Nektar::MultiRegions::ContField Class Reference

This class is the abstraction of a global continuous two- dimensional spectral/hp element expansion which approximates the solution of a set of partial differential equations. More...

#include <ContField.h>

Inheritance diagram for Nektar::MultiRegions::ContField:

Public Member Functions
	ContField ()
	The default constructor. More...
	ContField (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph2D, const std::string &variable="DefaultVar", const bool DeclareCoeffPhysArrays=true, const bool CheckIfSingularSystem=false, const Collections::ImplementationType ImpType=Collections::eNoImpType)
	This constructor sets up global continuous field based on an input mesh and boundary conditions. More...
	ContField (const ContField &In, const SpatialDomains::MeshGraphSharedPtr &graph2D, const std::string &variable, const bool DeclareCoeffPhysArrays=true, const bool CheckIfSingularSystem=false)
	Construct a global continuous field with solution type based on another field but using a separate input mesh and boundary conditions. More...
	ContField (const ContField &In, bool DeclareCoeffPhysArrays=true)
	The copy constructor. More...
	ContField (const LibUtilities::SessionReaderSharedPtr &pSession, const ExpList &In)
	Copy constructor. More...
virtual	~ContField ()
	The default destructor. More...
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) const
	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	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Performs the global forward transformation of a function \(f(\boldsymbol{x})\), subject to the boundary conditions specified. More...
void	MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Multiply a solution by the inverse mass matrix. More...
void	LaplaceSolve (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray, const Array< OneD, Array< OneD, NekDouble >> &variablecoeffs=NullNekDoubleArrayOfArray, NekDouble time=0.0)
	Solves the two-dimensional Laplace equation, subject to the boundary conditions specified. More...
void	LinearAdvectionEigs (const NekDouble ax, const NekDouble ay, Array< OneD, NekDouble > &Real, Array< OneD, NekDouble > &Imag, Array< OneD, NekDouble > &Evecs=NullNekDouble1DArray)
	Compute the eigenvalues of the linear advection operator. More...
const Array< OneD, const MultiRegions::ExpListSharedPtr > &	GetBndCondExpansions ()
	Returns the boundary conditions expansion. More...
const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > &	GetBndConditions ()
	Returns the boundary conditions. More...
int	GetGlobalMatrixNnz (const GlobalMatrixKey &gkey)
void	GlobalSolve (const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
	Solves the linear system specified by the key key. More...
const GJPStabilisationSharedPtr	GetGJPForcing ()
void	SetGJPForcing (const GJPStabilisationSharedPtr &GJPData)
Public Member Functions inherited from Nektar::MultiRegions::DisContField
	DisContField ()
	Default constructor. More...
	DisContField (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph, const std::string &variable, const bool SetUpJustDG=true, const bool DeclareCoeffPhysArrays=true, const Collections::ImplementationType ImpType=Collections::eNoImpType, const std::string bcvariable="NotSet")
	Constructs a 1D discontinuous field based on a mesh and boundary conditions. More...
	DisContField (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::CompositeMap &domain, const SpatialDomains::BoundaryConditions &Allbcs, const std::string &variable, const LibUtilities::CommSharedPtr &comm, bool SetToOneSpaceDimensions=false, const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Constructor for a DisContField from a List of subdomains New Constructor for arterial network. More...
	DisContField (const DisContField &In, const bool DeclareCoeffPhysArrays=true)
	Constructs a 1D discontinuous field based on an existing field. More...
	DisContField (const DisContField &In, const SpatialDomains::MeshGraphSharedPtr &graph, const std::string &variable, const bool SetUpJustDG=false, const bool DeclareCoeffPhysArrays=true)
	DisContField (const ExpList &In)
	Constructs a 1D discontinuous field based on an existing field. (needed in order to use ContField( const ExpList &In) constructor. More...
virtual	~DisContField ()
	Destructor. More...
GlobalLinSysSharedPtr	GetGlobalBndLinSys (const GlobalLinSysKey &mkey)
	For a given key, returns the associated global linear system. More...
bool	SameTypeOfBoundaryConditions (const DisContField &In)
	Check to see if expansion has the same BCs as In. More...
std::vector< bool > &	GetNegatedFluxNormal (void)
NekDouble	L2_DGDeriv (const int dir, const Array< OneD, const NekDouble > &soln)
	Calculate the \( L^2 \) error of the \( Q_{\rm dir} \) derivative using the consistent DG evaluation of \( Q_{\rm dir} \). More...
void	EvaluateHDGPostProcessing (Array< OneD, NekDouble > &outarray)
	Evaluate HDG post-processing to increase polynomial order of solution. More...
void	GetLocTraceToTraceMap (LocTraceToTraceMapSharedPtr &LocTraceToTraceMap)
Public Member Functions inherited from Nektar::MultiRegions::ExpList
	ExpList (const ExpansionType Type=eNoType)
	The default constructor using a type. More...
	ExpList (const ExpList &in, const bool DeclareCoeffPhysArrays=true)
	The copy constructor. More...
	ExpList (const ExpList &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...
	ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph, const bool DeclareCoeffPhysArrays=true, const std::string &var="DefaultVar", const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Generate an ExpList from a meshgraph graph and session file. More...
	ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::ExpansionInfoMap &expansions, const bool DeclareCoeffPhysArrays=true, const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Sets up a list of local expansions based on an expansion Map. More...
	ExpList (const SpatialDomains::PointGeomSharedPtr &geom)
	Specialised constructors for 0D Expansions Wrapper around LocalRegion::PointExp - used in PrePacing.cpp. More...
	ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const Array< OneD, const ExpListSharedPtr > &bndConstraint, const Array< OneD, const SpatialDomains ::BoundaryConditionShPtr > &bndCond, const LocalRegions::ExpansionVector &locexp, const SpatialDomains::MeshGraphSharedPtr &graph, const LibUtilities::CommSharedPtr &comm, const bool DeclareCoeffPhysArrays=true, const std::string variable="DefaultVar", const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Generate expansions for the trace space expansions used in DisContField. More...
	ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const LocalRegions::ExpansionVector &locexp, const SpatialDomains::MeshGraphSharedPtr &graph, const bool DeclareCoeffPhysArrays, const std::string variable, const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Generate an trace ExpList from a meshgraph graph and session file. More...
	ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::CompositeMap &domain, const SpatialDomains::MeshGraphSharedPtr &graph, const bool DeclareCoeffPhysArrays=true, const std::string variable="DefaultVar", bool SetToOneSpaceDimension=false, const LibUtilities::CommSharedPtr comm=LibUtilities::CommSharedPtr(), const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Constructor based on domain information only for 1D & 2D boundary conditions. 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...
void	MultiplyByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	multiply the metric jacobi and quadrature weights More...
void	DivideByQuadratureMetric (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Divided by the metric jacobi and quadrature weights. More...
void	IProductWRTBase (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	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 of all local expansion modes \(\phi_n^e(\boldsymbol{x})\). More...
void	FwdTransLocalElmt (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)
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)
void	MultiplyByMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
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 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, 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, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
	Solve Advection Diffusion Reaction. More...
void	FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
void	BwdTrans (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	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	GetCoords (const int eid, Array< OneD, NekDouble > &coord_0, Array< OneD, NekDouble > &coord_1=NullNekDouble1DArray, Array< OneD, NekDouble > &coord_2=NullNekDouble1DArray)
void	HomogeneousFwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool Shuff=true, bool UnShuff=true)
void	HomogeneousBwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool Shuff=true, bool UnShuff=true)
void	DealiasedProd (const Array< OneD, NekDouble > &inarray1, const Array< OneD, NekDouble > &inarray2, Array< OneD, NekDouble > &outarray)
void	DealiasedDotProd (const Array< OneD, Array< OneD, NekDouble >> &inarray1, const Array< OneD, Array< OneD, NekDouble >> &inarray2, Array< OneD, Array< OneD, NekDouble >> &outarray)
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 ()
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 associated with the homogeneous expansion. More...
NekDouble	GetHomoLen (void)
	This function returns the Width of homogeneous direction associated with the homogeneous expansion. More...
void	SetHomoLen (const NekDouble lhom)
	This function sets the Width of homogeneous direction associated 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 cachedId=-1, NekDouble maxDistance=1e6)
	This function returns the index of the local elemental expansion containing the arbitrary point given by gloCoord, within a distance tolerance of tol. More...
int	GetExpIndex (const Array< OneD, const NekDouble > &gloCoords, Array< OneD, NekDouble > &locCoords, NekDouble tol=0.0, bool returnNearestElmt=false, int cachedId=-1, NekDouble maxDistance=1e6)
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 ()
const Array< OneD, const NekDouble > &	GetBndCondBwdWeight ()
	Get the weight value for boundary conditions. More...
void	SetBndCondBwdWeight (const int index, const NekDouble value)
	Set the weight value for boundary conditions. More...
std::shared_ptr< ExpList > &	UpdateBndCondExpansion (int i)
void	Upwind (const Array< OneD, const NekDouble > &Vn, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)
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)
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	GetElmtNormalLength (Array< OneD, NekDouble > &lengthsFwd, Array< OneD, NekDouble > &lengthsBwd)
	Get the length of elements in boundary normal direction. More...
void	GetBwdWeight (Array< OneD, NekDouble > &weightAver, Array< OneD, NekDouble > &weightJump)
	Get the weight value for boundary conditions for boundary average and jump calculations. More...
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, bool FillBnd=true, bool PutFwdInBwdOnBCs=false, bool DoExchange=true)
void	FillBwdWithBoundCond (const Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd, bool PutFwdInBwdOnBCs=false)
void	AddTraceQuadPhysToField (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &field)
	Add Fwd and Bwd value to field, a reverse procedure of GetFwdBwdTracePhys. More...
void	AddTraceQuadPhysToOffDiag (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &field)
void	GetLocTraceFromTracePts (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &locTraceFwd, Array< OneD, NekDouble > &locTraceBwd)
void	FillBwdWithBwdWeight (Array< OneD, NekDouble > &weightave, Array< OneD, NekDouble > &weightjmp)
	Fill Bwd with boundary conditions. More...
void	PeriodicBwdCopy (const Array< OneD, const NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)
	Copy and fill the Periodic boundaries. More...
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)
	This function calculates the result of the multiplication of a matrix of type specified by mkey with a vector given by inarray. More...
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)
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 () const
	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)
const Array< OneD, const std::pair< int, int > > &	GetCoeffsToElmt () const
	Get m_coeffs to elemental value map. More...
void	AddTraceJacToElmtJac (const Array< OneD, const DNekMatSharedPtr > &FwdMat, const Array< OneD, const DNekMatSharedPtr > &BwdMat, Array< OneD, DNekMatSharedPtr > &fieldMat)
	inverse process of v_GetFwdBwdTracePhys. Given Trace integration of Fwd and Bwd Jacobian, with dimension NtotalTrace*TraceCoef*TracePhys. return Elemental Jacobian matrix with dimension NtotalElement*ElementCoef*ElementPhys. More...
void	GetMatIpwrtDeriveBase (const Array< OneD, const Array< OneD, NekDouble >> &inarray, const int nDirctn, Array< OneD, DNekMatSharedPtr > &mtxPerVar)
void	GetMatIpwrtDeriveBase (const TensorOfArray3D< NekDouble > &inarray, Array< OneD, DNekMatSharedPtr > &mtxPerVar)
void	GetDiagMatIpwrtBase (const Array< OneD, const Array< OneD, NekDouble >> &inarray, Array< OneD, DNekMatSharedPtr > &mtxPerVar)
void	AddTraceIntegralToOffDiag (const Array< OneD, const NekDouble > &FwdFlux, const Array< OneD, const NekDouble > &BwdFlux, Array< OneD, NekDouble > &outarray)
void	AddRightIPTPhysDerivBase (const int dir, const Array< OneD, const DNekMatSharedPtr > ElmtJacQuad, Array< OneD, DNekMatSharedPtr > ElmtJacCoef)
void	AddRightIPTBaseMatrix (const Array< OneD, const DNekMatSharedPtr > ElmtJacQuad, Array< OneD, DNekMatSharedPtr > ElmtJacCoef)
const LocTraceToTraceMapSharedPtr &	GetLocTraceToTraceMap () const
std::vector< bool > &	GetLeftAdjacentTraces (void)

