Abstraction of a global continuous one-dimensional spectral/hp element expansion which approximates the solution of a set of partial differential equations. More...
#include <ContField1D.h>
Public Member Functions | |
| ContField1D () | |
| Default constructor. More... | |
| ContField1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const std::string &variable="DefaultVar", const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| Set up global continuous field based on an input mesh and boundary conditions. More... | |
| ContField1D (const ContField1D &In) | |
| Copy constructor. More... | |
| ContField1D (const LibUtilities::SessionReaderSharedPtr &pSession, const ExpList1D &In) | |
| Copy constructor. More... | |
| virtual | ~ContField1D () |
| Destructor. More... | |
| void | FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| Perform global forward transformation of a function \(f(x)\),. More... | |
| void | BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| This function performs the backward transformation of the spectral/hp element expansion. More... | |
| void | MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| const Array< OneD, const MultiRegions::ExpListSharedPtr > & | GetBndCondExpansions () |
| Return the boundary conditions expansion. More... | |
| const Array< OneD, const SpatialDomains ::BoundaryConditionShPtr > & | GetBndConditions () |
| void | Assemble () |
| Assembles the global coefficients \(\boldsymbol{\hat{u}}_g\) from the local coefficients \(\boldsymbol{\hat{u}}_l\). More... | |
| void | Assemble (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| Assembles the global coefficients \(\boldsymbol{\hat{u}}_g\) from the local coefficients \(\boldsymbol{\hat{u}}_l\). More... | |
| const AssemblyMapCGSharedPtr & | GetLocalToGlobalMap () const |
| Returns the map from local to global level. More... | |
| void | IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| Calculates the inner product of a function \(f(x)\) with respect to all global expansion modes \(\phi_n^e(x)\). More... | |
| void | GeneralMatrixOp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| Calculates the result of the multiplication of a global matrix of type specified by mkey with a vector given by inarray. More... | |
 Public Member Functions inherited from Nektar::MultiRegions::DisContField1D | |
| DisContField1D () | |
| Default constructor. More... | |
| DisContField1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const std::string &variable, const bool SetUpJustDG=true, const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| Constructs a 1D discontinuous field based on a mesh and boundary conditions. More... | |
| DisContField1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::CompositeMap &domain, const SpatialDomains::BoundaryConditions &Allbcs, const std::string &variable, bool SetToOneSpaceDimensions=false, const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| Constructor for a DisContField1D from a List of subdomains New Constructor for arterial network. More... | |
| DisContField1D (const DisContField1D &In) | |
| Constructs a 1D discontinuous field based on an existing field. More... | |
| DisContField1D (const ExpList1D &In) | |
| Constructs a 1D discontinuous field based on an existing field. (needed in order to use ContField( const ExpList1D &In) constructor. More... | |
| virtual | ~DisContField1D () |
| Destructor. More... | |
| GlobalLinSysSharedPtr | GetGlobalBndLinSys (const GlobalLinSysKey &mkey) |
| For a given key, returns the associated global linear system. More... | |
| std::vector< bool > & | GetNegatedFluxNormal (void) |
| Public Member Functions inherited from Nektar::MultiRegions::ExpList1D | |
| ExpList1D () | |
| The default constructor. More... | |
| ExpList1D (const ExpList1D &In, const bool DeclareCoeffPhysArrays=true) | |
| The copy constructor. More... | |
| ExpList1D (const ExpList1D &In, const std::vector< unsigned int > &eIDs, const bool DeclareCoeffPhysArrays=true, const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| Constructor copying only elements defined in eIds. More... | |
| ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const LibUtilities::BasisKey &Ba, const SpatialDomains::MeshGraphSharedPtr &graph1D, const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| Construct an ExpList1D from a given graph. More... | |
| ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const bool DeclareCoeffPhysArrays=true, const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| This constructor sets up a list of local expansions based on an input graph1D. More... | |
| ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::CompositeMap &domain, const bool DeclareCoeffPhysArrays=true, const std::string var="DefaultVar", bool SetToOneSpaceDimension=false, const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| This constructor sets up a list of local expansions based on an input compositeMap. More... | |
| ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::CompositeMap &domain, const SpatialDomains::MeshGraphSharedPtr &graph2D, const bool DeclareCoeffPhysArrays=true, const std::string variable="DefaultVar", const LibUtilities::CommSharedPtr comm=LibUtilities::CommSharedPtr(), const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| Specialised constructor for Neumann boundary conditions in DisContField2D and ContField2D. More... | |
| ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::CompositeMap &domain, const SpatialDomains::MeshGraphSharedPtr &graph1D, int i, const bool DeclareCoeffPhysArrays=true, const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const Array< OneD, const ExpListSharedPtr > &bndConstraint, const Array< OneD, const SpatialDomains ::BoundaryConditionShPtr > &bndCond, const LocalRegions::ExpansionVector &locexp, const SpatialDomains::MeshGraphSharedPtr &graph2D, const PeriodicMap &periodicEdges, const bool DeclareCoeffPhysArrays=true, const std::string variable="DefaultVar", const Collections::ImplementationType ImpType=Collections::eNoImpType) | |
| Specialised constructor for trace expansions. More... | |
| virtual | ~ExpList1D () |
| Destructor. More... | |
| void | PostProcess (LibUtilities::KernelSharedPtr kernel, Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray, NekDouble h, int elmId=0) |
| Performs the post-processing on a specified element. More... | |
| void | PeriodicEval (Array< OneD, NekDouble > &inarray1, Array< OneD, NekDouble > &inarray2, NekDouble h, int nmodes, Array< OneD, NekDouble > &outarray) |
| Evaluates the global spectral/hp expansion at some arbitray set of points. More... | |
| void | ParNormalSign (Array< OneD, NekDouble > &normsign) |
| Set up the normals on each expansion. More... | |
| Public Member Functions inherited from Nektar::MultiRegions::ExpList | |
| ExpList () | |
| The default constructor. More... | |
| ExpList (const LibUtilities::SessionReaderSharedPtr &pSession) | |
| The default constructor. More... | |
| ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph) | |
| The default constructor. More... | |
| ExpList (const ExpList &in, const std::vector< unsigned int > &eIDs, const bool DeclareCoeffPhysArrays=true) | |
| Constructor copying only elements defined in eIds. More... | |
| ExpList (const ExpList &in, const bool DeclareCoeffPhysArrays=true) | |
| The copy constructor. More... | |
| virtual | ~ExpList () |
| The default destructor. More... | |
| int | GetNcoeffs (void) const |
| Returns the total number of local degrees of freedom \(N_{\mathrm{eof}}=\sum_{e=1}^{{N_{\mathrm{el}}}}N^{e}_m\). More... | |
| int | GetNcoeffs (const int eid) const |
| Returns the total number of local degrees of freedom for element eid. More... | |
| ExpansionType | GetExpType (void) |
| Returns the type of the expansion. More... | |
| void | SetExpType (ExpansionType Type) |
| Returns the type of the expansion. More... | |
| int | EvalBasisNumModesMax (void) const |
| Evaulates the maximum number of modes in the elemental basis order over all elements. More... | |
| const Array< OneD, int > | EvalBasisNumModesMaxPerExp (void) const |
| Returns the vector of the number of modes in the elemental basis order over all elements. More... | |
| int | GetTotPoints (void) const |
| Returns the total number of quadrature points m_npoints \(=Q_{\mathrm{tot}}\). More... | |
| int | GetTotPoints (const int eid) const |
| Returns the total number of quadrature points for eid's element \(=Q_{\mathrm{tot}}\). More... | |
