mkey);
1139}
Member Data Documentation
◆ m_matrixManager
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private |
Definition at line 245 of file TriExp.h.
Referenced by v_DropLocMatrix(), v_FwdTrans(), and v_GetLocMatrix().
◆ m_staticCondMatrixManager
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private |
Definition at line 247 of file TriExp.h.
Referenced by v_DropLocStaticCondMatrix(), v_FwdTransBndConstrained(), and v_GetLocStaticCondMatrix().