Protected Member Functions
GlobalMatrixSharedPtr	GetGlobalMatrix (const GlobalMatrixKey &mkey)
	Returns the global matrix specified by mkey. More...
GlobalLinSysSharedPtr	GetGlobalLinSys (const GlobalLinSysKey &mkey)
	Returns the linear system specified by the key mkey. More...
GlobalLinSysSharedPtr	GenGlobalLinSys (const GlobalLinSysKey &mkey)
virtual void	v_ImposeDirichletConditions (Array< OneD, NekDouble > &outarray)
	Impose the Dirichlet Boundary Conditions on outarray. More...
virtual void	v_FillBndCondFromField ()
virtual void	v_FillBndCondFromField (const int nreg)
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_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_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Template method virtual forwarder for FwdTrans(). More...
virtual void	v_SmoothField (Array< OneD, NekDouble > &field)
	Template method virtual forwarded for SmoothField(). More...
virtual void	v_MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	Template method virtual forwarder for MultiplyByInvMassMatrix(). More...
virtual void	v_HelmSolve (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const StdRegions::ConstFactorMap &factors, const StdRegions::VarCoeffMap &varcoeff, const MultiRegions::VarFactorsMap &varfactors, const Array< OneD, const NekDouble > &dirForcing, const bool PhysSpaceForcing)
	Solves the two-dimensional Helmholtz equation, subject to the boundary conditions specified. More...
virtual void	v_LinearAdvectionDiffusionReactionSolve (const Array< OneD, Array< OneD, NekDouble >> &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
void	v_LinearAdvectionReactionSolve (const Array< OneD, Array< OneD, NekDouble >> &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
virtual const Array< OneD, const SpatialDomains ::BoundaryConditionShPtr > &	v_GetBndConditions ()
	Template method virtual forwarder for GetBndConditions(). More...
virtual void	v_ClearGlobalLinSysManager (void)
Protected Member Functions inherited from Nektar::MultiRegions::DisContField
void	GenerateBoundaryConditionExpansion (const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::BoundaryConditions &bcs, const std::string variable, const bool DeclareCoeffPhysArrays=true)
	Discretises the boundary conditions. More...
void	FindPeriodicTraces (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 const LocTraceToTraceMapSharedPtr &	v_GetLocTraceToTraceMap (void) const
virtual std::vector< bool > &	v_GetLeftAdjacentTraces (void)
virtual void	v_AddTraceIntegral (const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)
	Add trace contributions into elemental coefficient spaces. More...
virtual void	v_AddFwdBwdTraceIntegral (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &outarray)
	Add trace contributions into elemental coefficient spaces. More...
virtual void	v_AddTraceQuadPhysToField (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &field)
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...
virtual void	v_GetLocTraceFromTracePts (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &locTraceFwd, Array< OneD, NekDouble > &locTraceBwd)
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 > &TraceID)
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...
virtual void	v_PeriodicBwdCopy (const Array< OneD, const NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)
virtual void	v_FillBwdWithBwdWeight (Array< OneD, NekDouble > &weightave, Array< OneD, NekDouble > &weightjmp)
	Fill the weight with m_bndCondBndWeight. More...
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, bool FillBnd=true, bool PutFwdInBwdOnBCs=false, bool DoExchange=true)
	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_FillBwdWithBoundCond (const Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd, bool PutFwdInBwdOnBCs)
virtual const Array< OneD, const NekDouble > &	v_GetBndCondBwdWeight ()
virtual void	v_SetBndCondBwdWeight (const int index, const NekDouble value)
void	SetUpDG (const std::string="DefaultVar")
	Set up all DG member variables and maps. More...
bool	IsLeftAdjacentTrace (const int n, const int e)
	This routine determines if an element is to the "left" of the adjacent trace, which arises from the idea there is a local normal direction between two elements (i.e. on the trace) and one elements would then be the left. More...
virtual void	v_GetPeriodicEntities (PeriodicMap &periodicVerts, PeriodicMap &periodicEdges, PeriodicMap &periodicFaces)
	Obtain a copy of the periodic edges and vertices for this field. More...
Protected Member Functions inherited from Nektar::MultiRegions::ExpList
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...
virtual int	v_GetNumElmts (void)
virtual 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)
virtual 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)
virtual const Array< OneD, const int > &	v_GetTraceBndMap ()
virtual void	v_GetNormals (Array< OneD, Array< OneD, NekDouble >> &normals)
	Populate normals with the normals of all expansions. More...
virtual void	v_AddTraceIntegral (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)
virtual void	v_AddTraceQuadPhysToOffDiag (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &field)
virtual const std::vector< bool > &	v_GetLeftAdjacentFaces (void) const
virtual void	v_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_FwdTransLocalElmt (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_FwdTransBndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
virtual void	v_IProductWRTBase (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_GetCoords (const int eid, Array< OneD, NekDouble > &xc0, Array< OneD, NekDouble > &xc1, Array< OneD, NekDouble > &xc2)
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, bool Shuff=true, bool UnShuff=true)
virtual void	v_HomogeneousBwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, bool Shuff=true, bool UnShuff=true)
virtual void	v_DealiasedProd (const Array< OneD, NekDouble > &inarray1, const Array< OneD, NekDouble > &inarray2, Array< OneD, NekDouble > &outarray)
virtual void	v_DealiasedDotProd (const Array< OneD, Array< OneD, NekDouble >> &inarray1, const Array< OneD, Array< OneD, NekDouble >> &inarray2, Array< OneD, Array< OneD, NekDouble >> &outarray)
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_SetUpPhysNormals ()
	: Set up a normal along the trace elements between two elements at elemental level More...
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_WriteVtkPieceHeader (std::ostream &outfile, int expansion, int istrip)
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)