| int | GetNpoints (void) const |
| Returns the total number of quadrature points m_npoints \(=Q_{\mathrm{tot}}\). More... | |
| int | Get1DScaledTotPoints (const NekDouble scale) const |
| Returns the total number of qudature points scaled by the factor scale on each 1D direction. More... | |
| void | SetWaveSpace (const bool wavespace) |
| Sets the wave space to the one of the possible configuration true or false. More... | |
| void | SetModifiedBasis (const bool modbasis) |
| Set Modified Basis for the stability analysis. More... | |
| void | SetPhys (int i, NekDouble val) |
| Set the i th value of m_phys to value val. More... | |
| bool | GetWaveSpace (void) const |
| This function returns the third direction expansion condition, which can be in wave space (coefficient) or not It is stored in the variable m_WaveSpace. More... | |
| void | SetPhys (const Array< OneD, const NekDouble > &inarray) |
| Fills the array m_phys. More... | |
| void | SetPhysArray (Array< OneD, NekDouble > &inarray) |
| Sets the array m_phys. More... | |
| void | SetPhysState (const bool physState) |
| This function manually sets whether the array of physical values \(\boldsymbol{u}_l\) (implemented as m_phys) is filled or not. More... | |
| bool | GetPhysState (void) const |
| This function indicates whether the array of physical values \(\boldsymbol{u}_l\) (implemented as m_phys) is filled or not. More... | |
| NekDouble | PhysIntegral (void) |
| This function integrates a function \(f(\boldsymbol{x})\) over the domain consisting of all the elements of the expansion. More... | |
| NekDouble | PhysIntegral (const Array< OneD, const NekDouble > &inarray) |
| This function integrates a function \(f(\boldsymbol{x})\) over the domain consisting of all the elements of the expansion. More... | |
| void | IProductWRTBase_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| This function calculates the inner product of a function \(f(\boldsymbol{x})\) with respect to all local expansion modes \(\phi_n^e(\boldsymbol{x})\). More... | |
| void | IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| void | IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| This function calculates the inner product of a function \(f(\boldsymbol{x})\) with respect to the derivative (in direction. More... | |
| void | IProductWRTDirectionalDerivBase (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| Directional derivative along a given direction. More... | |
| void | IProductWRTDerivBase (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, NekDouble > &outarray) |
| This function calculates the inner product of a function \(f(\boldsymbol{x})\) with respect to the derivative (in direction. More... | |
| void | FwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| This function elementally evaluates the forward transformation of a function \(u(\boldsymbol{x})\) onto the global spectral/hp expansion. More... | |
| void | FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| void | ExponentialFilter (Array< OneD, NekDouble > &array, const NekDouble alpha, const NekDouble exponent, const NekDouble cutoff) |
| void | MultiplyByElmtInvMass (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| This function elementally mulplies the coefficient space of Sin my the elemental inverse of the mass matrix. More... | |
| void | MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| void | SmoothField (Array< OneD, NekDouble > &field) |
| Smooth a field across elements. More... | |
| void | HelmSolve (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const FlagList &flags, const StdRegions::ConstFactorMap &factors, const StdRegions::VarCoeffMap &varcoeff=StdRegions::NullVarCoeffMap, const MultiRegions::VarFactorsMap &varfactors=MultiRegions::NullVarFactorsMap, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray, const bool PhysSpaceForcing=true) |
| Solve helmholtz problem. More... | |
| void | LinearAdvectionDiffusionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray) |
| Solve Advection Diffusion Reaction. More... | |
| void | LinearAdvectionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray) |
| Solve Advection Diffusion Reaction. More... | |
| void | FwdTrans_BndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| void | BwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| This function elementally evaluates the backward transformation of the global spectral/hp element expansion. More... | |
| void | BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| void | GetCoords (Array< OneD, NekDouble > &coord_0, Array< OneD, NekDouble > &coord_1=NullNekDouble1DArray, Array< OneD, NekDouble > &coord_2=NullNekDouble1DArray) |
| This function calculates the coordinates of all the elemental quadrature points \(\boldsymbol{x}_i\). More... | |
| void | HomogeneousFwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true) |
| void | HomogeneousBwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true) |
| void | DealiasedProd (const Array< OneD, NekDouble > &inarray1, const Array< OneD, NekDouble > &inarray2, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| void | DealiasedDotProd (const Array< OneD, Array< OneD, NekDouble > > &inarray1, const Array< OneD, Array< OneD, NekDouble > > &inarray2, Array< OneD, Array< OneD, NekDouble > > &outarray, CoeffState coeffstate=eLocal) |
| void | GetBCValues (Array< OneD, NekDouble > &BndVals, const Array< OneD, NekDouble > &TotField, int BndID) |
| void | NormVectorIProductWRTBase (Array< OneD, const NekDouble > &V1, Array< OneD, const NekDouble > &V2, Array< OneD, NekDouble > &outarray, int BndID) |
| void | NormVectorIProductWRTBase (Array< OneD, Array< OneD, NekDouble > > &V, Array< OneD, NekDouble > &outarray) |
| void | ApplyGeomInfo () |
| Apply geometry information to each expansion. More... | |
| void | Reset () |
| Reset geometry information and reset matrices. More... | |
| void | WriteTecplotHeader (std::ostream &outfile, std::string var="") |
| void | WriteTecplotZone (std::ostream &outfile, int expansion=-1) |
| void | WriteTecplotField (std::ostream &outfile, int expansion=-1) |
| void | WriteTecplotConnectivity (std::ostream &outfile, int expansion=-1) |
| void | WriteVtkHeader (std::ostream &outfile) |
| void | WriteVtkFooter (std::ostream &outfile) |
| void | WriteVtkPieceHeader (std::ostream &outfile, int expansion, int istrip=0) |
| void | WriteVtkPieceFooter (std::ostream &outfile, int expansion) |
| void | WriteVtkPieceData (std::ostream &outfile, int expansion, std::string var="v") |
| int | GetCoordim (int eid) |
| This function returns the dimension of the coordinates of the element eid. More... | |
| void | SetCoeff (int i, NekDouble val) |
| Set the i th coefficiient in m_coeffs to value val. More... | |
| void | SetCoeffs (int i, NekDouble val) |
| Set the i th coefficiient in m_coeffs to value val. More... | |
| void | SetCoeffsArray (Array< OneD, NekDouble > &inarray) |
| Set the m_coeffs array to inarray. More... | |
| int | GetShapeDimension () |
| This function returns the dimension of the shape of the element eid. More... | |
| const Array< OneD, const NekDouble > & | GetCoeffs () const |
| This function returns (a reference to) the array \(\boldsymbol{\hat{u}}_l\) (implemented as m_coeffs) containing all local expansion coefficients. More... | |
| void | ImposeDirichletConditions (Array< OneD, NekDouble > &outarray) |
| Impose Dirichlet Boundary Conditions onto Array. More... | |
| void | FillBndCondFromField (void) |
| Fill Bnd Condition expansion from the values stored in expansion. More... | |
| void | FillBndCondFromField (const int nreg) |
| Fill Bnd Condition expansion in nreg from the values stored in expansion. More... | |
| void | LocalToGlobal (bool useComm=true) |
| Gathers the global coefficients \(\boldsymbol{\hat{u}}_g\) from the local coefficients \(\boldsymbol{\hat{u}}_l\). More... | |
| void | LocalToGlobal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool useComm=true) |
| void | GlobalToLocal (void) |
| Scatters from the global coefficients \(\boldsymbol{\hat{u}}_g\) to the local coefficients \(\boldsymbol{\hat{u}}_l\). More... | |
| void | GlobalToLocal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| NekDouble | GetCoeff (int i) |
| Get the i th value (coefficient) of m_coeffs. More... | |
| NekDouble | GetCoeffs (int i) |
| Get the i th value (coefficient) of m_coeffs. More... | |
| const Array< OneD, const NekDouble > & | GetPhys () const |
