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 <ContField2D.h>

Inheritance diagram for Nektar::MultiRegions::ContField2D:

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Collaboration diagram for Nektar::MultiRegions::ContField2D:

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Public Member Functions
	ContField2D ()
	The default constructor. More...

	ContField2D (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...

	ContField2D (const ContField2D &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...

	ContField2D (const ContField2D &In, bool DeclareCoeffPhysArrays=true)
	The copy constructor. More...

virtual	~ContField2D ()
	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	IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
	Calculates the inner product of a function $f(\boldsymbol{x})$ with respect to all global expansion modes $\phi_n^e(\boldsymbol{x})$ . More...

void	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
	Performs the global forward transformation of a function $f(\boldsymbol{x})$ , subject to the boundary conditions specified. More...

void	BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
	Performs the backward transformation of the spectral/hp element expansion. More...

void	MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
	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, CoeffState coeffstate=eLocal)
	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)

Public Member Functions inherited from Nektar::MultiRegions::DisContField2D
	DisContField2D ()
	Default constructor. More...

	DisContField2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph2D, const std::string &variable, const bool SetUpJustDG=true, const bool DeclareCoeffPhysArrays=true, const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Constructs a global discontinuous field based on an input mesh with boundary conditions. More...

	DisContField2D (const DisContField2D &In, const SpatialDomains::MeshGraphSharedPtr &graph2D, const std::string &variable, const bool SetUpJustDG=false, const bool DeclareCoeffPhysArrays=true)

	DisContField2D (const DisContField2D &In, const bool DeclareCoeffPhysArrays=true)

virtual	~DisContField2D ()
	Default destructor. More...

GlobalLinSysSharedPtr	GetGlobalBndLinSys (const GlobalLinSysKey &mkey)

NekDouble	L2_DGDeriv (const int dir, const Array< OneD, const NekDouble > &soln)
	Calculate the 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...

virtual ExpListSharedPtr &	v_GetTrace ()

Public Member Functions inherited from Nektar::MultiRegions::ExpList2D
	ExpList2D ()
	Default constructor. More...

	ExpList2D (const ExpList2D &In, const bool DeclareCoeffPhysArrays=true)
	Copy constructor. More...

	ExpList2D (const ExpList2D &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...

	ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph2D, const bool DelcareCoeffPhysArrays=true, const std::string &var="DefaultVar", const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Sets up a list of local expansions based on an input mesh. More...

	ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::ExpansionMap &expansions, const bool DeclareCoeffPhysArrays=true, const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Sets up a list of local expansions based on an expansion Map. More...

	ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const LibUtilities::BasisKey &TriBa, const LibUtilities::BasisKey &TriBb, const LibUtilities::BasisKey &QuadBa, const LibUtilities::BasisKey &QuadBb, const SpatialDomains::MeshGraphSharedPtr &graph2D, const LibUtilities::PointsType TriNb=LibUtilities::SIZE_PointsType, const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Sets up a list of local expansions based on an input mesh and separately defined basiskeys. More...

	ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const Array< OneD, const ExpListSharedPtr > &bndConstraint, const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > &bndCond, const LocalRegions::ExpansionVector &locexp, const SpatialDomains::MeshGraphSharedPtr &graph3D, const PeriodicMap &periodicFaces, const bool DeclareCoeffPhysArrays=true, const std::string variable="DefaultVar", const Collections::ImplementationType ImpType=Collections::eNoImpType)

	ExpList2D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::CompositeMap &domain, const SpatialDomains::MeshGraphSharedPtr &graph3D, const std::string variable="DefaultVar", const Collections::ImplementationType ImpType=Collections::eNoImpType)
	Specialised constructor for Neumann boundary conditions in DisContField3D and ContField3D. More...

virtual	~ExpList2D ()
	Destructor. More...

Public Member Functions inherited from Nektar::MultiRegions::ExpList
	ExpList ()
	The default constructor. More...

	ExpList (const LibUtilities::SessionReaderSharedPtr &pSession)
	The default constructor. More...

	ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
	The default constructor. More...

	ExpList (const ExpList &in, const std::vector< unsigned int > &eIDs, const bool DeclareCoeffPhysArrays=true)
	Constructor copying only elements defined in eIds. More...

	ExpList (const ExpList &in, const bool DeclareCoeffPhysArrays=true)
	The copy constructor. More...

virtual	~ExpList ()
	The default destructor. More...

int	GetNcoeffs (void) const
	Returns the total number of local degrees of freedom $N_{\mathrm{eof}}=\sum_{e=1}^{{N_{\mathrm{el}}}}N^{e}_m$ . More...

int	GetNcoeffs (const int eid) const
	Returns the total number of local degrees of freedom for element eid. More...

ExpansionType	GetExpType (void)
	Returns the type of the expansion. More...

void	SetExpType (ExpansionType Type)
	Returns the type of the expansion. More...

int	EvalBasisNumModesMax (void) const
	Evaulates the maximum number of modes in the elemental basis order over all elements. More...

const Array< OneD, int >	EvalBasisNumModesMaxPerExp (void) const
	Returns the vector of the number of modes in the elemental basis order over all elements. More...

int	GetTotPoints (void) const
	Returns the total number of quadrature points m_npoints $=Q_{\mathrm{tot}}$ . More...

int	GetTotPoints (const int eid) const
	Returns the total number of quadrature points for eid's element $=Q_{\mathrm{tot}}$ . More...

int	GetNpoints (void) const
	Returns the total number of quadrature points m_npoints $=Q_{\mathrm{tot}}$ . More...

int	Get1DScaledTotPoints (const NekDouble scale) const
	Returns the total number of qudature points scaled by the factor scale on each 1D direction. More...

void	SetWaveSpace (const bool wavespace)
	Sets the wave space to the one of the possible configuration true or false. More...

void	SetModifiedBasis (const bool modbasis)
	Set Modified Basis for the stability analysis. More...

void	SetPhys (int i, NekDouble val)
	Set the i th value of m_phys to value val. More...

bool	GetWaveSpace (void) const
	This function returns the third direction expansion condition, which can be in wave space (coefficient) or not It is stored in the variable m_WaveSpace. More...

void	SetPhys (const Array< OneD, const NekDouble > &inarray)
	Fills the array m_phys. More...

void	SetPhysArray (Array< OneD, NekDouble > &inarray)
	Sets the array m_phys. More...

void	SetPhysState (const bool physState)
	This function manually sets whether the array of physical values $\boldsymbol{u}_l$ (implemented as m_phys) is filled or not. More...

bool	GetPhysState (void) const
	This function indicates whether the array of physical values $\boldsymbol{u}_l$ (implemented as m_phys) is filled or not. More...