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...
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...
GJPStabilisationSharedPtr	m_GJPData
	Data for Gradient Jump Penalisation (GJP) stabilisaiton. More...
Protected Attributes inherited from Nektar::MultiRegions::DisContField
int	m_numDirBndCondExpansions
	The number of boundary segments on which Dirichlet boundary conditions are imposed. More...
Array< OneD, MultiRegions::ExpListSharedPtr >	m_bndCondExpansions
	An object which contains the discretised boundary conditions. More...
Array< OneD, NekDouble >	m_bndCondBndWeight
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_boundaryTraces
	A set storing the global IDs of any boundary Verts. More...
PeriodicMap	m_periodicVerts
	A map which identifies groups of periodic vertices. More...
PeriodicMap	m_periodicEdges
	A map which identifies pairs of periodic edges. More...
PeriodicMap	m_periodicFaces
	A map which identifies pairs of periodic faces. 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_leftAdjacentTraces
LocTraceToTraceMapSharedPtr	m_locTraceToTraceMap
Protected Attributes inherited from Nektar::MultiRegions::ExpList
ExpansionType	m_expType
	Exapnsion type. More...
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< bool >	m_collectionsDoInit
	Vector of bools to act as an initialise on first call flag. More...
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...
Array< OneD, std::pair< int, int > >	m_coeffsToElmt
	m_coeffs to elemental value map More...
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...

Additional Inherited Members
Public Attributes inherited from Nektar::MultiRegions::DisContField
Array< OneD, int >	m_BCtoElmMap
Array< OneD, int >	m_BCtoTraceMap
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

This class is the abstraction of a global continuous two- dimensional spectral/hp element expansion which approximates the solution of a set of partial differential equations.

The class ContField 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 one-dimensional spectral/hp 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 continuous fields. This class should be used when solving 2D problems using a standard Galerkin approach.

Definition at line 56 of file ContField.h.

Constructor & Destructor Documentation

ContField() [1/5]

Nektar::MultiRegions::ContField::ContField

(

)

The default constructor.

Definition at line 89 of file ContField.cpp.

    : DisContField(), m_locToGloMap(), m_globalMat(),
      m_globalLinSysManager(
          std::bind(&ContField::GenGlobalLinSys, this, std::placeholders::_1),
          std::string("GlobalLinSys"))
{
}

ContField() [2/5]

Nektar::MultiRegions::ContField::ContField	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const SpatialDomains::MeshGraphSharedPtr &	graph,
		const std::string &	variable = "DefaultVar",
		const bool	DeclareCoeffPhysArrays = true,
		const bool	CheckIfSingularSystem = false,
		const Collections::ImplementationType	ImpType = Collections::eNoImpType
	)

This constructor sets up global continuous field based on an input mesh and boundary conditions.

Given a mesh graph, 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 \(\hat{u}_n\) and allocates memory for the array #m_contCoeffs. 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

graph	A 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 118 of file ContField.cpp.

    : DisContField(pSession, graph, variable, false, DeclareCoeffPhysArrays,
                   ImpType),
      m_globalMat(MemoryManager<GlobalMatrixMap>::AllocateSharedPtr()),
      m_globalLinSysManager(
          std::bind(&ContField::GenGlobalLinSys, this, std::placeholders::_1),
          std::string("GlobalLinSys"))
{
    m_locToGloMap = MemoryManager<AssemblyMapCG>::AllocateSharedPtr(
        m_session, m_ncoeffs, *this, m_bndCondExpansions, m_bndConditions,
        CheckIfSingularSystem, variable, m_periodicVerts, m_periodicEdges,
        m_periodicFaces);
 
    if (m_session->DefinesCmdLineArgument("verbose"))
    {
        m_locToGloMap->PrintStats(std::cout, variable);
    }
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::DisContField::m_bndCondExpansions, Nektar::MultiRegions::DisContField::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Nektar::MultiRegions::DisContField::m_periodicEdges, Nektar::MultiRegions::DisContField::m_periodicFaces, Nektar::MultiRegions::DisContField::m_periodicVerts, and Nektar::MultiRegions::ExpList::m_session.

ContField() [3/5]

Nektar::MultiRegions::ContField::ContField	(	const ContField &	In,
		const SpatialDomains::MeshGraphSharedPtr &	graph,
		const std::string &	variable,
		const bool	DeclareCoeffPhysArrays = true,
		const bool	CheckIfSingularSystem = false
	)

Construct a global continuous field with solution type based on another field but using a separate input mesh and boundary conditions.

Given a mesh graph, 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 \(\hat{u}_n\) and allocates memory for the array m_coeffs. 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

In	Existing ContField object used to provide the local to global mapping information and global solution type.
graph	A mesh, containing information about the domain and the spectral/hp element expansion.
bcs	The boundary conditions.
bc_loc

Definition at line 165 of file ContField.cpp.

    : DisContField(In, graph, variable, false, DeclareCoeffPhysArrays),
      m_globalMat(MemoryManager<GlobalMatrixMap>::AllocateSharedPtr()),
      m_globalLinSysManager(
          std::bind(&ContField::GenGlobalLinSys, this, std::placeholders::_1),
          std::string("GlobalLinSys")),
      m_GJPData(In.m_GJPData)
{
    if (!SameTypeOfBoundaryConditions(In) || CheckIfSingularSystem)
    {
        m_locToGloMap = MemoryManager<AssemblyMapCG>::AllocateSharedPtr(
            m_session, m_ncoeffs, *this, m_bndCondExpansions, m_bndConditions,
            CheckIfSingularSystem, variable, m_periodicVerts, m_periodicEdges,
            m_periodicFaces);
 
        if (m_session->DefinesCmdLineArgument("verbose"))
        {
            m_locToGloMap->PrintStats(std::cout, variable);
        }
    }
    else
    {
        m_locToGloMap = In.m_locToGloMap;
    }
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::DisContField::m_bndCondExpansions, Nektar::MultiRegions::DisContField::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Nektar::MultiRegions::DisContField::m_periodicEdges, Nektar::MultiRegions::DisContField::m_periodicFaces, Nektar::MultiRegions::DisContField::m_periodicVerts, Nektar::MultiRegions::ExpList::m_session, and Nektar::MultiRegions::DisContField::SameTypeOfBoundaryConditions().