| This function returns (a reference to) the array \(\boldsymbol{u}_l\) (implemented as m_phys) containing the function \(u^{\delta}(\boldsymbol{x})\) evaluated at the quadrature points. More... | |
| NekDouble | Linf (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray) |
| This function calculates the \(L_\infty\) error of the global spectral/hp element approximation. More... | |
| NekDouble | L2 (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray) |
| This function calculates the \(L_2\) error with respect to soln of the global spectral/hp element approximation. More... | |
| NekDouble | H1 (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray) |
| Calculates the \(H^1\) error of the global spectral/hp element approximation. More... | |
| NekDouble | Integral (const Array< OneD, const NekDouble > &inarray) |
| NekDouble | VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &inarray) |
| Array< OneD, const NekDouble > | HomogeneousEnergy (void) |
| This function calculates the energy associated with each one of the modesof a 3D homogeneous nD expansion. More... | |
| void | SetHomo1DSpecVanVisc (Array< OneD, NekDouble > visc) |
| This function sets the Spectral Vanishing Viscosity in homogeneous1D expansion. More... | |
| Array< OneD, const unsigned int > | GetZIDs (void) |
| This function returns a vector containing the wave numbers in z-direction associated with the 3D homogenous expansion. Required if a parellelisation is applied in the Fourier direction. More... | |
| LibUtilities::TranspositionSharedPtr | GetTransposition (void) |
| This function returns the transposition class associaed with the homogeneous expansion. More... | |
| NekDouble | GetHomoLen (void) |
| This function returns the Width of homogeneous direction associaed with the homogeneous expansion. More... | |
| void | SetHomoLen (const NekDouble lhom) |
| This function sets the Width of homogeneous direction associaed with the homogeneous expansion. More... | |
| Array< OneD, const unsigned int > | GetYIDs (void) |
| This function returns a vector containing the wave numbers in y-direction associated with the 3D homogenous expansion. Required if a parellelisation is applied in the Fourier direction. More... | |
| void | PhysInterp1DScaled (const NekDouble scale, const Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| This function interpolates the physical space points in inarray to outarray using the same points defined in the expansion but where the number of points are rescaled by 1DScale. More... | |
| void | PhysGalerkinProjection1DScaled (const NekDouble scale, const Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| This function Galerkin projects the physical space points in inarray to outarray where inarray is assumed to be defined in the expansion but where the number of points are rescaled by 1DScale. More... | |
| int | GetExpSize (void) |
| This function returns the number of elements in the expansion. More... | |
| int | GetNumElmts (void) |
| This function returns the number of elements in the expansion which may be different for a homogeoenous extended expansionp. More... | |
| const std::shared_ptr< LocalRegions::ExpansionVector > | GetExp () const |
| This function returns the vector of elements in the expansion. More... | |
| LocalRegions::ExpansionSharedPtr & | GetExp (int n) const |
| This function returns (a shared pointer to) the local elemental expansion of the \(n^{\mathrm{th}}\) element. More... | |
| LocalRegions::ExpansionSharedPtr & | GetExp (const Array< OneD, const NekDouble > &gloCoord) |
| This function returns (a shared pointer to) the local elemental expansion containing the arbitrary point given by gloCoord. More... | |
| int | GetExpIndex (const Array< OneD, const NekDouble > &gloCoord, NekDouble tol=0.0, bool returnNearestElmt=false) |
| int | GetExpIndex (const Array< OneD, const NekDouble > &gloCoords, Array< OneD, NekDouble > &locCoords, NekDouble tol=0.0, bool returnNearestElmt=false) |
| NekDouble | PhysEvaluate (const Array< OneD, const NekDouble > &coords, const Array< OneD, const NekDouble > &phys) |
| int | GetCoeff_Offset (int n) const |
| Get the start offset position for a global list of m_coeffs correspoinding to element n. More... | |
| int | GetPhys_Offset (int n) const |
| Get the start offset position for a global list of m_phys correspoinding to element n. More... | |
| Array< OneD, NekDouble > & | UpdateCoeffs () |
| This function returns (a reference to) the array \(\boldsymbol{\hat{u}}_l\) (implemented as m_coeffs) containing all local expansion coefficients. More... | |
| Array< OneD, NekDouble > & | UpdatePhys () |
| This function returns (a reference to) the array \(\boldsymbol{u}_l\) (implemented as m_phys) containing the function \(u^{\delta}(\boldsymbol{x})\) evaluated at the quadrature points. More... | |
| void | PhysDeriv (Direction edir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d) |
| 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) |
| This function discretely evaluates the derivative of a function \(f(\boldsymbol{x})\) on the domain consisting of all elements of the expansion. More... | |
| void | PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d) |
| void | CurlCurl (Array< OneD, Array< OneD, NekDouble > > &Vel, Array< OneD, Array< OneD, NekDouble > > &Q) |
| void | PhysDirectionalDeriv (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| void | GetMovingFrames (const SpatialDomains::GeomMMF MMFdir, const Array< OneD, const NekDouble > &CircCentre, Array< OneD, Array< OneD, NekDouble > > &outarray) |
| const Array< OneD, const std::shared_ptr< ExpList > > & | GetBndCondExpansions () |
| std::shared_ptr< ExpList > & | UpdateBndCondExpansion (int i) |
| void | Upwind (const Array< OneD, const Array< OneD, NekDouble > > &Vec, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind) |
| void | Upwind (const Array< OneD, const NekDouble > &Vn, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind) |
| std::shared_ptr< ExpList > & | GetTrace () |
| std::shared_ptr< AssemblyMapDG > & | GetTraceMap (void) |
| const Array< OneD, const int > & | GetTraceBndMap (void) |
| void | GetNormals (Array< OneD, Array< OneD, NekDouble > > &normals) |
| void | AddTraceIntegral (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray) |
| void | AddTraceIntegral (const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) |
| void | AddFwdBwdTraceIntegral (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &outarray) |
| void | GetFwdBwdTracePhys (Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd) |
| void | GetFwdBwdTracePhys (const Array< OneD, const NekDouble > &field, Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd) |
| const std::vector< bool > & | GetLeftAdjacentFaces (void) const |
| void | ExtractTracePhys (Array< OneD, NekDouble > &outarray) |
| void | ExtractTracePhys (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & | GetBndConditions () |
| Array< OneD, SpatialDomains::BoundaryConditionShPtr > & | UpdateBndConditions () |
| void | EvaluateBoundaryConditions (const NekDouble time=0.0, const std::string varName="", const NekDouble=NekConstants::kNekUnsetDouble, const NekDouble=NekConstants::kNekUnsetDouble) |
| void | GeneralMatrixOp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| This function calculates the result of the multiplication of a matrix of type specified by mkey with a vector given by inarray. More... | |
| void | GeneralMatrixOp_IterPerExp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| void | SetUpPhysNormals () |
| void | GetBoundaryToElmtMap (Array< OneD, int > &ElmtID, Array< OneD, int > &EdgeID) |
| void | GetBndElmtExpansion (int i, std::shared_ptr< ExpList > &result, const bool DeclareCoeffPhysArrays=true) |
| void | ExtractElmtToBndPhys (int i, const Array< OneD, NekDouble > &elmt, Array< OneD, NekDouble > &boundary) |
| void | ExtractPhysToBndElmt (int i, const Array< OneD, const NekDouble > &phys, Array< OneD, NekDouble > &bndElmt) |
| void | ExtractPhysToBnd (int i, const Array< OneD, const NekDouble > &phys, Array< OneD, NekDouble > &bnd) |
| void | GetBoundaryNormals (int i, Array< OneD, Array< OneD, NekDouble > > &normals) |
| void | GeneralGetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef, int NumHomoDir=0, Array< OneD, LibUtilities::BasisSharedPtr > &HomoBasis=LibUtilities::NullBasisSharedPtr1DArray, std::vector< NekDouble > &HomoLen=LibUtilities::NullNekDoubleVector, bool homoStrips=false, std::vector< unsigned int > &HomoSIDs=LibUtilities::NullUnsignedIntVector, std::vector< unsigned int > &HomoZIDs=LibUtilities::NullUnsignedIntVector, std::vector< unsigned int > &HomoYIDs=LibUtilities::NullUnsignedIntVector) |