NekDouble	PhysIntegral (void)
	This function integrates a function $f(\boldsymbol{x})$ over the domain consisting of all the elements of the expansion. More...

NekDouble	PhysIntegral (const Array< OneD, const NekDouble > &inarray)
	This function integrates a function $f(\boldsymbol{x})$ over the domain consisting of all the elements of the expansion. More...

void	IProductWRTBase_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function calculates the inner product of a function $f(\boldsymbol{x})$ with respect to all {local} expansion modes $\phi_n^e(\boldsymbol{x})$ . More...

void	IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)

void	IProductWRTDerivBase (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function calculates the inner product of a function $f(\boldsymbol{x})$ with respect to the derivative (in direction. More...

void	IProductWRTDerivBase (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, NekDouble > &outarray)
	This function calculates the inner product of a function $f(\boldsymbol{x})$ with respect to the derivative (in direction. More...

void	FwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function elementally evaluates the forward transformation of a function $u(\boldsymbol{x})$ onto the global spectral/hp expansion. More...

void	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)

void	MultiplyByElmtInvMass (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function elementally mulplies the coefficient space of Sin my the elemental inverse of the mass matrix. More...

void	MultiplyByInvMassMatrix (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)

void	SmoothField (Array< OneD, NekDouble > &field)
	Smooth a field across elements. More...

void	HelmSolve (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const FlagList &flags, const StdRegions::ConstFactorMap &factors, const StdRegions::VarCoeffMap &varcoeff=StdRegions::NullVarCoeffMap, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray, const bool PhysSpaceForcing=true)
	Solve helmholtz problem. More...

void	LinearAdvectionDiffusionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
	Solve Advection Diffusion Reaction. More...

void	LinearAdvectionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
	Solve Advection Diffusion Reaction. More...

void	FwdTrans_BndConstrained (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	BwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This function elementally evaluates the backward transformation of the global spectral/hp element expansion. More...

void	BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)

void	GetCoords (Array< OneD, NekDouble > &coord_0, Array< OneD, NekDouble > &coord_1=NullNekDouble1DArray, Array< OneD, NekDouble > &coord_2=NullNekDouble1DArray)
	This function calculates the coordinates of all the elemental quadrature points $\boldsymbol{x}_i$ . More...

void	HomogeneousFwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true)

void	HomogeneousBwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true)

void	DealiasedProd (const Array< OneD, NekDouble > &inarray1, const Array< OneD, NekDouble > &inarray2, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)

void	DealiasedDotProd (const Array< OneD, Array< OneD, NekDouble > > &inarray1, const Array< OneD, Array< OneD, NekDouble > > &inarray2, Array< OneD, Array< OneD, NekDouble > > &outarray, CoeffState coeffstate=eLocal)

void	GetBCValues (Array< OneD, NekDouble > &BndVals, const Array< OneD, NekDouble > &TotField, int BndID)

void	NormVectorIProductWRTBase (Array< OneD, const NekDouble > &V1, Array< OneD, const NekDouble > &V2, Array< OneD, NekDouble > &outarray, int BndID)

void	NormVectorIProductWRTBase (Array< OneD, Array< OneD, NekDouble > > &V, Array< OneD, NekDouble > &outarray)

void	ApplyGeomInfo ()
	Apply geometry information to each expansion. More...

void	Reset ()
	Reset geometry information and reset matrices. More...

void	WriteTecplotHeader (std::ostream &outfile, std::string var="")

void	WriteTecplotZone (std::ostream &outfile, int expansion=-1)

void	WriteTecplotField (std::ostream &outfile, int expansion=-1)

void	WriteTecplotConnectivity (std::ostream &outfile, int expansion=-1)

void	WriteVtkHeader (std::ostream &outfile)

void	WriteVtkFooter (std::ostream &outfile)

void	WriteVtkPieceHeader (std::ostream &outfile, int expansion, int istrip=0)

void	WriteVtkPieceFooter (std::ostream &outfile, int expansion)

void	WriteVtkPieceData (std::ostream &outfile, int expansion, std::string var="v")

int	GetCoordim (int eid)
	This function returns the dimension of the coordinates of the element eid. More...

void	SetCoeff (int i, NekDouble val)
	Set the i th coefficiient in m_coeffs to value val. More...

void	SetCoeffs (int i, NekDouble val)
	Set the i th coefficiient in m_coeffs to value val. More...

void	SetCoeffsArray (Array< OneD, NekDouble > &inarray)
	Set the m_coeffs array to inarray. More...

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 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 error of the global spectral/hp element approximation. More...

NekDouble	Integral (const Array< OneD, const NekDouble > &inarray)

Array< OneD, const NekDouble >	HomogeneousEnergy (void)
	This function calculates the energy associated with each one of the modesof a 3D homogeneous nD expansion. More...

void	SetHomo1DSpecVanVisc (Array< OneD, NekDouble > visc)
	This function sets the Spectral Vanishing Viscosity in homogeneous1D expansion. More...

Array< OneD, const unsigned int >	GetZIDs (void)
	This function returns a vector containing the wave numbers in z-direction associated with the 3D homogenous expansion. Required if a parellelisation is applied in the Fourier direction. More...

LibUtilities::TranspositionSharedPtr	GetTransposition (void)
	This function returns the transposition class associaed with the homogeneous expansion. More...

NekDouble	GetHomoLen (void)
	This function returns the Width of homogeneous direction associaed with the homogeneous expansion. More...

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 boost::shared_ptr < LocalRegions::ExpansionVector >	GetExp () const
	This function returns the vector of elements in the expansion. More...

LocalRegions::ExpansionSharedPtr &	GetExp (int n) const
	This function returns (a shared pointer to) the local elemental expansion of the $n^{\mathrm{th}}$ element. More...

LocalRegions::ExpansionSharedPtr &	GetExp (const Array< OneD, const NekDouble > &gloCoord)
	This function returns (a shared pointer to) the local elemental expansion containing the arbitrary point given by gloCoord. More...

int	GetExpIndex (const Array< OneD, const NekDouble > &gloCoord, NekDouble tol=0.0, bool returnNearestElmt=false)

int	GetExpIndex (const Array< OneD, const NekDouble > &gloCoords, Array< OneD, NekDouble > &locCoords, NekDouble tol=0.0, bool returnNearestElmt=false)