ContField() [4/5]

Nektar::MultiRegions::ContField::ContField	(	const ContField &	In,
		bool	DeclareCoeffPhysArrays = true
	)

The copy constructor.

Initialises the object as a copy of an existing ContField object.

Parameters

In	Existing ContField object.
DeclareCoeffPhysArrays	bool to declare if m_phys and m_coeffs should be declared. Default is true

Definition at line 200 of file ContField.cpp.

    : DisContField(In, DeclareCoeffPhysArrays), m_locToGloMap(In.m_locToGloMap),
      m_globalMat(In.m_globalMat),
      m_globalLinSysManager(In.m_globalLinSysManager), m_GJPData(In.m_GJPData)
{
}

ContField() [5/5]

Nektar::MultiRegions::ContField::ContField	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const ExpList &	In
	)

Copy constructor.

Constructs a continuous field as a copy of an existing explist field and adding all the boundary conditions.

Parameters

In	Existing explist1D field .

Definition at line 213 of file ContField.cpp.

    : DisContField(In), m_locToGloMap(),
      m_globalLinSysManager(
          std::bind(&ContField::GenGlobalLinSys, this, std::placeholders::_1),
          std::string("GlobalLinSys"))
{
    m_locToGloMap = MemoryManager<AssemblyMapCG>::AllocateSharedPtr(
        pSession, m_ncoeffs, In);
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.

~ContField()

Nektar::MultiRegions::ContField::~ContField ( )

virtual

The default destructor.

Definition at line 227 of file ContField.cpp.

{
}

Member Function Documentation

Assemble() [1/2]

void Nektar::MultiRegions::ContField::Assemble ( )

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.

Note

The array m_coeffs should be filled with the local coefficients \(\boldsymbol{\hat{u}}_l\) and that the resulting global coefficients \(\boldsymbol{\hat{u}}_g\) will be stored in m_coeffs.

Definition at line 304 of file ContField.h.

{
    m_locToGloMap->Assemble(m_coeffs, m_coeffs);
}

References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.

Assemble() [2/2]

void Nektar::MultiRegions::ContField::Assemble ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  ) const

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 336 of file ContField.h.

{
    m_locToGloMap->Assemble(inarray, outarray);
}

References m_locToGloMap.

FwdTrans()

void Nektar::MultiRegions::ContField::FwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

Performs the global forward transformation of a function \(f(\boldsymbol{x})\), subject to the boundary conditions specified.

Given a function \(f(\boldsymbol{x})\) 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 \(f(\boldsymbol{x})\) evaluated at the quadrature points \(\boldsymbol{x}_i\) 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

Sin	An ExpList, containing the discrete evaluation of \(f(\boldsymbol{x})\) at the quadrature points in its array m_phys.

Definition at line 248 of file ContField.cpp.

{
    // Inner product of forcing
    Array<OneD, NekDouble> wsp(m_ncoeffs);
    IProductWRTBase(inarray, wsp);
 
    // Solve the system
    GlobalLinSysKey key(StdRegions::eMass, m_locToGloMap);
 
    GlobalSolve(key, wsp, outarray);
}

References Nektar::StdRegions::eMass, GlobalSolve(), Nektar::MultiRegions::ExpList::IProductWRTBase(), m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.

Referenced by v_FwdTrans().

GenGlobalLinSys()

GlobalLinSysSharedPtr Nektar::MultiRegions::ContField::GenGlobalLinSys ( const GlobalLinSysKey &  mkey )

protected

Definition at line 551 of file ContField.cpp.

{
    ASSERTL1(mkey.LocToGloMapIsDefined(),
             "To use method must have a AssemblyMap "
             "attached to key");
    return ExpList::GenGlobalLinSys(mkey, m_locToGloMap);
}

References ASSERTL1, Nektar::MultiRegions::ExpList::GenGlobalLinSys(), Nektar::MultiRegions::GlobalMatrixKey::LocToGloMapIsDefined(), and m_locToGloMap.

GetBndCondExpansions()

const Array< OneD, const MultiRegions::ExpListSharedPtr > & Nektar::MultiRegions::ContField::GetBndCondExpansions ( )

inline

Returns the boundary conditions expansion.

Definition at line 348 of file ContField.h.

{
    return m_bndCondExpansions;
}

References Nektar::MultiRegions::DisContField::m_bndCondExpansions.

GetBndConditions()

const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField::GetBndConditions ( )

inline

Returns the boundary conditions.

Definition at line 354 of file ContField.h.

{
    return m_bndConditions;
}

References Nektar::MultiRegions::DisContField::m_bndConditions.

Referenced by v_GetBndConditions().

GetGJPForcing()

const GJPStabilisationSharedPtr Nektar::MultiRegions::ContField::GetGJPForcing ( )

inline

Definition at line 149 of file ContField.h.

    {
        // initialize if required
        if (!m_GJPData)
        {
            m_GJPData = MemoryManager<GJPStabilisation>::AllocateSharedPtr(
                GetSharedThisPtr());
        }
 
        return m_GJPData;
    }

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::ExpList::GetSharedThisPtr(), and m_GJPData.

GetGlobalLinSys()

GlobalLinSysSharedPtr Nektar::MultiRegions::ContField::GetGlobalLinSys ( const GlobalLinSysKey &  mkey )

protected

Returns the linear system specified by the key 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	This key uniquely defines the requested linear system.

Definition at line 546 of file ContField.cpp.

{
    return m_globalLinSysManager[mkey];
}

References m_globalLinSysManager.

Referenced by GlobalSolve().

GetGlobalMatrix()

GlobalMatrixSharedPtr Nektar::MultiRegions::ContField::GetGlobalMatrix ( const GlobalMatrixKey &  mkey )

protected

Returns the global matrix specified by mkey.

Returns the global matrix associated with the given GlobalMatrixKey. If the global matrix has not yet been constructed on this field, it is first constructed using GenGlobalMatrix().

Parameters

mkey	Global matrix key.

Returns

Assocated global matrix.

Definition at line 516 of file ContField.cpp.

{
    ASSERTL1(mkey.LocToGloMapIsDefined(),
             "To use method must have a AssemblyMap "
             "attached to key");
 
    GlobalMatrixSharedPtr glo_matrix;
    auto matrixIter = m_globalMat->find(mkey);
 
    if (matrixIter == m_globalMat->end())
    {
        glo_matrix           = GenGlobalMatrix(mkey, m_locToGloMap);
        (*m_globalMat)[mkey] = glo_matrix;
    }
    else
    {
        glo_matrix = matrixIter->second;
    }
 
    return glo_matrix;
}

References ASSERTL1, Nektar::MultiRegions::ExpList::GenGlobalMatrix(), Nektar::MultiRegions::GlobalMatrixKey::LocToGloMapIsDefined(), m_globalMat, and m_locToGloMap.

GetGlobalMatrixNnz()

int Nektar::MultiRegions::ContField::GetGlobalMatrixNnz ( const GlobalMatrixKey &  gkey )

inline

Definition at line 359 of file ContField.h.