| const NekOptimize::GlobalOptParamSharedPtr & | GetGlobalOptParam (void) |
| std::map< int, RobinBCInfoSharedPtr > | GetRobinBCInfo () |
| void | GetPeriodicEntities (PeriodicMap &periodicVerts, PeriodicMap &periodicEdges, PeriodicMap &periodicFaces=NullPeriodicMap) |
| std::vector< LibUtilities::FieldDefinitionsSharedPtr > | GetFieldDefinitions () |
| void | GetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef) |
| void | AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata) |
| Append the element data listed in elements fielddef->m_ElementIDs onto fielddata. More... | |
| void | AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, Array< OneD, NekDouble > &coeffs) |
| Append the data in coeffs listed in elements fielddef->m_ElementIDs onto fielddata. More... | |
| void | ExtractElmtDataToCoeffs (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, std::string &field, Array< OneD, NekDouble > &coeffs) |
| Extract the data in fielddata into the coeffs using the basic ExpList Elemental expansions rather than planes in homogeneous case. More... | |
| void | ExtractCoeffsToCoeffs (const std::shared_ptr< ExpList > &fromExpList, const Array< OneD, const NekDouble > &fromCoeffs, Array< OneD, NekDouble > &toCoeffs) |
| Extract the data from fromField using fromExpList the coeffs using the basic ExpList Elemental expansions rather than planes in homogeneous case. More... | |
| void | ExtractDataToCoeffs (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, std::string &field, Array< OneD, NekDouble > &coeffs) |
| Extract the data in fielddata into the coeffs. More... | |
| void | GenerateElementVector (const int ElementID, const NekDouble scalar1, const NekDouble scalar2, Array< OneD, NekDouble > &outarray) |
| Generate vector v such that v[i] = scalar1 if i is in the element < ElementID. Otherwise, v[i] = scalar2. More... | |
| std::shared_ptr< ExpList > | GetSharedThisPtr () |
| Returns a shared pointer to the current object. More... | |
| std::shared_ptr< LibUtilities::SessionReader > | GetSession () const |
| Returns the session object. More... | |
| std::shared_ptr< LibUtilities::Comm > | GetComm () |
| Returns the comm object. More... | |
| SpatialDomains::MeshGraphSharedPtr | GetGraph () |
| LibUtilities::BasisSharedPtr | GetHomogeneousBasis (void) |
| std::shared_ptr< ExpList > & | GetPlane (int n) |
| void | CreateCollections (Collections::ImplementationType ImpType=Collections::eNoImpType) |
| Construct collections of elements containing a single element type and polynomial order from the list of expansions. More... | |
| void | ClearGlobalLinSysManager (void) |
Protected Attributes | |
| AssemblyMapCGSharedPtr | m_locToGloMap |
| (A shared pointer to) the object which contains all the required information for the transformation from local to global degrees of freedom. More... | |
| CoeffState | m_coeffState |
| A enum list declaring how to interpret coeffs, i.e. eLocal, eHybrid or eGlobal. More... | |
| GlobalMatrixMapShPtr | m_globalMat |
| (A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once. More... | |
| LibUtilities::NekManager< GlobalLinSysKey, GlobalLinSys > | m_globalLinSysManager |
| A manager which collects all the global linear systems being assembled, such that they should be constructed only once. More... | |
| Protected Attributes inherited from Nektar::MultiRegions::DisContField1D | |
| int | m_numDirBndCondExpansions |
| The number of boundary segments on which Dirichlet boundary conditions are imposed. More... | |
| Array< OneD, MultiRegions::ExpListSharedPtr > | m_bndCondExpansions |
| Discretised boundary conditions. More... | |
| Array< OneD, SpatialDomains::BoundaryConditionShPtr > | m_bndConditions |
| An array which contains the information about the boundary condition on the different boundary regions. More... | |
| GlobalLinSysMapShPtr | m_globalBndMat |
| Global boundary matrix. More... | |
| ExpListSharedPtr | m_trace |
| Trace space storage for points between elements. More... | |
| AssemblyMapDGSharedPtr | m_traceMap |
| Local to global DG mapping for trace space. More... | |
| std::set< int > | m_boundaryVerts |
| A set storing the global IDs of any boundary edges. More... | |
| PeriodicMap | m_periodicVerts |
| A map which identifies groups of periodic vertices. More... | |
| std::vector< int > | m_periodicFwdCopy |
| A vector indicating degress of freedom which need to be copied from forwards to backwards space in case of a periodic boundary condition. More... | |
| std::vector< int > | m_periodicBwdCopy |
| std::vector< bool > | m_leftAdjacentVerts |
| Protected Attributes inherited from Nektar::MultiRegions::ExpList | |
| LibUtilities::CommSharedPtr | m_comm |
| Communicator. More... | |
| LibUtilities::SessionReaderSharedPtr | m_session |
| Session. More... | |
| SpatialDomains::MeshGraphSharedPtr | m_graph |
| Mesh associated with this expansion list. More... | |
| int | m_ncoeffs |
| The total number of local degrees of freedom. m_ncoeffs \(=N_{\mathrm{eof}}=\sum_{e=1}^{{N_{\mathrm{el}}}}N^{e}_l\). More... | |
| int | m_npoints |
| Array< OneD, NekDouble > | m_coeffs |
| Concatenation of all local expansion coefficients. More... | |
| Array< OneD, NekDouble > | m_phys |
| The global expansion evaluated at the quadrature points. More... | |
| bool | m_physState |
| The state of the array m_phys. More... | |
| std::shared_ptr< LocalRegions::ExpansionVector > | m_exp |
| The list of local expansions. More... | |
| Collections::CollectionVector | m_collections |
| std::vector< int > | m_coll_coeff_offset |
| Offset of elemental data into the array m_coeffs. More... | |
| std::vector< int > | m_coll_phys_offset |
| Offset of elemental data into the array m_phys. More... | |
| Array< OneD, int > | m_coeff_offset |
| Offset of elemental data into the array m_coeffs. More... | |
| Array< OneD, int > | m_phys_offset |
| Offset of elemental data into the array m_phys. More... | |
| NekOptimize::GlobalOptParamSharedPtr | m_globalOptParam |
| BlockMatrixMapShPtr | m_blockMat |
| bool | m_WaveSpace |
| std::unordered_map< int, int > | m_elmtToExpId |
| Mapping from geometry ID of element to index inside m_exp. More... | |
Private Member Functions | |
| GlobalLinSysSharedPtr | GetGlobalLinSys (const GlobalLinSysKey &mkey) |
| Returns the linear system specified by mkey. More... | |
| GlobalLinSysSharedPtr | GenGlobalLinSys (const GlobalLinSysKey &mkey) |
| void | GlobalSolve (const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray) |
| Solve the linear system specified by the key key. More... | |
| virtual void | v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate) |
| Perform a forward transform. More... | |
| virtual void | v_MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate) |
| virtual void | v_ImposeDirichletConditions (Array< OneD, NekDouble > &outarray) |
| Impose the Dirichlet Boundary Conditions on outarray. More... | |
| virtual void | v_GlobalToLocal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| Scatters from the global coefficients \(\boldsymbol{\hat{u}}_g\) to the local coefficients \(\boldsymbol{\hat{u}}_l\). More... | |
| virtual void | v_GlobalToLocal (void) |
| virtual void | v_LocalToGlobal (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool useComm) |
| Gathers the global coefficients \(\boldsymbol{\hat{u}}_g\) from the local coefficients \(\boldsymbol{\hat{u}}_l\). More... | |
| virtual void | v_LocalToGlobal (bool useComm) |
| virtual void | v_HelmSolve (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const FlagList &flags, const StdRegions::ConstFactorMap &factors, const StdRegions::VarCoeffMap &varcoeff, const MultiRegions::VarFactorsMap &varfactors, const Array< OneD, const NekDouble > &dirForcing, const bool PhysSpaceForcing) |
| virtual const Array< OneD, const SpatialDomains ::BoundaryConditionShPtr > & | v_GetBndConditions () |
| virtual void | v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate) |
| virtual void | v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate) |
| virtual void | v_GeneralMatrixOp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate) |
| Calculates the result of the multiplication of a global matrix of type specified by mkey with a vector given by inarray. More... | |
| virtual void | v_ClearGlobalLinSysManager (void) |
Additional Inherited Members | |
| Public Attributes inherited from Nektar::MultiRegions::ExpList | |