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)

const Array< OneD, const boost::shared_ptr< ExpList > > &	GetBndCondExpansions ()

boost::shared_ptr< ExpList > &	UpdateBndCondExpansion (int i)

void	Upwind (const Array< OneD, const Array< OneD, NekDouble > > &Vec, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)

void	Upwind (const Array< OneD, const NekDouble > &Vn, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)

boost::shared_ptr< ExpList > &	GetTrace ()

boost::shared_ptr < AssemblyMapDG > &	GetTraceMap (void)

const Array< OneD, const int > &	GetTraceBndMap (void)

void	GetNormals (Array< OneD, Array< OneD, NekDouble > > &normals)

void	AddTraceIntegral (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)

void	AddTraceIntegral (const Array< OneD, const NekDouble > &Fn, Array< OneD, NekDouble > &outarray)

void	AddFwdBwdTraceIntegral (const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &outarray)

void	GetFwdBwdTracePhys (Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)

void	GetFwdBwdTracePhys (const Array< OneD, const NekDouble > &field, Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)

const std::vector< bool > &	GetLeftAdjacentFaces (void) const

void	ExtractTracePhys (Array< OneD, NekDouble > &outarray)

void	ExtractTracePhys (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

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

Array< OneD, SpatialDomains::BoundaryConditionShPtr > &	UpdateBndConditions ()

void	EvaluateBoundaryConditions (const NekDouble time=0.0, const std::string varName="", const NekDouble=NekConstants::kNekUnsetDouble, const NekDouble=NekConstants::kNekUnsetDouble)

void	GeneralMatrixOp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
	This function calculates the result of the multiplication of a matrix of type specified by mkey with a vector given by inarray. More...

void	GeneralMatrixOp_IterPerExp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	SetUpPhysNormals ()

void	GetBoundaryToElmtMap (Array< OneD, int > &ElmtID, Array< OneD, int > &EdgeID)

void	GetBndElmtExpansion (int i, boost::shared_ptr< ExpList > &result, const bool DeclareCoeffPhysArrays=true)

void	ExtractElmtToBndPhys (int i, Array< OneD, NekDouble > &elmt, Array< OneD, NekDouble > &boundary)

void	ExtractPhysToBndElmt (int i, const Array< OneD, const NekDouble > &phys, Array< OneD, NekDouble > &bndElmt)

void	ExtractPhysToBnd (int i, const Array< OneD, const NekDouble > &phys, Array< OneD, NekDouble > &bnd)

void	GetBoundaryNormals (int i, Array< OneD, Array< OneD, NekDouble > > &normals)

void	GeneralGetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef, int NumHomoDir=0, Array< OneD, LibUtilities::BasisSharedPtr > &HomoBasis=LibUtilities::NullBasisSharedPtr1DArray, std::vector< NekDouble > &HomoLen=LibUtilities::NullNekDoubleVector, bool homoStrips=false, std::vector< unsigned int > &HomoSIDs=LibUtilities::NullUnsignedIntVector, std::vector< unsigned int > &HomoZIDs=LibUtilities::NullUnsignedIntVector, std::vector< unsigned int > &HomoYIDs=LibUtilities::NullUnsignedIntVector)

const NekOptimize::GlobalOptParamSharedPtr &	GetGlobalOptParam (void)

std::map< int, RobinBCInfoSharedPtr >	GetRobinBCInfo ()

void	GetPeriodicEntities (PeriodicMap &periodicVerts, PeriodicMap &periodicEdges, PeriodicMap &periodicFaces=NullPeriodicMap)

std::vector < LibUtilities::FieldDefinitionsSharedPtr >	GetFieldDefinitions ()

void	GetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef)

void	AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata)
	Append the element data listed in elements fielddef->m_ElementIDs onto fielddata. More...

void	AppendFieldData (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, Array< OneD, NekDouble > &coeffs)
	Append the data in coeffs listed in elements fielddef->m_ElementIDs onto fielddata. More...

void	ExtractElmtDataToCoeffs (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, std::string &field, Array< OneD, NekDouble > &coeffs)
	Extract the data in fielddata into the coeffs using the basic ExpList Elemental expansions rather than planes in homogeneous case. More...

void	ExtractCoeffsToCoeffs (const boost::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...

boost::shared_ptr< ExpList >	GetSharedThisPtr ()
	Returns a shared pointer to the current object. More...

boost::shared_ptr < LibUtilities::SessionReader >	GetSession () const
	Returns the session object. More...

boost::shared_ptr < LibUtilities::Comm >	GetComm ()
	Returns the comm object. More...

SpatialDomains::MeshGraphSharedPtr	GetGraph ()

LibUtilities::BasisSharedPtr	GetHomogeneousBasis (void)

boost::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)

Private Member Functions
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...

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_BwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
	Template method virtual forwarder for FwdTrans(). More...

virtual void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
	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, CoeffState coeffstate)
	Template method virtual forwarder for MultiplyByInvMassMatrix(). More...

virtual void	v_HelmSolve (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const FlagList &flags, const StdRegions::ConstFactorMap &factors, const StdRegions::VarCoeffMap &varcoeff, const Array< OneD, const NekDouble > &dirForcing, const bool PhysSpaceForcing)
	Solves the two-dimensional Helmholtz equation, subject to the boundary conditions specified. More...

virtual void	v_GeneralMatrixOp (const GlobalMatrixKey &gkey, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
	Calculates the result of the multiplication of a global matrix of type specified by mkey with a vector given by inarray. More...

virtual void	v_LinearAdvectionDiffusionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)

void	v_LinearAdvectionReactionSolve (const Array< OneD, Array< OneD, NekDouble > > &velocity, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, const NekDouble lambda, CoeffState coeffstate=eLocal, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)

virtual const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > &	v_GetBndConditions ()
	Template method virtual forwarder for GetBndConditions(). More...

virtual void	v_ClearGlobalLinSysManager (void)

Private 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...

Additional Inherited Members
Public Attributes inherited from Nektar::MultiRegions::DisContField2D
Array< OneD, int >	m_BCtoElmMap

Array< OneD, int >	m_BCtoEdgMap

Public Attributes inherited from Nektar::MultiRegions::ExpList
ExpansionType	m_expType

Protected Member Functions inherited from Nektar::MultiRegions::DisContField2D
const Array< OneD, const LibUtilities::BasisSharedPtr > &	GetBase () const
	This function gets the shared point to basis. More...