{
    ASSERTL1(gkey.LocToGloMapIsDefined(),
             "To use method must have a AssemblyMap "
             "attached to key");
 
    auto matrixIter = m_globalMat->find(gkey);
 
    if (matrixIter == m_globalMat->end())
    {
        return 0;
    }
    else
    {
        return matrixIter->second->GetNumNonZeroEntries();
    }
 
    return 0;
}

References ASSERTL1, Nektar::MultiRegions::GlobalMatrixKey::LocToGloMapIsDefined(), and m_globalMat.

GetLocalToGlobalMap()

const AssemblyMapCGSharedPtr & Nektar::MultiRegions::ContField::GetLocalToGlobalMap ( ) const

inline

Returns the map from local to global level.

Definition at line 342 of file ContField.h.

{
    return m_locToGloMap;
}

References m_locToGloMap.

GlobalSolve()

void Nektar::MultiRegions::ContField::GlobalSolve	(	const GlobalLinSysKey &	key,
		const Array< OneD, const NekDouble > &	locrhs,
		Array< OneD, NekDouble > &	inout,
		const Array< OneD, const NekDouble > &	dirForcing = NullNekDouble1DArray
	)

Solves 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

mkey	This key uniquely defines the linear system to be solved.
locrhs	contains the forcing term in local coefficient space

Note

inout contains initial guess and final output in local coeffs.

Definition at line 489 of file ContField.cpp.

{
    int NumDirBcs   = m_locToGloMap->GetNumGlobalDirBndCoeffs();
    int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
 
    // STEP 1: SET THE DIRICHLET DOFS TO THE RIGHT VALUE
    //         IN THE SOLUTION ARRAY
    v_ImposeDirichletConditions(inout);
 
    // STEP 2: CALCULATE THE HOMOGENEOUS COEFFICIENTS
    if (contNcoeffs - NumDirBcs > 0)
    {
        GlobalLinSysSharedPtr LinSys = GetGlobalLinSys(key);
        LinSys->Solve(locrhs, inout, m_locToGloMap, dirForcing);
    }
}

References GetGlobalLinSys(), m_locToGloMap, and v_ImposeDirichletConditions().

Referenced by FwdTrans(), LaplaceSolve(), MultiplyByInvMassMatrix(), v_HelmSolve(), v_LinearAdvectionDiffusionReactionSolve(), and v_LinearAdvectionReactionSolve().

LaplaceSolve()

void Nektar::MultiRegions::ContField::LaplaceSolve	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const Array< OneD, const NekDouble > &	dirForcing = NullNekDouble1DArray,
		const Array< OneD, Array< OneD, NekDouble >> &	variablecoeffs = NullNekDoubleArrayOfArray,
		NekDouble	time = 0.0
	)

Solves the two-dimensional Laplace equation, subject to the boundary conditions specified.

Consider the two dimensional Laplace equation,

\[\nabla\cdot\left(\boldsymbol{\sigma}\nabla u(\boldsymbol{x})\right) = f(\boldsymbol{x}),\]

supplemented with appropriate boundary conditions (which are contained in the data member m_bndCondExpansions). In the equation above \(\boldsymbol{\sigma}\) is the (symmetric positive definite) diffusion tensor:

\[ \sigma = \left[ \begin{array}{cc} \sigma_{00}(\boldsymbol{x},t) & \sigma_{01}(\boldsymbol{x},t) \\ \sigma_{01}(\boldsymbol{x},t) & \sigma_{11}(\boldsymbol{x},t) \end{array} \right]. \]

Applying a \(C^0\) continuous Galerkin discretisation, this equation leads to the following linear system:

\[\boldsymbol{L} \boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}}\]

where \(\boldsymbol{L}\) is the Laplacian matrix. 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 \(f(\boldsymbol{x})\) evaluated at the quadrature points \(\boldsymbol{x}_i\) should be contained in the variable m_phys of the ExpList object Sin. The resulting global coefficients \(\boldsymbol{\hat{u}}_g\) are stored in the array m_coeffs.

Parameters

Sin	An ExpList, containing the discrete evaluation of the forcing function \(f(\boldsymbol{x})\) at the quadrature points in its array m_phys.
variablecoeffs	The (optional) parameter containing the coefficients evaluated at the quadrature points. It is an Array of (three) arrays which stores the laplacian coefficients in the following way \[\mathrm{variablecoeffs} = \left[ \begin{array}{c} \left[\sigma_{00}(\boldsymbol{x_i},t)\right]_i \\ \left[\sigma_{01}(\boldsymbol{x_i},t)\right]_i \\ \left[\sigma_{11}(\boldsymbol{x_i},t)\right]_i \end{array}\right] \] If this argument is not passed to the function, the following equation will be solved: \[\nabla^2u(\boldsymbol{x}) = f(\boldsymbol{x}),\]
time	The time-level at which the coefficients are evaluated

Definition at line 340 of file ContField.cpp.

{
    // Inner product of forcing
    Array<OneD, NekDouble> wsp(m_ncoeffs);
    IProductWRTBase(inarray, wsp);
 
    // Note -1.0 term necessary to invert forcing function to
    // be consistent with matrix definition
    Vmath::Neg(m_ncoeffs, wsp, 1);
 
    // Forcing function with weak boundary conditions
    int i, j;
    int bndcnt = 0;
    Array<OneD, NekDouble> sign =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsSign();
    const Array<OneD, const int> map =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsMap();
 
    // Add weak boundary conditions to forcing
    for (i = 0; i < m_bndCondExpansions.size(); ++i)
    {
        if (m_bndConditions[i]->GetBoundaryConditionType() ==
                SpatialDomains::eNeumann ||
            m_bndConditions[i]->GetBoundaryConditionType() ==
                SpatialDomains::eRobin)
        {
            const Array<OneD, NekDouble> bndcoeff =
                (m_bndCondExpansions[i])->GetCoeffs();
 
            if (m_locToGloMap->GetSignChange())
            {
                for (j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                {
                    wsp[map[bndcnt + j]] += sign[bndcnt + j] * bndcoeff[j];
                }
            }
            else
            {
                for (j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                {
                    wsp[map[bndcnt + j]] += bndcoeff[bndcnt + j];
                }
            }
        }
 
        bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
    }
 
    StdRegions::VarCoeffMap varcoeffs;
    varcoeffs[StdRegions::eVarCoeffD00] = variablecoeffs[0];
    varcoeffs[StdRegions::eVarCoeffD01] = variablecoeffs[1];
    varcoeffs[StdRegions::eVarCoeffD11] = variablecoeffs[3];
    varcoeffs[StdRegions::eVarCoeffD22] = variablecoeffs[5];
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorTime] = time;
 
    // Solve the system
    GlobalLinSysKey key(StdRegions::eLaplacian, m_locToGloMap, factors,
                        varcoeffs);
 
    GlobalSolve(key, wsp, outarray, dirForcing);
}

References Nektar::StdRegions::eFactorTime, Nektar::StdRegions::eLaplacian, Nektar::SpatialDomains::eNeumann, Nektar::SpatialDomains::eRobin, Nektar::StdRegions::eVarCoeffD00, Nektar::StdRegions::eVarCoeffD01, Nektar::StdRegions::eVarCoeffD11, Nektar::StdRegions::eVarCoeffD22, Nektar::MultiRegions::ExpList::GetCoeffs(), Nektar::MultiRegions::ExpList::GetNcoeffs(), GlobalSolve(), Nektar::MultiRegions::ExpList::IProductWRTBase(), Nektar::MultiRegions::DisContField::m_bndCondExpansions, Nektar::MultiRegions::DisContField::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Vmath::Neg(), and sign.

LinearAdvectionEigs()

void Nektar::MultiRegions::ContField::LinearAdvectionEigs	(	const NekDouble	ax,
		const NekDouble	ay,
		Array< OneD, NekDouble > &	Real,
		Array< OneD, NekDouble > &	Imag,
		Array< OneD, NekDouble > &	Evecs = NullNekDouble1DArray
	)

Compute the eigenvalues of the linear advection operator.

Constructs the GlobalLinearSysKey for the linear advection operator with the supplied parameters, and computes the eigenvectors and eigenvalues of the associated matrix.