| ExpansionType | m_expType |
| Protected Member Functions inherited from Nektar::MultiRegions::DisContField1D | |
| void | GenerateBoundaryConditionExpansion (const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::BoundaryConditions &bcs, const std::string variable) |
| Discretises the boundary conditions. More... | |
| void | FindPeriodicVertices (const SpatialDomains::BoundaryConditions &bcs, const std::string variable) |
| Generate a associative map of periodic vertices in a mesh. More... | |
| virtual ExpListSharedPtr & | v_GetTrace () |
| virtual AssemblyMapDGSharedPtr & | v_GetTraceMap (void) |
| virtual void | v_AddTraceIntegral (const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray) |
| virtual void | v_GetFwdBwdTracePhys (Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd) |
| virtual void | v_GetFwdBwdTracePhys (const Array< OneD, const NekDouble > &field, Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd) |
| This method extracts the "forward" and "backward" trace data from the array field and puts the data into output vectors Fwd and Bwd. More... | |
| virtual void | v_ExtractTracePhys (Array< OneD, NekDouble > &outarray) |
| virtual void | v_ExtractTracePhys (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| This method extracts the trace (verts in 1D) from the field inarray and puts the values in outarray. More... | |
| void | SetBoundaryConditionExpansion (const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::BoundaryConditions &bcs, const std::string variable, Array< OneD, MultiRegions::ExpListSharedPtr > &bndCondExpansions, Array< OneD, SpatialDomains ::BoundaryConditionShPtr > &bndConditions) |
| Populates the list of boundary condition expansions. More... | |
| void | SetMultiDomainBoundaryConditionExpansion (const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::BoundaryConditions &bcs, const std::string variable, Array< OneD, MultiRegions::ExpListSharedPtr > &bndCondExpansions, Array< OneD, SpatialDomains ::BoundaryConditionShPtr > &bndConditions, int subdomain) |
| Populates the list of boundary condition expansions in multidomain case. More... | |
| void | GenerateFieldBnd1D (SpatialDomains::BoundaryConditions &bcs, const std::string variable) |
| virtual std::map< int, RobinBCInfoSharedPtr > | v_GetRobinBCInfo () |
| virtual const Array< OneD, const MultiRegions::ExpListSharedPtr > & | v_GetBndCondExpansions () |
| virtual MultiRegions::ExpListSharedPtr & | v_UpdateBndCondExpansion (int i) |
| virtual Array< OneD, SpatialDomains::BoundaryConditionShPtr > & | v_UpdateBndConditions () |
| virtual void | v_GetBoundaryToElmtMap (Array< OneD, int > &ElmtID, Array< OneD, int > &VertID) |
| virtual void | v_GetBndElmtExpansion (int i, std::shared_ptr< ExpList > &result, const bool DeclareCoeffPhysArrays) |
| virtual void | v_Reset () |
| Reset this field, so that geometry information can be updated. More... | |
| virtual void | v_EvaluateBoundaryConditions (const NekDouble time=0.0, const std::string varName="", const NekDouble x2_in=NekConstants::kNekUnsetDouble, const NekDouble x3_in=NekConstants::kNekUnsetDouble) |
| Evaluate all boundary conditions at a given time.. More... | |
| Protected Member Functions inherited from Nektar::MultiRegions::ExpList1D | |
| void | v_Upwind (const Array< OneD, const Array< OneD, NekDouble > > &Vec, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind) |
| Upwind the Fwd and Bwd states based on the velocity field given by Vec. More... | |
| void | v_Upwind (const Array< OneD, const NekDouble > &Vn, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind) |
| Upwind the Fwd and Bwd states based on the one- dimensional normal velocity field given by Vn. More... | |
| void | v_GetNormals (Array< OneD, Array< OneD, NekDouble > > &normals) |
| Populate normals with the normals of all expansions. More... | |
| Protected Member Functions inherited from Nektar::MultiRegions::ExpList | |
| void | SetCoeffPhysOffsets () |
| Definition of the total number of degrees of freedom and quadrature points and offsets to access data. More... | |
| std::shared_ptr< DNekMat > | GenGlobalMatrixFull (const GlobalLinSysKey &mkey, const std::shared_ptr< AssemblyMapCG > &locToGloMap) |
| const DNekScalBlkMatSharedPtr | GenBlockMatrix (const GlobalMatrixKey &gkey) |
| This function assembles the block diagonal matrix of local matrices of the type mtype. More... | |
| const DNekScalBlkMatSharedPtr & | GetBlockMatrix (const GlobalMatrixKey &gkey) |
| void | MultiplyByBlockMatrix (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| std::shared_ptr< GlobalMatrix > | GenGlobalMatrix (const GlobalMatrixKey &mkey, const std::shared_ptr< AssemblyMapCG > &locToGloMap) |
| Generates a global matrix from the given key and map. More... | |
| void | GlobalEigenSystem (const std::shared_ptr< DNekMat > &Gmat, Array< OneD, NekDouble > &EigValsReal, Array< OneD, NekDouble > &EigValsImag, Array< OneD, NekDouble > &EigVecs=NullNekDouble1DArray) |
| std::shared_ptr< GlobalLinSys > | GenGlobalLinSys (const GlobalLinSysKey &mkey, const std::shared_ptr< AssemblyMapCG > &locToGloMap) |
| This operation constructs the global linear system of type mkey. More... | |
| std::shared_ptr< GlobalLinSys > | GenGlobalBndLinSys (const GlobalLinSysKey &mkey, const AssemblyMapSharedPtr &locToGloMap) |
| Generate a GlobalLinSys from information provided by the key "mkey" and the mapping provided in LocToGloBaseMap. More... | |
| void | ReadGlobalOptimizationParameters () |
| virtual int | v_GetNumElmts (void) |
| virtual const Array< OneD, const int > & | v_GetTraceBndMap () |
| virtual void | v_AddTraceIntegral (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray) |
| virtual void | v_AddFwdBwdTraceIntegral (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &outarray) |
| virtual const std::vector< bool > & | v_GetLeftAdjacentFaces (void) const |
| virtual void | v_LinearAdvectionDiffusionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray) |
| virtual void | v_LinearAdvectionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray) |
| virtual void | v_FillBndCondFromField () |
| virtual void | v_FillBndCondFromField (const int nreg) |
| virtual void | v_BwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| virtual void | v_FwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| virtual void | v_FwdTrans_BndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| virtual void | v_SmoothField (Array< OneD, NekDouble > &field) |
| virtual void | v_IProductWRTBase_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| virtual void | v_GetCoords (Array< OneD, NekDouble > &coord_0, Array< OneD, NekDouble > &coord_1, Array< OneD, NekDouble > &coord_2=NullNekDouble1DArray) |
| virtual void | v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2) |
| virtual void | v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d) |
| virtual void | v_PhysDeriv (Direction edir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d) |
| virtual void | v_CurlCurl (Array< OneD, Array< OneD, NekDouble > > &Vel, Array< OneD, Array< OneD, NekDouble > > &Q) |
| virtual void | v_PhysDirectionalDeriv (const Array< OneD, const NekDouble > &direction, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| virtual void | v_GetMovingFrames (const SpatialDomains::GeomMMF MMFdir, const Array< OneD, const NekDouble > &CircCentre, Array< OneD, Array< OneD, NekDouble > > &outarray) |
| virtual void | v_HomogeneousFwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true) |
| virtual void | v_HomogeneousBwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true) |
| virtual void | v_DealiasedProd (const Array< OneD, NekDouble > &inarray1, const Array< OneD, NekDouble > &inarray2, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal) |
| virtual void | v_DealiasedDotProd (const Array< OneD, Array< OneD, NekDouble > > &inarray1, const Array< OneD, Array< OneD, NekDouble > > &inarray2, Array< OneD, Array< OneD, NekDouble > > &outarray, CoeffState coeffstate=eLocal) |
| virtual void | v_GetBCValues (Array< OneD, NekDouble > &BndVals, const Array< OneD, NekDouble > &TotField, int BndID) |
| virtual void | v_NormVectorIProductWRTBase (Array< OneD, const NekDouble > &V1, Array< OneD, const NekDouble > &V2, Array< OneD, NekDouble > &outarray, int BndID) |
| virtual void | v_NormVectorIProductWRTBase (Array< OneD, Array< OneD, NekDouble > > &V, Array< OneD, NekDouble > &outarray) |
| virtual void | v_ExtractElmtToBndPhys (const int i, const Array< OneD, NekDouble > &elmt, Array< OneD, NekDouble > &boundary) |