LibUtilities::BasisType	GetBasisType (const int dir) const
	This function returns the type of basis used in the dir direction. More...

void	SetUpDG (const std::string="DefaultVar")
	Set up all DG member variables and maps. More...

bool	SameTypeOfBoundaryConditions (const DisContField2D &In)

void	GenerateBoundaryConditionExpansion (const SpatialDomains::MeshGraphSharedPtr &graph2D, const SpatialDomains::BoundaryConditions &bcs, const std::string &variable, const bool DeclareCoeffPhysArrays=true)
	This function discretises the boundary conditions by setting up a list of one-dimensional boundary expansions. More...

void	FindPeriodicEdges (const SpatialDomains::BoundaryConditions &bcs, const std::string &variable)
	Determine the periodic edges and vertices for the given graph. More...

bool	IsLeftAdjacentEdge (const int n, const int e)

virtual void	v_GetFwdBwdTracePhys (const Array< OneD, const NekDouble > &field, Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)
	This method extracts the "forward" and "backward" trace data from the array field and puts the data into output vectors Fwd and Bwd. More...

virtual void	v_GetFwdBwdTracePhys (Array< OneD, NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd)

virtual void	v_AddTraceIntegral (const Array< OneD, const NekDouble > &Fx, const Array< OneD, const NekDouble > &Fy, Array< OneD, NekDouble > &outarray)

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_ExtractTracePhys (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This method extracts the trace (edges in 2D) from the field inarray and puts the values in outarray. More...

virtual void	v_ExtractTracePhys (Array< OneD, NekDouble > &outarray)

virtual void	v_GetBoundaryToElmtMap (Array< OneD, int > &ElmtID, Array< OneD, int > &EdgeID)
	Set up a list of element IDs and edge IDs that link to the boundary conditions. More...

virtual void	v_GetBndElmtExpansion (int i, boost::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_GetPeriodicEntities (PeriodicMap &periodicVerts, PeriodicMap &periodicEdges, PeriodicMap &periodicFaces)
	Obtain a copy of the periodic edges and vertices for this field. More...

virtual AssemblyMapDGSharedPtr &	v_GetTraceMap ()

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_EvaluateBoundaryConditions (const NekDouble time=0.0, const std::string varName="", const NekDouble x2_in=NekConstants::kNekUnsetDouble, const NekDouble x3_in=NekConstants::kNekUnsetDouble)

virtual std::map< int, RobinBCInfoSharedPtr >	v_GetRobinBCInfo ()
	Search through the edge expansions and identify which ones have Robin/Mixed type boundary conditions. More...

Protected Member Functions inherited from Nektar::MultiRegions::ExpList2D
void	v_Upwind (const Array< OneD, const NekDouble > &Vn, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)
	Upwind the Fwd and Bwd states based on the one- dimensional normal velocity field given by Vn. More...

void	v_GetNormals (Array< OneD, Array< OneD, NekDouble > > &normals)
	For each local element, copy the normals stored in the element list into the array normals. More...

Protected Member Functions inherited from Nektar::MultiRegions::ExpList
void	SetCoeffPhysOffsets ()
	Definition of the total number of degrees of freedom and quadrature points and offsets to access data. More...

boost::shared_ptr< DNekMat >	GenGlobalMatrixFull (const GlobalLinSysKey &mkey, const boost::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)

boost::shared_ptr< GlobalMatrix >	GenGlobalMatrix (const GlobalMatrixKey &mkey, const boost::shared_ptr< AssemblyMapCG > &locToGloMap)
	Generates a global matrix from the given key and map. More...

void	GlobalEigenSystem (const boost::shared_ptr< DNekMat > &Gmat, Array< OneD, NekDouble > &EigValsReal, Array< OneD, NekDouble > &EigValsImag, Array< OneD, NekDouble > &EigVecs=NullNekDouble1DArray)

boost::shared_ptr< GlobalLinSys >	GenGlobalLinSys (const GlobalLinSysKey &mkey, const boost::shared_ptr< AssemblyMapCG > &locToGloMap)
	This operation constructs the global linear system of type mkey. More...

boost::shared_ptr< GlobalLinSys >	GenGlobalBndLinSys (const GlobalLinSysKey &mkey, const AssemblyMapSharedPtr &locToGloMap)
	Generate a GlobalLinSys from information provided by the key "mkey" and the mapping provided in LocToGloBaseMap. More...

void	ReadGlobalOptimizationParameters ()

virtual int	v_GetNumElmts (void)

virtual 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 const Array< OneD, const int > &	v_GetTraceBndMap ()

virtual const std::vector< bool > &	v_GetLeftAdjacentFaces (void) const

virtual void	v_BwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_FwdTrans_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)

virtual void	v_IProductWRTBase_IterPerExp (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_GetCoords (Array< OneD, NekDouble > &coord_0, Array< OneD, NekDouble > &coord_1, Array< OneD, NekDouble > &coord_2=NullNekDouble1DArray)

virtual void	v_PhysDeriv (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d0, Array< OneD, NekDouble > &out_d1, Array< OneD, NekDouble > &out_d2)

virtual void	v_PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d)

virtual void	v_PhysDeriv (Direction edir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d)

virtual void	v_CurlCurl (Array< OneD, Array< OneD, NekDouble > > &Vel, Array< OneD, Array< OneD, NekDouble > > &Q)

virtual void	v_HomogeneousFwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true)

virtual void	v_HomogeneousBwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal, bool Shuff=true, bool UnShuff=true)

virtual void	v_DealiasedProd (const Array< OneD, NekDouble > &inarray1, const Array< OneD, NekDouble > &inarray2, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)

virtual void	v_DealiasedDotProd (const Array< OneD, Array< OneD, NekDouble > > &inarray1, const Array< OneD, Array< OneD, NekDouble > > &inarray2, Array< OneD, Array< OneD, NekDouble > > &outarray, CoeffState coeffstate=eLocal)

virtual void	v_GetBCValues (Array< OneD, NekDouble > &BndVals, const Array< OneD, NekDouble > &TotField, int BndID)

virtual void	v_NormVectorIProductWRTBase (Array< OneD, const NekDouble > &V1, Array< OneD, const NekDouble > &V2, Array< OneD, NekDouble > &outarray, int BndID)

virtual void	v_NormVectorIProductWRTBase (Array< OneD, Array< OneD, NekDouble > > &V, Array< OneD, NekDouble > &outarray)

virtual void	v_ExtractElmtToBndPhys (int i, Array< OneD, NekDouble > &elmt, Array< OneD, NekDouble > &boundary)

virtual void	v_ExtractPhysToBndElmt (int i, const Array< OneD, const NekDouble > &phys, Array< OneD, NekDouble > &bndElmt)

virtual void	v_ExtractPhysToBnd (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 boost::shared_ptr< ExpList > &fromExpList, const Array< OneD, const NekDouble > &fromCoeffs, Array< OneD, NekDouble > &toCoeffs)

virtual void	v_WriteTecplotHeader (std::ostream &outfile, std::string var="")

virtual void	v_WriteTecplotZone (std::ostream &outfile, int expansion)

virtual void	v_WriteTecplotField (std::ostream &outfile, int expansion)

virtual void	v_WriteTecplotConnectivity (std::ostream &outfile, int expansion)

virtual void	v_WriteVtkPieceData (std::ostream &outfile, int expansion, std::string var)

virtual NekDouble	v_L2 (const Array< OneD, const NekDouble > &phys, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray)

virtual NekDouble	v_Integral (const Array< OneD, const NekDouble > &inarray)

virtual Array< OneD, const NekDouble >	v_HomogeneousEnergy (void)

virtual LibUtilities::TranspositionSharedPtr	v_GetTransposition (void)

virtual NekDouble	v_GetHomoLen (void)

virtual Array< OneD, const unsigned int >	v_GetZIDs (void)

virtual Array< OneD, const unsigned int >	v_GetYIDs (void)

void	ExtractFileBCs (const std::string &fileName, LibUtilities::CommSharedPtr comm, const std::string &varName, const boost::shared_ptr< ExpList > locExpList)