Parameters

ax	Advection parameter, x.
ay	Advection parameter, y.
Real	Computed eigenvalues, real component.
Imag	Computed eigenvalues, imag component.
Evecs	Computed eigenvectors.

Definition at line 417 of file ContField.cpp.

{
    // Solve the system
    Array<OneD, Array<OneD, NekDouble>> vel(2);
    Array<OneD, NekDouble> vel_x(m_npoints, ax);
    Array<OneD, NekDouble> vel_y(m_npoints, ay);
    vel[0] = vel_x;
    vel[1] = vel_y;
 
    StdRegions::VarCoeffMap varcoeffs;
    varcoeffs[StdRegions::eVarCoeffVelX] =
        Array<OneD, NekDouble>(m_npoints, ax);
    varcoeffs[StdRegions::eVarCoeffVelY] =
        Array<OneD, NekDouble>(m_npoints, ay);
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorTime] = 0.0;
    GlobalLinSysKey key(StdRegions::eLinearAdvectionReaction, m_locToGloMap,
                        factors, varcoeffs);
 
    DNekMatSharedPtr Gmat = GenGlobalMatrixFull(key, m_locToGloMap);
    Gmat->EigenSolve(Real, Imag, Evecs);
}

References CG_Iterations::ax, Nektar::StdRegions::eFactorTime, Nektar::StdRegions::eLinearAdvectionReaction, Nektar::StdRegions::eVarCoeffVelX, Nektar::StdRegions::eVarCoeffVelY, Nektar::MultiRegions::ExpList::GenGlobalMatrixFull(), m_locToGloMap, and Nektar::MultiRegions::ExpList::m_npoints.

MultiplyByInvMassMatrix()

void Nektar::MultiRegions::ContField::MultiplyByInvMassMatrix	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

Multiply a solution by the inverse mass matrix.

Computes the matrix vector product \( \mathbf{y} = \mathbf{M}^{-1}\mathbf{x} \).

Parameters

inarray	Input vector \(\mathbf{x}\).
outarray	Output vector \(\mathbf{y}\).

Definition at line 283 of file ContField.cpp.

{
 
    GlobalLinSysKey key(StdRegions::eMass, m_locToGloMap);
    GlobalSolve(key, inarray, outarray);
}

References Nektar::StdRegions::eMass, GlobalSolve(), and m_locToGloMap.

Referenced by v_MultiplyByInvMassMatrix(), and v_SmoothField().

SetGJPForcing()

void Nektar::MultiRegions::ContField::SetGJPForcing ( const GJPStabilisationSharedPtr &  GJPData )

inline

Definition at line 161 of file ContField.h.

    {
        m_GJPData = GJPData;
    }

References m_GJPData.

v_ClearGlobalLinSysManager()

void Nektar::MultiRegions::ContField::v_ClearGlobalLinSysManager ( void  )

protectedvirtual

Reset the GlobalLinSys Manager

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 1028 of file ContField.cpp.

{
    m_globalLinSysManager.ClearManager("GlobalLinSys");
}

References m_globalLinSysManager.

v_FillBndCondFromField() [1/2]

void Nektar::MultiRegions::ContField::v_FillBndCondFromField ( void  )

protectedvirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 627 of file ContField.cpp.

{
    int bndcnt = 0;
 
    Array<OneD, NekDouble> sign =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsSign();
    const Array<OneD, const int> bndmap =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsMap();
 
    for (int i = 0; i < m_bndCondExpansions.size(); ++i)
    {
        Array<OneD, NekDouble> &coeffs = m_bndCondExpansions[i]->UpdateCoeffs();
 
        if (m_locToGloMap->GetSignChange())
        {
            for (int j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
            {
                coeffs[j] = sign[bndcnt + j] * m_coeffs[bndmap[bndcnt + j]];
            }
        }
        else
        {
            for (int j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
            {
                coeffs[j] = m_coeffs[bndmap[bndcnt + j]];
            }
        }
 
        bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
    }
}

References Nektar::MultiRegions::ExpList::GetNcoeffs(), Nektar::MultiRegions::DisContField::m_bndCondExpansions, Nektar::MultiRegions::ExpList::m_coeffs, m_locToGloMap, and sign.

v_FillBndCondFromField() [2/2]

void Nektar::MultiRegions::ContField::v_FillBndCondFromField ( const int  nreg )

protectedvirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 659 of file ContField.cpp.

{
    int bndcnt = 0;
 
    ASSERTL1(nreg < m_bndCondExpansions.size(),
             "nreg is out or range since this many boundary "
             "regions to not exist");
 
    Array<OneD, NekDouble> sign =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsSign();
    const Array<OneD, const int> bndmap =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsMap();
 
    // Now fill in all other Dirichlet coefficients.
    Array<OneD, NekDouble> &coeffs = m_bndCondExpansions[nreg]->UpdateCoeffs();
 
    for (int j = 0; j < nreg; ++j)
    {
        bndcnt += m_bndCondExpansions[j]->GetNcoeffs();
    }
 
    if (m_locToGloMap->GetSignChange())
    {
        for (int j = 0; j < (m_bndCondExpansions[nreg])->GetNcoeffs(); ++j)
        {
            coeffs[j] = sign[bndcnt + j] * m_coeffs[bndmap[bndcnt + j]];
        }
    }
    else
    {
        for (int j = 0; j < (m_bndCondExpansions[nreg])->GetNcoeffs(); ++j)
        {
            coeffs[j] = m_coeffs[bndmap[bndcnt + j]];
        }
    }
}

References ASSERTL1, Nektar::MultiRegions::ExpList::GetNcoeffs(), Nektar::MultiRegions::DisContField::m_bndCondExpansions, Nektar::MultiRegions::ExpList::m_coeffs, m_locToGloMap, and sign.

v_FwdTrans()

void Nektar::MultiRegions::ContField::v_FwdTrans ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

protectedvirtual

Template method virtual forwarder for FwdTrans().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 562 of file ContField.cpp.

{
    FwdTrans(inarray, outarray);
}

References FwdTrans().

v_GetBndConditions()

const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField::v_GetBndConditions ( void  )

protectedvirtual

Template method virtual forwarder for GetBndConditions().

Reimplemented from Nektar::MultiRegions::DisContField.

Definition at line 1020 of file ContField.cpp.

{
    return GetBndConditions();
}

References GetBndConditions().

v_GlobalToLocal() [1/2]

void Nektar::MultiRegions::ContField::v_GlobalToLocal ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

protectedvirtual

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.

Note

The array m_coeffs should be filled with the global coefficients \(\boldsymbol{\hat{u}}_g\) and that the resulting local coefficients \(\boldsymbol{\hat{u}}_l\) will be stored in m_coeffs.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 720 of file ContField.cpp.

{
    m_locToGloMap->GlobalToLocal(inarray, outarray);
}

References m_locToGloMap.

v_GlobalToLocal() [2/2]

void Nektar::MultiRegions::ContField::v_GlobalToLocal ( void  )

protectedvirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 726 of file ContField.cpp.

{
    m_locToGloMap->GlobalToLocal(m_coeffs, m_coeffs);
}

References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.

v_HelmSolve()

void Nektar::MultiRegions::ContField::v_HelmSolve ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray, const StdRegions::ConstFactorMap &  factors, const StdRegions::VarCoeffMap &  pvarcoeff, const MultiRegions::VarFactorsMap &  varfactors, const Array< OneD, const NekDouble > &  dirForcing, const bool  PhysSpaceForcing  )

protectedvirtual

Solves the two-dimensional Helmholtz equation, subject to the boundary conditions specified.