| virtual void | v_ExtractPhysToBndElmt (const int i, const Array< OneD, const NekDouble > &phys, Array< OneD, NekDouble > &bndElmt) |
| virtual void | v_ExtractPhysToBnd (const int i, const Array< OneD, const NekDouble > &phys, Array< OneD, NekDouble > &bnd) |
| virtual void | v_GetBoundaryNormals (int i, Array< OneD, Array< OneD, NekDouble > > &normals) |
| virtual std::vector< LibUtilities::FieldDefinitionsSharedPtr > | v_GetFieldDefinitions (void) |
| virtual void | v_GetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef) |
| virtual void | v_AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata) |
| virtual void | v_AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, Array< OneD, NekDouble > &coeffs) |
| virtual void | v_ExtractDataToCoeffs (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, std::string &field, Array< OneD, NekDouble > &coeffs) |
| Extract data from raw field data into expansion list. More... | |
| virtual void | v_ExtractCoeffsToCoeffs (const std::shared_ptr< ExpList > &fromExpList, const Array< OneD, const NekDouble > &fromCoeffs, Array< OneD, NekDouble > &toCoeffs) |
| virtual void | v_WriteTecplotHeader (std::ostream &outfile, std::string var="") |
| virtual void | v_WriteTecplotZone (std::ostream &outfile, int expansion) |
| virtual void | v_WriteTecplotField (std::ostream &outfile, int expansion) |
| virtual void | v_WriteTecplotConnectivity (std::ostream &outfile, int expansion) |
| virtual void | v_WriteVtkPieceData (std::ostream &outfile, int expansion, std::string var) |
| virtual NekDouble | v_L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray) |
| virtual NekDouble | v_Integral (const Array< OneD, const NekDouble > &inarray) |
| virtual NekDouble | v_VectorFlux (const Array< OneD, Array< OneD, NekDouble > > &inarray) |
| virtual Array< OneD, const NekDouble > | v_HomogeneousEnergy (void) |
| virtual LibUtilities::TranspositionSharedPtr | v_GetTransposition (void) |
| virtual NekDouble | v_GetHomoLen (void) |
| virtual void | v_SetHomoLen (const NekDouble lhom) |
| virtual Array< OneD, const unsigned int > | v_GetZIDs (void) |
| virtual Array< OneD, const unsigned int > | v_GetYIDs (void) |
| virtual void | v_PhysInterp1DScaled (const NekDouble scale, const Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| virtual void | v_PhysGalerkinProjection1DScaled (const NekDouble scale, const Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray) |
| void | ExtractFileBCs (const std::string &fileName, LibUtilities::CommSharedPtr comm, const std::string &varName, const std::shared_ptr< ExpList > locExpList) |
| Static Protected Member Functions inherited from Nektar::MultiRegions::ExpList | |
| static SpatialDomains::BoundaryConditionShPtr | GetBoundaryCondition (const SpatialDomains::BoundaryConditionCollection &collection, unsigned int index, const std::string &variable) |
Detailed Description
Abstraction of a global continuous one-dimensional spectral/hp element expansion which approximates the solution of a set of partial differential equations.
As opposed to the class #ContExpList1D, the class ContField1D is able to incorporate the boundary conditions imposed to the problem to be solved. Therefore, the class is equipped with three additional data members:
- m_bndCondExpansions
- #m_bndTypes
- #m_bndCondEquations
The first data structure, m_bndCondExpansions, contains the point Expansion on the boundary, #m_bndTypes stores information about the type of boundary condition on the different parts of the boundary while #m_bndCondEquations holds the equation of the imposed boundary conditions.
Furthermore, in case of Dirichlet boundary conditions, this class is capable of lifting a known solution satisfying these boundary conditions. If we denote the unknown solution by \(u^{\mathcal{H}}(\boldsymbol{x})\) and the known Dirichlet boundary conditions by \(u^{\mathcal{D}}(\boldsymbol{x})\), the expansion then can be decomposed as
\[ u^{\delta}(\boldsymbol{x}_i)=u^{\mathcal{D}}(\boldsymbol{x}_i)+ u^{\mathcal{H}}(\boldsymbol{x}_i)=\sum_{n=0}^{N^{\mathcal{D}}-1} \hat{u}_n^{\mathcal{D}}\Phi_n(\boldsymbol{x}_i)+ \sum_{n={N^{\mathcal{D}}}}^{N_{\mathrm{dof}} -1}\hat{u}_n^{\mathcal{H}} \Phi_n(\boldsymbol{x}_i).\]
This lifting is accomplished by ordering the known global degrees of freedom, prescribed by the Dirichlet boundary conditions, first in the global array \(\boldsymbol{\hat{u}}\), that is,
\[\boldsymbol{\hat{u}}=\left[ \begin{array}{c} \boldsymbol{\hat{u}}^{\mathcal{D}}\\ \boldsymbol{\hat{u}}^{\mathcal{H}} \end{array} \right].\]
Such kind of expansions are also referred to as continuoous fields. This class should be used when solving 2D problems using a standard Galerkin approach.
Definition at line 55 of file ContField1D.h.
Constructor & Destructor Documentation
◆ ContField1D() [1/4]
| Nektar::MultiRegions::ContField1D::ContField1D | ( | ) |
Default constructor.
Constructs an empty 1D continuous field.
Definition at line 85 of file ContField1D.cpp.
◆ ContField1D() [2/4]
| Nektar::MultiRegions::ContField1D::ContField1D | ( | const LibUtilities::SessionReaderSharedPtr & | pSession, |
| const SpatialDomains::MeshGraphSharedPtr & | graph1D, | ||
| const std::string & | variable = "DefaultVar", |
||
| const Collections::ImplementationType | ImpType = Collections::eNoImpType |
||
| ) |
Set up global continuous field based on an input mesh and boundary conditions.
Given a mesh graph1D, containing information about the domain and the spectral/hp element expansion, this constructor fills the list of local expansions m_exp with the proper expansions, calculates the total number of quadrature points \(\boldsymbol{x}_i\) and local expansion coefficients \(\hat{u}^e_n\) and allocates memory for the arrays m_coeffs and m_phys. Furthermore, it constructs the mapping array (contained in m_locToGloMap) for the transformation between local elemental level and global level, it calculates the total number global expansion coefficients \(\hat{u}_n\). The constructor also discretises the boundary conditions, specified by the argument bcs, by expressing them in terms of the coefficient of the expansion on the boundary.
- Parameters
-
graph1D A 1D mesh, containing information about the domain and the spectral/hp element expansion. bcs The boundary conditions. variable An optional parameter to indicate for which variable the field should be constructed.
Definition at line 116 of file ContField1D.cpp.
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::DisContField1D::m_bndCondExpansions, Nektar::MultiRegions::DisContField1D::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Nektar::MultiRegions::DisContField1D::m_periodicVerts, and Nektar::MultiRegions::ExpList::m_session.
◆ ContField1D() [3/4]
| Nektar::MultiRegions::ContField1D::ContField1D | ( | const ContField1D & | In | ) |
Copy constructor.
Constructs a 1D continuous field as a copy of an existing field including all boundary conditions.
- Parameters
-
In Existing continuous field to duplicate.
Definition at line 144 of file ContField1D.cpp.
◆ ContField1D() [4/4]
| Nektar::MultiRegions::ContField1D::ContField1D | ( | const LibUtilities::SessionReaderSharedPtr & | pSession, |
| const ExpList1D & | In | ||
| ) |
Copy constructor.
Constructs a 1D continuous field as a copy of an existing explist 1D field and adding all the boundary conditions.
- Parameters
-
In Existing explist1D field .
Definition at line 158 of file ContField1D.cpp.
References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.
◆ ~ContField1D()
|
virtual |
Member Function Documentation
◆ Assemble() [1/2]
|
inline |
Assembles the global coefficients \(\boldsymbol{\hat{u}}_g\) from the local coefficients \(\boldsymbol{\hat{u}}_l\).
This operation is evaluated as:
\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}_g[\mbox{map}[e][i]] = \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]+\mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}^{e}[i]$\\ \> \> continue\\ \> continue \end{tabbing}
where map \([e][i]\) is the mapping array and sign \([e][i]\) is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the gather operation \(\boldsymbol{\hat{u}}_g=\mathcal{A}^{T}\boldsymbol{\hat{u}}_l\), where \(\mathcal{A}\) is the \(N_{\mathrm{eof}}\times N_{\mathrm{dof}}\) permutation matrix.
Definition at line 276 of file ContField1D.h.
References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.
Referenced by IProductWRTBase(), MultiplyByInvMassMatrix(), v_GeneralMatrixOp(), and v_HelmSolve().