Static Protected Member Functions inherited from Nektar::MultiRegions::ExpList
static SpatialDomains::BoundaryConditionShPtr	GetBoundaryCondition (const SpatialDomains::BoundaryConditionCollection &collection, unsigned int index, const std::string &variable)

Protected Attributes inherited from Nektar::MultiRegions::DisContField2D
Array< OneD, LibUtilities::BasisSharedPtr >	m_base

Array< OneD, MultiRegions::ExpListSharedPtr >	m_bndCondExpansions
	An object which contains the discretised boundary conditions. More...

Array< OneD, SpatialDomains::BoundaryConditionShPtr >	m_bndConditions
	An array which contains the information about the boundary condition on the different boundary regions. More...

GlobalLinSysMapShPtr	m_globalBndMat

ExpListSharedPtr	m_trace

AssemblyMapDGSharedPtr	m_traceMap

LocTraceToTraceMapSharedPtr	m_locTraceToTraceMap

Array< OneD, Array< OneD, unsigned int > >	m_mapEdgeToElmn

Array< OneD, Array< OneD, unsigned int > >	m_signEdgeToElmn

Array< OneD, StdRegions::Orientation >	m_edgedir

std::set< int >	m_boundaryEdges
	A set storing the global IDs of any boundary edges. 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...

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_leftAdjacentEdges

Protected Attributes inherited from Nektar::MultiRegions::ExpList
LibUtilities::CommSharedPtr	m_comm
	Communicator. More...

LibUtilities::SessionReaderSharedPtr	m_session
	Session. More...

SpatialDomains::MeshGraphSharedPtr	m_graph
	Mesh associated with this expansion list. More...

int	m_ncoeffs
	The total number of local degrees of freedom. m_ncoeffs $=N_{\mathrm{eof}}=\sum_{e=1}^{{N_{\mathrm{el}}}}N^{e}_l$ . More...

int	m_npoints

Array< OneD, NekDouble >	m_coeffs
	Concatenation of all local expansion coefficients. More...

Array< OneD, NekDouble >	m_phys
	The global expansion evaluated at the quadrature points. More...

bool	m_physState
	The state of the array m_phys. More...

boost::shared_ptr < LocalRegions::ExpansionVector >	m_exp
	The list of local expansions. More...

Collections::CollectionVector	m_collections

std::vector< int >	m_coll_coeff_offset
	Offset of elemental data into the array m_coeffs. More...

std::vector< int >	m_coll_phys_offset
	Offset of elemental data into the array m_phys. More...

Array< OneD, int >	m_coeff_offset
	Offset of elemental data into the array m_coeffs. More...

Array< OneD, int >	m_phys_offset
	Offset of elemental data into the array m_phys. More...

NekOptimize::GlobalOptParamSharedPtr	m_globalOptParam

BlockMatrixMapShPtr	m_blockMat

bool	m_WaveSpace

boost::unordered_map< int, int >	m_elmtToExpId
	Mapping from geometry ID of element to index inside m_exp. More...

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 ContField2D 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 ContField2D.h.

Constructor & Destructor Documentation

Nektar::MultiRegions::ContField2D::ContField2D ( )

The default constructor.

Definition at line 88 of file ContField2D.cpp.

                                 :
             DisContField2D(),
             m_locToGloMap(),
             m_globalMat(),
             m_globalLinSysManager(
                     boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
                     std::string("GlobalLinSys"))
         {
         }

Nektar::MultiRegions::ContField2D::ContField2D	(	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.

Given a mesh graph2D, 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

graph2D	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 120 of file ContField2D.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Nektar::MultiRegions::DisContField2D::m_periodicEdges, Nektar::MultiRegions::DisContField2D::m_periodicVerts, and Nektar::MultiRegions::ExpList::m_session.

                                                                      :
             DisContField2D(pSession,graph2D,variable,false,DeclareCoeffPhysArrays,ImpType),
             m_globalMat(MemoryManager<GlobalMatrixMap>::AllocateSharedPtr()),
             m_globalLinSysManager(
                     boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
                     std::string("GlobalLinSys"))
         {
             m_locToGloMap = MemoryManager<AssemblyMapCG>
                 ::AllocateSharedPtr(m_session,m_ncoeffs,*this,
                                     m_bndCondExpansions,
                                     m_bndConditions,
                                     CheckIfSingularSystem,
                                     variable,
                                     m_periodicVerts,
                                     m_periodicEdges);
 
             if (m_session->DefinesCmdLineArgument("verbose"))
             {
                 m_locToGloMap->PrintStats(std::cout, variable);
             }
         }

Nektar::MultiRegions::ContField2D::ContField2D	(	const ContField2D &	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.

Given a mesh graph2D, 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 ContField2D object used to provide the local to global mapping information and global solution type.
graph2D	A mesh, containing information about the domain and the spectral/hp element expansion.
bcs	The boundary conditions.
bc_loc

Definition at line 172 of file ContField2D.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Nektar::MultiRegions::DisContField2D::m_periodicEdges, Nektar::MultiRegions::DisContField2D::m_periodicVerts, Nektar::MultiRegions::ExpList::m_session, and Nektar::MultiRegions::DisContField2D::SameTypeOfBoundaryConditions().

                                                                   :
             DisContField2D(In,graph2D,variable,false,DeclareCoeffPhysArrays),
             m_globalMat   (MemoryManager<GlobalMatrixMap>::AllocateSharedPtr()),
             m_globalLinSysManager(
                     boost::bind(&ContField2D::GenGlobalLinSys, this, _1),
                     std::string("GlobalLinSys"))
         {
             if(!SameTypeOfBoundaryConditions(In) || CheckIfSingularSystem)
             {
                 m_locToGloMap = MemoryManager<AssemblyMapCG>
                     ::AllocateSharedPtr(m_session, m_ncoeffs,*this,
                                         m_bndCondExpansions,
                                         m_bndConditions,
                                         CheckIfSingularSystem,
                                         variable,
                                         m_periodicVerts,
                                         m_periodicEdges);
 
                 if (m_session->DefinesCmdLineArgument("verbose"))
                 {
                     m_locToGloMap->PrintStats(std::cout, variable);
                 }
             }
             else
             {
                 m_locToGloMap = In.m_locToGloMap;
             }
         }

Nektar::MultiRegions::ContField2D::ContField2D	(	const ContField2D &	In,
		bool	DeclareCoeffPhysArrays = `true`
	)

The copy constructor.