Consider the two dimensional Helmholtz equation,

\[\nabla^2u(\boldsymbol{x})-\lambda u(\boldsymbol{x}) = f(\boldsymbol{x}),\]

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:

\[\left(\boldsymbol{L}+\lambda\boldsymbol{M}\right) \boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}}\]

where \(\boldsymbol{L}\) and \(\boldsymbol{M}\) are the Laplacian and mass matrix respectively. This function solves the system above for the global coefficients \(\boldsymbol{\hat{u}}\) by a call to the function GlobalSolve. It is assumed #m_coeff contains an initial estimate for the solution.

The values of the function \(f(\boldsymbol{x})\) evaluated at the quadrature points \(\boldsymbol{x}_i\) should be contained in the variable m_phys of the ExpList object inarray.

Parameters

inarray	An ExpList, containing the discrete evaluation of the forcing function \(f(\boldsymbol{x})\) at the quadrature points in its array m_phys.
factors	The parameter \(\lambda\) of the Helmholtz equation is specified through the factors map

Reimplemented from Nektar::MultiRegions::DisContField.

Definition at line 807 of file ContField.cpp.

{
    int i, j;
 
    //----------------------------------
    //  Setup RHS Inner product
    //----------------------------------
    // Inner product of forcing
    Array<OneD, NekDouble> wsp(m_ncoeffs);
    if (PhysSpaceForcing)
    {
        IProductWRTBase(inarray, wsp);
        // Note -1.0 term necessary to invert forcing function to
        // be consistent with matrix definition
        Vmath::Neg(m_ncoeffs, wsp, 1);
    }
    else
    {
        Vmath::Smul(m_ncoeffs, -1.0, inarray, 1, wsp, 1);
    }
 
    int bndcnt = 0;
    Array<OneD, NekDouble> sign =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsSign();
    const Array<OneD, const int> map =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsMap();
    // Add weak boundary conditions to forcing
    for (i = 0; i < m_bndCondExpansions.size(); ++i)
    {
        if (m_bndConditions[i]->GetBoundaryConditionType() ==
                SpatialDomains::eNeumann ||
            m_bndConditions[i]->GetBoundaryConditionType() ==
                SpatialDomains::eRobin)
        {
            const Array<OneD, NekDouble> bndcoeff =
                (m_bndCondExpansions[i])->GetCoeffs();
 
            if (m_locToGloMap->GetSignChange())
            {
                for (j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                {
                    wsp[map[bndcnt + j]] += sign[bndcnt + j] * bndcoeff[j];
                }
            }
            else
            {
                for (j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                {
                    wsp[map[bndcnt + j]] += bndcoeff[j];
                }
            }
        }
        bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
    }
 
    StdRegions::MatrixType mtype = StdRegions::eHelmholtz;
 
    StdRegions::VarCoeffMap varcoeff(pvarcoeff);
    if (factors.count(StdRegions::eFactorGJP))
    {
        // initialize if required
        if (!m_GJPData)
        {
            m_GJPData = MemoryManager<GJPStabilisation>::AllocateSharedPtr(
                GetSharedThisPtr());
        }
 
        if (m_GJPData->IsSemiImplicit())
        {
            mtype = StdRegions::eHelmholtzGJP;
        }
 
        // to set up forcing need initial guess in physical space
        Array<OneD, NekDouble> phys(m_npoints), tmp;
        BwdTrans(outarray, phys);
        NekDouble scale = -1.0 * factors.find(StdRegions::eFactorGJP)->second;
 
        m_GJPData->Apply(
            phys, wsp,
            pvarcoeff.count(StdRegions::eVarCoeffGJPNormVel)
                ? pvarcoeff.find(StdRegions::eVarCoeffGJPNormVel)->second
                : NullNekDouble1DArray,
            scale);
 
        varcoeff.erase(StdRegions::eVarCoeffGJPNormVel);
    }
 
    GlobalLinSysKey key(mtype, m_locToGloMap, factors, varcoeff, varfactors);
 
    GlobalSolve(key, wsp, outarray, dirForcing);
}

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::ExpList::BwdTrans(), Nektar::StdRegions::eFactorGJP, Nektar::StdRegions::eHelmholtz, Nektar::StdRegions::eHelmholtzGJP, Nektar::SpatialDomains::eNeumann, Nektar::SpatialDomains::eRobin, Nektar::StdRegions::eVarCoeffGJPNormVel, Nektar::MultiRegions::ExpList::GetCoeffs(), Nektar::MultiRegions::ExpList::GetNcoeffs(), Nektar::MultiRegions::ExpList::GetSharedThisPtr(), GlobalSolve(), Nektar::MultiRegions::ExpList::IProductWRTBase(), Nektar::MultiRegions::DisContField::m_bndCondExpansions, Nektar::MultiRegions::DisContField::m_bndConditions, m_GJPData, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Nektar::MultiRegions::ExpList::m_npoints, Vmath::Neg(), Nektar::NullNekDouble1DArray, sign, and Vmath::Smul().

v_ImposeDirichletConditions()

void Nektar::MultiRegions::ContField::v_ImposeDirichletConditions ( Array< OneD, NekDouble > &  outarray )

protectedvirtual

Impose the Dirichlet Boundary Conditions on outarray.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 568 of file ContField.cpp.

{
    int i, j;
    int bndcnt = 0;
 
    Array<OneD, NekDouble> sign =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsSign();
    const Array<OneD, const int> map =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsMap();
 
    for (i = 0; i < m_bndCondExpansions.size(); ++i)
    {
        if (m_bndConditions[i]->GetBoundaryConditionType() ==
            SpatialDomains::eDirichlet)
        {
            const Array<OneD, NekDouble> bndcoeff =
                (m_bndCondExpansions[i])->GetCoeffs();
 
            if (m_locToGloMap->GetSignChange())
            {
                for (j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                {
                    outarray[map[bndcnt + j]] = sign[bndcnt + j] * bndcoeff[j];
                }
            }
            else
            {
                for (j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                {
                    outarray[map[bndcnt + j]] = bndcoeff[j];
                }
            }
        }
        bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
    }
 
    // communicate local Dirichlet coeffs that are just
    // touching a dirichlet boundary on another partition
    set<int> &ParallelDirBndSign = m_locToGloMap->GetParallelDirBndSign();
 
    for (auto &it : ParallelDirBndSign)
    {
        outarray[it] *= -1;
    }
 
    m_locToGloMap->UniversalAbsMaxBnd(outarray);
 
    for (auto &it : ParallelDirBndSign)
    {
        outarray[it] *= -1;
    }
 
    set<ExtraDirDof> &copyLocalDirDofs = m_locToGloMap->GetCopyLocalDirDofs();
    for (auto &it : copyLocalDirDofs)
    {
        outarray[std::get<0>(it)] = outarray[std::get<1>(it)] * std::get<2>(it);
    }
}

References Nektar::SpatialDomains::eDirichlet, Nektar::MultiRegions::ExpList::GetCoeffs(), Nektar::MultiRegions::ExpList::GetNcoeffs(), Nektar::MultiRegions::DisContField::m_bndCondExpansions, Nektar::MultiRegions::DisContField::m_bndConditions, m_locToGloMap, and sign.

Referenced by GlobalSolve().

v_LinearAdvectionDiffusionReactionSolve()

void Nektar::MultiRegions::ContField::v_LinearAdvectionDiffusionReactionSolve ( const Array< OneD, Array< OneD, NekDouble >> &  velocity, const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray, const NekDouble  lambda, const Array< OneD, const NekDouble > &  dirForcing = NullNekDouble1DArray  )

protectedvirtual

First compute the inner product of forcing function with respect to base, and then solve the system with the linear advection operator.

Parameters

velocity	Array of advection velocities in physical space
inarray	Forcing function.
outarray	Result.
lambda	reaction coefficient
dirForcing	Dirichlet Forcing.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 917 of file ContField.cpp.