◆ Assemble() [2/2]
|
inline |
Assembles the global coefficients \(\boldsymbol{\hat{u}}_g\) from the local coefficients \(\boldsymbol{\hat{u}}_l\).
This operation is evaluated as:
\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}_g[\mbox{map}[e][i]] = \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]+\mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}^{e}[i]$\\ \> \> continue\\ \> continue \end{tabbing}
where map \([e][i]\) is the mapping array and sign \([e][i]\) is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the gather operation \(\boldsymbol{\hat{u}}_g=\mathcal{A}^{T}\boldsymbol{\hat{u}}_l\), where \(\mathcal{A}\) is the \(N_{\mathrm{eof}}\times N_{\mathrm{dof}}\) permutation matrix.
- Parameters
-
inarray An array of size \(N_\mathrm{eof}\) containing the local degrees of freedom \(\boldsymbol{x}_l\). outarray The resulting global degrees of freedom \(\boldsymbol{x}_g\) will be stored in this array of size \(N_\mathrm{dof}\).
Definition at line 308 of file ContField1D.h.
References m_locToGloMap.
◆ BwdTrans()
| void Nektar::MultiRegions::ContField1D::BwdTrans | ( | const Array< OneD, const NekDouble > & | inarray, |
| Array< OneD, NekDouble > & | outarray, | ||
| CoeffState | coeffstate = eLocal |
||
| ) |
This function performs the backward transformation of the spectral/hp element expansion.
Given the coefficients of an expansion, this function evaluates the spectral/hp expansion \(u^{\delta}(x)\) at the quadrature points \(x_i\). This operation is evaluated locally by the function ExpList::BwdTrans.
The coefficients of the expansion should be contained in the variable m_coeffs of the ExpList object In. The resulting physical values at the quadrature points \(u^{\delta}(x_i)\) are stored in the array m_phys.
Definition at line 229 of file ContField1D.cpp.
References Nektar::MultiRegions::ExpList::BwdTrans_IterPerExp(), Nektar::MultiRegions::eLocal, and Nektar::MultiRegions::ExpList::GlobalToLocal().
Referenced by v_BwdTrans().
◆ FwdTrans()
| void Nektar::MultiRegions::ContField1D::FwdTrans | ( | const Array< OneD, const NekDouble > & | inarray, |
| Array< OneD, NekDouble > & | outarray, | ||
| CoeffState | coeffstate = eLocal |
||
| ) |
Perform global forward transformation of a function \(f(x)\),.
Given a function \(f(x)\) defined at the quadrature points, this function determines the unknown global coefficients \(\boldsymbol{\hat{u}}^{\mathcal{H}}\) employing a discrete Galerkin projection from physical space to coefficient space. The operation is evaluated by the function GlobalSolve using the global mass matrix.
The values of the function \(f(x)\) evaluated at the quadrature points \(x_i\) should be contained in the variable m_phys of the ExpList object Sin. The resulting global coefficients \(\hat{u}_g\) are stored in the array m_coeffs.
- Parameters
-
inarray Discrete \(f(x)\). outarray Storage for result. coeffstate
Definition at line 195 of file ContField1D.cpp.
References Nektar::MultiRegions::eGlobal, Nektar::MultiRegions::eLocal, Nektar::StdRegions::eMass, GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.
Referenced by v_FwdTrans().
◆ GeneralMatrixOp()
| void Nektar::MultiRegions::ContField1D::GeneralMatrixOp | ( | const GlobalMatrixKey & | gkey, |
| const Array< OneD, const NekDouble > & | inarray, | ||
| Array< OneD, NekDouble > & | outarray, | ||
| CoeffState | coeffstate = eLocal |
||
| ) |
Calculates the result of the multiplication of a global matrix of type specified by mkey with a vector given by inarray.
◆ GenGlobalLinSys()
|
private |
Definition at line 372 of file ContField1D.cpp.
References ASSERTL1, Nektar::MultiRegions::ExpList::GenGlobalLinSys(), Nektar::MultiRegions::GlobalMatrixKey::LocToGloMapIsDefined(), and m_locToGloMap.
◆ GetBndCondExpansions()
|
inline |
Return the boundary conditions expansion.
Definition at line 243 of file ContField1D.h.
References Nektar::MultiRegions::DisContField1D::m_bndCondExpansions.
◆ GetBndConditions()
|
inline |
Definition at line 249 of file ContField1D.h.
References Nektar::MultiRegions::DisContField1D::m_bndConditions.
Referenced by v_GetBndConditions().
◆ GetGlobalLinSys()
|
private |
Returns the linear system specified by mkey.
The function searches the map #m_globalLinSys to see if the global matrix has been created before. If not, it calls the function #GenglobalLinSys to generate the requested global system.
- Parameters
-
mkey Key specifying the linear system.
- Returns
- Pointer to the required linear system.
Definition at line 366 of file ContField1D.cpp.
References m_globalLinSysManager.
Referenced by GlobalSolve().
◆ GetLocalToGlobalMap()
|
inline |
Returns the map from local to global level.
Definition at line 316 of file ContField1D.h.
References m_locToGloMap.
◆ GlobalSolve()
|
private |
Solve the linear system specified by the key key.
Given a linear system specified by the key key,
\[\boldsymbol{M}\boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}},\]
this function solves this linear system taking into account the boundary conditions specified in the data member m_bndCondExpansions. Therefore, it adds an array \(\boldsymbol{\hat{g}}\) which represents the non-zero surface integral resulting from the weak boundary conditions (e.g. Neumann boundary conditions) to the right hand side, that is,
\[\boldsymbol{M}\boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}}+ \boldsymbol{\hat{g}}.\]
Furthermore, it lifts the known degrees of freedom which are prescribed by the Dirichlet boundary conditions. As these known coefficients \(\boldsymbol{\hat{u}}^{\mathcal{D}}\) are numbered first in the global coefficient array \(\boldsymbol{\hat{u}}_g\), the linear system can be decomposed as,
\[\left[\begin{array}{cc} \boldsymbol{M}^{\mathcal{DD}}&\boldsymbol{M}^{\mathcal{DH}}\\ \boldsymbol{M}^{\mathcal{HD}}&\boldsymbol{M}^{\mathcal{HH}} \end{array}\right] \left[\begin{array}{c} \boldsymbol{\hat{u}}^{\mathcal{D}}\\ \boldsymbol{\hat{u}}^{\mathcal{H}} \end{array}\right]= \left[\begin{array}{c} \boldsymbol{\hat{f}}^{\mathcal{D}}\\ \boldsymbol{\hat{f}}^{\mathcal{H}} \end{array}\right]+ \left[\begin{array}{c} \boldsymbol{\hat{g}}^{\mathcal{D}}\\ \boldsymbol{\hat{g}}^{\mathcal{H}} \end{array}\right] \]
which will then be solved for the unknown coefficients \(\boldsymbol{\hat{u}}^{\mathcal{H}}\) as,
\[ \boldsymbol{M}^{\mathcal{HH}}\boldsymbol{\hat{u}}^{\mathcal{H}} = \boldsymbol{\hat{f}}^{\mathcal{H}} +\boldsymbol{\hat{g}}^{\mathcal{H}} -\boldsymbol{M}^{\mathcal{HD}}\boldsymbol{\hat{u}}^{\mathcal{D}}\]
- Parameters
-
key Specifes the linear system to solve. rhs Forcing term \(\boldsymbol{f}\). inout Solution vector \(\boldsymbol{\hat{u}}\). dirForcing .
Definition at line 337 of file ContField1D.cpp.
References GetGlobalLinSys(), m_locToGloMap, and v_ImposeDirichletConditions().
Referenced by FwdTrans(), MultiplyByInvMassMatrix(), and v_HelmSolve().
◆ IProductWRTBase()
| void Nektar::MultiRegions::ContField1D::IProductWRTBase | ( | const Array< OneD, const NekDouble > & | inarray, |
| Array< OneD, NekDouble > & | outarray, | ||
| CoeffState | coeffstate = eLocal |
||
| ) |
Calculates the inner product of a function \(f(x)\) with respect to all global expansion modes \(\phi_n^e(x)\).
The operation is evaluated locally (i.e. with respect to all local expansion modes) by the function ExpList::IProductWRTBase. The inner product with respect to the global expansion modes is than obtained by a global assembly operation.