Initialises the object as a copy of an existing ContField2D object.

Parameters

In	Existing ContField2D object.
DeclareCoeffPhysArrays	bool to declare if m_phys and m_coeffs should be declared. Default is true

Definition at line 212 of file ContField2D.cpp.

                                                                                   :
             DisContField2D(In,DeclareCoeffPhysArrays),
             m_locToGloMap(In.m_locToGloMap),
             m_globalMat(In.m_globalMat),
             m_globalLinSysManager(In.m_globalLinSysManager)
         {
         }

Nektar::MultiRegions::ContField2D::~ContField2D ( )

virtual

The default destructor.

Definition at line 224 of file ContField2D.cpp.

225 {

226 }

Member Function Documentation

void Nektar::MultiRegions::ContField2D::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 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 316 of file ContField2D.h.

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

Referenced by IProductWRTBase(), MultiplyByInvMassMatrix(), v_GeneralMatrixOp(), and v_HelmSolve().

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

void Nektar::MultiRegions::ContField2D::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 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 348 of file ContField2D.h.

References m_locToGloMap.

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

void Nektar::MultiRegions::ContField2D::BwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate = `eLocal`
	)

inline

Performs the backward transformation of the spectral/hp element expansion.

Given the coefficients of an expansion, this function evaluates the spectral/hp expansion $u^{\delta}(\boldsymbol{x})$ at the quadrature points $\boldsymbol{x}_i$ . This operation is evaluated locally by the function ExpList::BwdTrans.

The coefficients of the expansion should be contained in the variable m_coeffs of the ExpList object In. The resulting physical values at the quadrature points $u^{\delta}(\boldsymbol{x}_i)$ are stored in the array m_phys.

Parameters

In	An ExpList, containing the local coefficients $\hat{u}_n^e$ in its array m_coeffs.

Definition at line 424 of file ContField2D.h.

References Nektar::MultiRegions::ExpList::BwdTrans_IterPerExp(), Nektar::StdRegions::eBwdTrans, Nektar::MultiRegions::eGlobal, GetGlobalMatrix(), Nektar::MultiRegions::ExpList::GlobalToLocal(), Nektar::MultiRegions::ExpList::m_globalOptParam, m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.

Referenced by v_BwdTrans(), and v_SmoothField().

         {
             if(coeffstate == eGlobal)
             {
                 bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
                                                         StdRegions::eBwdTrans);
 
                 if(doGlobalOp)
                 {
                     GlobalMatrixKey gkey(StdRegions::eBwdTrans,m_locToGloMap);
                     GlobalMatrixSharedPtr mat = GetGlobalMatrix(gkey);
                     mat->Multiply(inarray,outarray);
                 }
                 else
                 {
                     Array<OneD, NekDouble> wsp(m_ncoeffs);
                     GlobalToLocal(inarray,wsp);
                     BwdTrans_IterPerExp(wsp,outarray);
                 }
             }
             else
             {
                 BwdTrans_IterPerExp(inarray,outarray);
             }
         }

void Nektar::MultiRegions::ContField2D::FwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate = `eLocal`
	)

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 246 of file ContField2D.cpp.

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

Referenced by v_FwdTrans().

         {
             // Inner product of forcing
             int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
             Array<OneD,NekDouble> wsp(contNcoeffs);
             IProductWRTBase(inarray,wsp,eGlobal);
 
             // Solve the system
             GlobalLinSysKey key(StdRegions::eMass, m_locToGloMap);
             
             if(coeffstate == eGlobal)
             {
                 GlobalSolve(key,wsp,outarray);
             }
             else
             {
                 Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
                 GlobalSolve(key,wsp,tmp);
                 GlobalToLocal(tmp,outarray);
             }
         }

GlobalLinSysSharedPtr Nektar::MultiRegions::ContField2D::GenGlobalLinSys ( const GlobalLinSysKey & mkey )

private

Definition at line 603 of file ContField2D.cpp.

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

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

const Array< OneD, const MultiRegions::ExpListSharedPtr > & Nektar::MultiRegions::ContField2D::GetBndCondExpansions ( )

inline

Returns the boundary conditions expansion.

Definition at line 454 of file ContField2D.h.

References Nektar::MultiRegions::DisContField2D::m_bndCondExpansions.

         {
             return m_bndCondExpansions;
         }

const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField2D::GetBndConditions ( )

inline

Returns the boundary conditions.

Definition at line 460 of file ContField2D.h.

References Nektar::MultiRegions::DisContField2D::m_bndConditions.

Referenced by v_GetBndConditions().

         {
             return m_bndConditions;
         }

GlobalLinSysSharedPtr Nektar::MultiRegions::ContField2D::GetGlobalLinSys ( const GlobalLinSysKey & mkey )

private

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 597 of file ContField2D.cpp.

References m_globalLinSysManager.

Referenced by GlobalSolve().

         {
             return m_globalLinSysManager[mkey];
         }

GlobalMatrixSharedPtr Nektar::MultiRegions::ContField2D::GetGlobalMatrix ( const GlobalMatrixKey & mkey )

private

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 565 of file ContField2D.cpp.

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

Referenced by BwdTrans(), IProductWRTBase(), and v_GeneralMatrixOp().

         {
             ASSERTL1(mkey.LocToGloMapIsDefined(),
                      "To use method must have a AssemblyMap "
                      "attached to key");
 
             GlobalMatrixSharedPtr glo_matrix;
             GlobalMatrixMap::iterator 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;
         }

int Nektar::MultiRegions::ContField2D::GetGlobalMatrixNnz ( const GlobalMatrixKey & gkey )

inline

Definition at line 465 of file ContField2D.h.

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

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

const AssemblyMapCGSharedPtr & Nektar::MultiRegions::ContField2D::GetLocalToGlobalMap ( ) const

inline

Returns the map from local to global level.

Definition at line 357 of file ContField2D.h.

References m_locToGloMap.

         {
             return  m_locToGloMap;
         }

void Nektar::MultiRegions::ContField2D::GlobalSolve	(	const GlobalLinSysKey &	key,
		const Array< OneD, const NekDouble > &	rhs,
		Array< OneD, NekDouble > &	inout,
		const Array< OneD, const NekDouble > &	dirForcing = `NullNekDouble1DArray`
	)

private

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.
Sin	An ExpList, containing the discrete evaluation of the forcing function $f(\boldsymbol{x})$ at the quadrature points in its array m_phys.
ScaleForcing	An optional parameter with which the forcing vector $\boldsymbol{\hat{f}}$ should be multiplied.