{
    // Inner product of forcing
    Array<OneD, NekDouble> wsp(m_ncoeffs);
    IProductWRTBase(inarray, wsp);
 
    // Note -1.0 term necessary to invert forcing function to
    // be consistent with matrix definition
    Vmath::Neg(m_ncoeffs, wsp, 1);
 
    // Forcing function with weak boundary conditions
    int i, j;
    int bndcnt = 0;
    Array<OneD, NekDouble> sign =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsSign();
    const Array<OneD, const int> map =
        m_locToGloMap->GetBndCondCoeffsToLocalCoeffsMap();
    // Add weak boundary conditions to forcing
    for (i = 0; i < m_bndCondExpansions.size(); ++i)
    {
        if (m_bndConditions[i]->GetBoundaryConditionType() ==
                SpatialDomains::eNeumann ||
            m_bndConditions[i]->GetBoundaryConditionType() ==
                SpatialDomains::eRobin)
        {
            const Array<OneD, NekDouble> bndcoeff =
                (m_bndCondExpansions[i])->GetCoeffs();
 
            if (m_locToGloMap->GetSignChange())
            {
                for (j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                {
                    wsp[map[bndcnt + j]] += sign[bndcnt + j] * bndcoeff[j];
                }
            }
            else
            {
                for (j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                {
                    wsp[map[bndcnt + j]] += bndcoeff[bndcnt + j];
                }
            }
        }
 
        bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
    }
 
    // Solve the system
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda] = lambda;
    StdRegions::VarCoeffMap varcoeffs;
    varcoeffs[StdRegions::eVarCoeffVelX] = velocity[0];
    varcoeffs[StdRegions::eVarCoeffVelY] = velocity[1];
    if (m_expType == e3D)
    {
        varcoeffs[StdRegions::eVarCoeffVelZ] = velocity[2];
    }
 
    GlobalLinSysKey key(StdRegions::eLinearAdvectionDiffusionReaction,
                        m_locToGloMap, factors, varcoeffs);
 
    GlobalSolve(key, wsp, outarray, dirForcing);
}

References Nektar::MultiRegions::e3D, Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eLinearAdvectionDiffusionReaction, Nektar::SpatialDomains::eNeumann, Nektar::SpatialDomains::eRobin, Nektar::StdRegions::eVarCoeffVelX, Nektar::StdRegions::eVarCoeffVelY, Nektar::StdRegions::eVarCoeffVelZ, Nektar::MultiRegions::ExpList::GetCoeffs(), Nektar::MultiRegions::ExpList::GetNcoeffs(), GlobalSolve(), Nektar::MultiRegions::ExpList::IProductWRTBase(), Nektar::MultiRegions::DisContField::m_bndCondExpansions, Nektar::MultiRegions::DisContField::m_bndConditions, Nektar::MultiRegions::ExpList::m_expType, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Vmath::Neg(), and sign.

v_LinearAdvectionReactionSolve()

void Nektar::MultiRegions::ContField::v_LinearAdvectionReactionSolve ( const Array< OneD, Array< OneD, NekDouble >> &  velocity, const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray, const NekDouble  lambda, const Array< OneD, const NekDouble > &  dirForcing = NullNekDouble1DArray  )

protectedvirtual

First compute the inner product of forcing function with respect to base, and then solve the system with the linear advection operator.

Parameters

velocity	Array of advection velocities in physical space
inarray	Forcing function.
outarray	Result.
lambda	reaction coefficient
dirForcing	Dirichlet Forcing.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 994 of file ContField.cpp.

{
    // Inner product of forcing
    Array<OneD, NekDouble> wsp(m_ncoeffs);
    IProductWRTBase(inarray, wsp);
 
    // Solve the system
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda] = lambda;
    StdRegions::VarCoeffMap varcoeffs;
    varcoeffs[StdRegions::eVarCoeffVelX] = velocity[0];
    varcoeffs[StdRegions::eVarCoeffVelY] = velocity[1];
    GlobalLinSysKey key(StdRegions::eLinearAdvectionReaction, m_locToGloMap,
                        factors, varcoeffs);
 
    GlobalSolve(key, wsp, outarray, dirForcing);
}

References Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eLinearAdvectionReaction, Nektar::StdRegions::eVarCoeffVelX, Nektar::StdRegions::eVarCoeffVelY, GlobalSolve(), Nektar::MultiRegions::ExpList::IProductWRTBase(), m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.

v_LocalToGlobal() [1/2]

void Nektar::MultiRegions::ContField::v_LocalToGlobal ( bool  useComm )

protectedvirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 765 of file ContField.cpp.

{
    m_locToGloMap->LocalToGlobal(m_coeffs, m_coeffs, useComm);
}

References Nektar::MultiRegions::ExpList::m_coeffs, and m_locToGloMap.

v_LocalToGlobal() [2/2]

void Nektar::MultiRegions::ContField::v_LocalToGlobal ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray, bool  useComm  )

protectedvirtual

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.

Note

The array m_coeffs should be filled with the local coefficients \(\boldsymbol{\hat{u}}_l\) and that the resulting global coefficients \(\boldsymbol{\hat{u}}_g\) will be stored in m_coeffs. Also if useComm is set to false then no communication call will be made to check if all values are consistent over processors

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 759 of file ContField.cpp.

{
    m_locToGloMap->LocalToGlobal(inarray, outarray, useComm);
}

References m_locToGloMap.

v_MultiplyByInvMassMatrix()

void Nektar::MultiRegions::ContField::v_MultiplyByInvMassMatrix ( const Array< OneD, const NekDouble > &  inarray, Array< OneD, NekDouble > &  outarray  )

protectedvirtual

Template method virtual forwarder for MultiplyByInvMassMatrix().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 774 of file ContField.cpp.

{
    MultiplyByInvMassMatrix(inarray, outarray);
}

References MultiplyByInvMassMatrix().

v_SmoothField()

void Nektar::MultiRegions::ContField::v_SmoothField ( Array< OneD, NekDouble > &  field )

protectedvirtual

Template method virtual forwarded for SmoothField().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 265 of file ContField.cpp.

{
    int Ncoeffs = m_locToGloMap->GetNumLocalCoeffs();
    Array<OneD, NekDouble> tmp1(Ncoeffs);
    Array<OneD, NekDouble> tmp2(Ncoeffs);
 
    IProductWRTBase(field, tmp1);
    MultiplyByInvMassMatrix(tmp1, tmp2);
    BwdTrans(tmp2, field);
}

References Nektar::MultiRegions::ExpList::BwdTrans(), Nektar::MultiRegions::ExpList::IProductWRTBase(), m_locToGloMap, and MultiplyByInvMassMatrix().

Member Data Documentation

m_GJPData

GJPStabilisationSharedPtr Nektar::MultiRegions::ContField::m_GJPData

protected

Data for Gradient Jump Penalisation (GJP) stabilisaiton.

Definition at line 186 of file ContField.h.

Referenced by GetGJPForcing(), SetGJPForcing(), and v_HelmSolve().

m_globalLinSysManager

LibUtilities::NekManager<GlobalLinSysKey, GlobalLinSys> Nektar::MultiRegions::ContField::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 183 of file ContField.h.

Referenced by GetGlobalLinSys(), and v_ClearGlobalLinSysManager().

m_globalMat

GlobalMatrixMapShPtr Nektar::MultiRegions::ContField::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 177 of file ContField.h.

Referenced by GetGlobalMatrix(), and GetGlobalMatrixNnz().

m_locToGloMap

AssemblyMapCGSharedPtr Nektar::MultiRegions::ContField::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 172 of file ContField.h.

Referenced by Assemble(), ContField(), FwdTrans(), GenGlobalLinSys(), GetGlobalMatrix(), GetLocalToGlobalMap(), GlobalSolve(), LaplaceSolve(), LinearAdvectionEigs(), MultiplyByInvMassMatrix(), v_FillBndCondFromField(), v_GlobalToLocal(), v_HelmSolve(), v_ImposeDirichletConditions(), v_LinearAdvectionDiffusionReactionSolve(), v_LinearAdvectionReactionSolve(), v_LocalToGlobal(), and v_SmoothField().