The values of the function \(f(x)\) evaluated at the quadrature points \(x_i\) should be contained in the variable m_phys of the ExpList object in. The result is stored in the array m_coeffs.
- Parameters
-
In An ExpList, containing the discrete evaluation of \(f(x)\) at the quadrature points in its array m_phys.
Definition at line 397 of file ContField1D.cpp.
References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::MultiRegions::ExpList::IProductWRTBase_IterPerExp(), and Nektar::MultiRegions::ExpList::m_ncoeffs.
Referenced by FwdTrans(), v_HelmSolve(), and v_IProductWRTBase().
◆ MultiplyByInvMassMatrix()
| void Nektar::MultiRegions::ContField1D::MultiplyByInvMassMatrix | ( | const Array< OneD, const NekDouble > & | inarray, |
| Array< OneD, NekDouble > & | outarray, | ||
| CoeffState | coeffstate = eLocal |
||
| ) |
Definition at line 252 of file ContField1D.cpp.
References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eMass, GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.
Referenced by v_MultiplyByInvMassMatrix().
◆ v_BwdTrans()
|
privatevirtual |
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 599 of file ContField1D.cpp.
References BwdTrans().
◆ v_ClearGlobalLinSysManager()
Reset the GlobalLinSys Manager
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 656 of file ContField1D.cpp.
References m_globalLinSysManager.
◆ v_FwdTrans()
|
privatevirtual |
Perform a forward transform.
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 415 of file ContField1D.cpp.
References FwdTrans().
◆ v_GeneralMatrixOp()
|
privatevirtual |
Calculates the result of the multiplication of a global matrix of type specified by mkey with a vector given by inarray.
This is equivalent to the operation:
\[\boldsymbol{M\hat{u}}_g\]
where \(\boldsymbol{M}\) is the global matrix of type specified by mkey. After scattering the global array inarray to local level, this operation is evaluated locally by the function ExpList::GeneralMatrixOp. The global result is then obtained by a global assembly procedure.
- Parameters
-
mkey This key uniquely defines the type matrix required for the operation. inarray The vector \(\boldsymbol{\hat{u}}_g\) of size \(N_{\mathrm{dof}}\). outarray The resulting vector of size \(N_{\mathrm{dof}}\).
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 631 of file ContField1D.cpp.
References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::MultiRegions::ExpList::GeneralMatrixOp_IterPerExp(), Nektar::MultiRegions::ExpList::GlobalToLocal(), and Nektar::MultiRegions::ExpList::m_ncoeffs.
◆ v_GetBndConditions()
|
privatevirtual |
Reimplemented from Nektar::MultiRegions::DisContField1D.
Definition at line 594 of file ContField1D.cpp.
References GetBndConditions().
◆ v_GlobalToLocal() [1/2]
|
privatevirtual |
Scatters from the global coefficients \(\boldsymbol{\hat{u}}_g\) to the local coefficients \(\boldsymbol{\hat{u}}_l\).
This operation is evaluated as:
\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}^{e}[i] = \mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]$ \\ \> \> continue \\ \> continue \end{tabbing}
where map \([e][i]\) is the mapping array and sign \([e][i]\) is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the scatter operation \(\boldsymbol{\hat{u}}_l=\mathcal{A}\boldsymbol{\hat{u}}_g\), where \(\mathcal{A}\) is the \(N_{\mathrm{eof}}\times N_{\mathrm{dof}}\) permutation matrix.
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 496 of file ContField1D.cpp.
References m_locToGloMap.
◆ v_GlobalToLocal() [2/2]
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 503 of file ContField1D.cpp.
References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.
◆ v_HelmSolve()
|
privatevirtual |
Consider the one dimensional Helmholtz equation,
\[\frac{d^2u}{dx^2}-\lambda u(x) = f(x),\]
supplemented with appropriate boundary conditions (which are contained in the data member m_bndCondExpansions). Applying a \(C^0\) continuous Galerkin discretisation, this equation leads to the following linear system:
\[\left( \boldsymbol{M}+\lambda\boldsymbol{L}\right) \boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}}\]
where \(\boldsymbol{M}\) and \(\boldsymbol{L}\) are the mass and Laplacian matrix respectively. This function solves the system above for the global coefficients \(\boldsymbol{\hat{u}}\) by a call to the function GlobalSolve.
The values of the function \(f(x)\) evaluated at the quadrature points \(\boldsymbol{x}_i\) should be contained in the variable m_phys of the ExpList object inarray. The resulting global coefficients \(\boldsymbol{\hat{u}}_g\) are stored in the array m_coeffs.
- Parameters
-
inarray Input containing forcing function \(\boldsymbol{f}\) at the quadrature points. outarray Output containing the coefficients \(\boldsymbol{u}_g\) lambda Parameter value. Sigma Coefficients of lambda. varcoeff Variable diffusivity coefficients. coeffstate dirForcing Dirichlet Forcing.
Reimplemented from Nektar::MultiRegions::DisContField1D.
Definition at line 538 of file ContField1D.cpp.
References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eHelmholtz, Nektar::SpatialDomains::eNeumann, Nektar::SpatialDomains::eRobin, Nektar::eUseGlobal, GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), Nektar::FlagList::isSet(), Nektar::MultiRegions::DisContField1D::m_bndCondExpansions, Nektar::MultiRegions::DisContField1D::m_bndConditions, m_locToGloMap, and Vmath::Neg().
◆ v_ImposeDirichletConditions()
|
privatevirtual |
Impose the Dirichlet Boundary Conditions on outarray.
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 431 of file ContField1D.cpp.
References Nektar::SpatialDomains::eDirichlet, Nektar::MultiRegions::DisContField1D::m_bndCondExpansions, Nektar::MultiRegions::DisContField1D::m_bndConditions, and m_locToGloMap.
Referenced by GlobalSolve().
◆ v_IProductWRTBase()
|
privatevirtual |
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 607 of file ContField1D.cpp.
References IProductWRTBase().
◆ v_LocalToGlobal() [1/2]
|
privatevirtual |
Gathers the global coefficients \(\boldsymbol{\hat{u}}_g\) from the local coefficients \(\boldsymbol{\hat{u}}_l\).
This operation is evaluated as:
\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}_g[\mbox{map}[e][i]] = \mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}^{e}[i]$\\ \> \> continue\\ \> continue \end{tabbing}
where map \([e][i]\) is the mapping array and sign \([e][i]\) is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the gather operation \(\boldsymbol{\hat{u}}_g=\mathcal{A}^{-1}\boldsymbol{\hat{u}}_l\), where \(\mathcal{A}\) is the \(N_{\mathrm{eof}}\times N_{\mathrm{dof}}\) permutation matrix.
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 463 of file ContField1D.cpp.
References m_locToGloMap.
◆ v_LocalToGlobal() [2/2]
|
privatevirtual |
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 471 of file ContField1D.cpp.
References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.
◆ v_MultiplyByInvMassMatrix()
|
privatevirtual |
Reimplemented from Nektar::MultiRegions::ExpList.
Definition at line 423 of file ContField1D.cpp.
References MultiplyByInvMassMatrix().
Member Data Documentation
◆ m_coeffState
|
protected |
A enum list declaring how to interpret coeffs, i.e. eLocal, eHybrid or eGlobal.
Definition at line 145 of file ContField1D.h.
◆ m_globalLinSysManager
|
protected |
A manager which collects all the global linear systems being assembled, such that they should be constructed only once.
Definition at line 155 of file ContField1D.h.
Referenced by GetGlobalLinSys(), and v_ClearGlobalLinSysManager().
◆ m_globalMat
|
protected |
(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once.
Definition at line 150 of file ContField1D.h.
◆ m_locToGloMap
|
protected |
(A shared pointer to) the object which contains all the required information for the transformation from local to global degrees of freedom.
Definition at line 140 of file ContField1D.h.
Referenced by Assemble(), ContField1D(), FwdTrans(), GenGlobalLinSys(), GetLocalToGlobalMap(), GlobalSolve(), MultiplyByInvMassMatrix(), v_GlobalToLocal(), v_HelmSolve(), v_ImposeDirichletConditions(), and v_LocalToGlobal().