Note: inout contains initial guess and final output.

Definition at line 536 of file ContField2D.cpp.

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

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

         {
             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(rhs,inout,m_locToGloMap,dirForcing);
             }
         }

void Nektar::MultiRegions::ContField2D::IProductWRTBase	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate = `eLocal`
	)

inline

Calculates the inner product of a function $f(\boldsymbol{x})$ with respect to all global expansion modes $\phi_n^e(\boldsymbol{x})$ .

The operation is evaluated locally (i.e. with respect to all local expansion modes) by the function ExpList::IProductWRTBase. The inner product with respect to the global expansion modes is than obtained by a global assembly operation.

The values of the function $f(\boldsymbol{x})$ evaluated at the quadrature points $\boldsymbol{x}_i$ should be contained in the variable m_phys of the ExpList object in. The result is stored in the array m_coeffs.

Parameters

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

Definition at line 378 of file ContField2D.h.

References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eIProductWRTBase, GetGlobalMatrix(), Nektar::MultiRegions::ExpList::IProductWRTBase_IterPerExp(), Nektar::MultiRegions::ExpList::m_globalOptParam, m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.

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

         {
             if(coeffstate == eGlobal)
             {
                 bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
                                                 StdRegions::eIProductWRTBase);
 
                 if(doGlobalOp)
                 {
                     GlobalMatrixKey gkey(StdRegions::eIProductWRTBase,
                                          m_locToGloMap);
                     GlobalMatrixSharedPtr mat = GetGlobalMatrix(gkey);
                     mat->Multiply(inarray,outarray);
                     m_locToGloMap->UniversalAssemble(outarray);
                 }
                 else
                 {
                     Array<OneD, NekDouble> wsp(m_ncoeffs);
                     IProductWRTBase_IterPerExp(inarray,wsp);
                     Assemble(wsp,outarray);
                 }
             }
             else
             {
                 IProductWRTBase_IterPerExp(inarray,outarray);
             }
         }

void Nektar::MultiRegions::ContField2D::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`,
		CoeffState	coeffstate = `eLocal`
	)

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 387 of file ContField2D.cpp.

References Nektar::SpatialDomains::eDirichlet, Nektar::StdRegions::eFactorTime, Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eLaplacian, Nektar::StdRegions::eVarCoeffD00, Nektar::StdRegions::eVarCoeffD11, Nektar::StdRegions::eVarCoeffD22, Nektar::MultiRegions::ExpList::GetNcoeffs(), GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, and Vmath::Neg().

         {
             // Inner product of forcing
             int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
             Array<OneD,NekDouble> wsp(contNcoeffs);
             IProductWRTBase(inarray,wsp,eGlobal);
             // 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;
             for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
             {
                 if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
                 {
                     for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                     {
                         wsp[m_locToGloMap
                             ->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
                             += (m_bndCondExpansions[i]->GetCoeffs())[j];
                     }
                 }
                 else
                 {
                     bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
                 }
             }
        
             StdRegions::VarCoeffMap varcoeffs;
             varcoeffs[StdRegions::eVarCoeffD00] = variablecoeffs[0];
             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);
 
             if(coeffstate == eGlobal)
             {
                 GlobalSolve(key,wsp,outarray,dirForcing);
             }
             else
             {
                 Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
                 GlobalSolve(key,wsp,tmp,dirForcing);
                 GlobalToLocal(tmp,outarray);
             }
         }

void Nektar::MultiRegions::ContField2D::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 457 of file ContField2D.cpp.

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

         {
             // 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);
         }

void Nektar::MultiRegions::ContField2D::MultiplyByInvMassMatrix	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate = `eLocal`
	)

Multiply a solution by the inverse mass matrix.

Computes the matrix vector product $\mathbf{y} = \mathbf{M}^{-1}\mathbf{x}$ . If coeffstate == eGlobal is set then the elemental system is used directly. If not set, the global system is assembled, the system is solved, and mapped back to the local elemental system.

Parameters

inarray	Input vector $\mathbf{x}$ .
outarray	Output vector $\mathbf{y}$ .
coeffState	Flag for using global system.

Definition at line 297 of file ContField2D.cpp.

References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eMass, GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), m_locToGloMap, and Vmath::Vcopy().

Referenced by v_MultiplyByInvMassMatrix(), and v_SmoothField().

         {
             GlobalLinSysKey key(StdRegions::eMass,m_locToGloMap);
             int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
 
             if(coeffstate == eGlobal)
             {
                 if(inarray.data() == outarray.data())
                 {
                     Array<OneD, NekDouble> tmp(contNcoeffs,0.0);
                     Vmath::Vcopy(contNcoeffs,inarray,1,tmp,1);
                     GlobalSolve(key,tmp,outarray);
                 }
                 else
                 {
                     GlobalSolve(key,inarray,outarray);
                 }
             }
             else
             {
                 Array<OneD, NekDouble> globaltmp(contNcoeffs,0.0);
 
                 if(inarray.data() == outarray.data())
                 {
                     Array<OneD,NekDouble> tmp(inarray.num_elements());
                     Vmath::Vcopy(inarray.num_elements(),inarray,1,tmp,1);
                     Assemble(tmp,outarray);
                 }
                 else
                 {
                     Assemble(inarray,outarray);
                 }
 
                 GlobalSolve(key,outarray,globaltmp);
                 GlobalToLocal(globaltmp,outarray);
             }
         }

void Nektar::MultiRegions::ContField2D::v_BwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate
	)

privatevirtual

Template method virtual forwarder for FwdTrans().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 616 of file ContField2D.cpp.

References BwdTrans().

         {
             BwdTrans(inarray,outarray,coeffstate);
         }

void Nektar::MultiRegions::ContField2D::v_ClearGlobalLinSysManager ( void )

privatevirtual

Reset the GlobalLinSys Manager

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 1118 of file ContField2D.cpp.

References m_globalLinSysManager.

         {
             m_globalLinSysManager.ClearManager("GlobalLinSys");
         }

void Nektar::MultiRegions::ContField2D::v_FillBndCondFromField ( void )

privatevirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 695 of file ContField2D.cpp.

References Nektar::MultiRegions::ExpList::GetNcoeffs(), Nektar::MultiRegions::ExpList::LocalToGlobal(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::ExpList::m_coeffs, m_locToGloMap, and sign.

         {
             NekDouble sign;
             int bndcnt = 0;
             const Array<OneD,const int> &bndMap = 
                 m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap();
             
             Array<OneD, NekDouble> tmp(m_locToGloMap->GetNumGlobalCoeffs());
             LocalToGlobal(m_coeffs,tmp);
             
             // Now fill in all other Dirichlet coefficients.
             for(int i = 0; i < m_bndCondExpansions.num_elements(); ++i)
             {
                 Array<OneD, NekDouble>& coeffs = m_bndCondExpansions[i]->UpdateCoeffs();
                 
                 for(int j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
                 {
                     sign = m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsSign(bndcnt);
                     coeffs[j] = sign * tmp[bndMap[bndcnt++]];
                 }
             }
         }

void Nektar::MultiRegions::ContField2D::v_FillBndCondFromField ( const int nreg )

privatevirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 719 of file ContField2D.cpp.

References ASSERTL1, Nektar::MultiRegions::ExpList::GetNcoeffs(), Nektar::MultiRegions::ExpList::LocalToGlobal(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::ExpList::m_coeffs, m_locToGloMap, and sign.

         {
             NekDouble sign;
             int bndcnt = 0;
             const Array<OneD,const int> &bndMap = 
                 m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap();
             
             Array<OneD, NekDouble> tmp(m_locToGloMap->GetNumGlobalCoeffs());
             LocalToGlobal(m_coeffs,tmp,false);
 
             ASSERTL1(nreg < m_bndCondExpansions.num_elements(),
                      "nreg is out or range since this many boundary "
                      "regions to not exist");
             
             // 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();
             }
             
             for(int j = 0; j < (m_bndCondExpansions[nreg])->GetNcoeffs(); ++j)
             {
                 sign = m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsSign(bndcnt);
                 coeffs[j] = sign * tmp[bndMap[bndcnt++]];
             }
         }

void Nektar::MultiRegions::ContField2D::v_FwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate
	)

privatevirtual

Template method virtual forwarder for FwdTrans().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 628 of file ContField2D.cpp.

References FwdTrans().

         {
             FwdTrans(inarray,outarray,coeffstate);
         }

void Nektar::MultiRegions::ContField2D::v_GeneralMatrixOp	(	const GlobalMatrixKey &	gkey,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate
	)

privatevirtual

Calculates the result of the multiplication of a global matrix of type specified by mkey with a vector given by inarray.

This is equivalent to the operation:

$\boldsymbol{M\hat{u}}_g$

where $\boldsymbol{M}$ is the global matrix of type specified by mkey. After scattering the global array inarray to local level, this operation is evaluated locally by the function ExpList::GeneralMatrixOp. The global result is then obtained by a global assembly procedure.

Parameters

mkey	This key uniquely defines the type matrix required for the operation.
inarray	The vector $\boldsymbol{\hat{u}}_g$ of size $N_{\mathrm{dof}}$ .
outarray	The resulting vector of size $N_{\mathrm{dof}}$ .

Reimplemented from Nektar::MultiRegions::DisContField2D.

Definition at line 958 of file ContField2D.cpp.

References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::MultiRegions::ExpList::GeneralMatrixOp_IterPerExp(), GetGlobalMatrix(), Nektar::MultiRegions::GlobalMatrixKey::GetMatrixType(), Nektar::MultiRegions::ExpList::GlobalToLocal(), Nektar::MultiRegions::ExpList::m_globalOptParam, m_locToGloMap, and Nektar::MultiRegions::ExpList::m_ncoeffs.

         {
             if(coeffstate == eGlobal)
             {
                 bool doGlobalOp = m_globalOptParam->DoGlobalMatOp(
                                                         gkey.GetMatrixType());
 
                 if(doGlobalOp)
                 {
                     GlobalMatrixSharedPtr mat = GetGlobalMatrix(gkey);
                     mat->Multiply(inarray,outarray);
                     m_locToGloMap->UniversalAssemble(outarray);
                 }
                 else
                 {
                     Array<OneD,NekDouble> tmp1(2*m_ncoeffs);
                     Array<OneD,NekDouble> tmp2(tmp1+m_ncoeffs);
                     GlobalToLocal(inarray,tmp1);
                     GeneralMatrixOp_IterPerExp(gkey,tmp1,tmp2);
                     Assemble(tmp2,outarray);
                 }
             }
             else
             {
                 GeneralMatrixOp_IterPerExp(gkey,inarray,outarray);
             }
         }

const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField2D::v_GetBndConditions ( void )

privatevirtual

Template method virtual forwarder for GetBndConditions().

Reimplemented from Nektar::MultiRegions::DisContField2D.

Definition at line 1109 of file ContField2D.cpp.

References GetBndConditions().

         {
             return GetBndConditions();
         }

void Nektar::MultiRegions::ContField2D::v_GlobalToLocal	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

privatevirtual

Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$ .

This operation is evaluated as:

$\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}^{e}[i] = \mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}_g[\mbox{map}[e][i]]$ \\ \> \> continue \\ \> continue \end{tabbing}$

where map $[e][i]$ is the mapping array and sign 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 773 of file ContField2D.cpp.

References m_locToGloMap.

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

void Nektar::MultiRegions::ContField2D::v_GlobalToLocal ( void )

privatevirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 781 of file ContField2D.cpp.

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

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

void Nektar::MultiRegions::ContField2D::v_HelmSolve	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const FlagList &	flags,
		const StdRegions::ConstFactorMap &	factors,
		const StdRegions::VarCoeffMap &	varcoeff,
		const Array< OneD, const NekDouble > &	dirForcing,
		const bool	PhysSpaceForcing
	)

privatevirtual

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. The resulting global coefficients $\boldsymbol{\hat{u}}_g$ are stored in the array #m_contCoeffs or m_coeffs depending on whether coeffstate is eGlobal or eLocal

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::DisContField2D.

Definition at line 871 of file ContField2D.cpp.

References Assemble(), Nektar::SpatialDomains::eDirichlet, Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eHelmholtz, Nektar::eUseGlobal, Nektar::MultiRegions::ExpList::GetNcoeffs(), GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), Nektar::FlagList::isSet(), Nektar::MultiRegions::ExpList::LocalToGlobal(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Vmath::Neg(), and Vmath::Vadd().

         {
             //----------------------------------
             //  Setup RHS Inner product
             //----------------------------------
             // Inner product of forcing
             int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
             Array<OneD,NekDouble> wsp(contNcoeffs);
             if(PhysSpaceForcing)
             {
                 IProductWRTBase(inarray,wsp,eGlobal);
             }
             else
             {
                 Assemble(inarray,wsp);
             }
             // Note -1.0 term necessary to invert forcing function to
             // be consistent with matrix definition
             Vmath::Neg(contNcoeffs, wsp, 1);
 
             // Fill weak boundary conditions
             int i,j;
             int bndcnt=0;
             Array<OneD, NekDouble> gamma(contNcoeffs, 0.0);
             
             for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
             {
                 if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
                 {
                     for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                     {
                         gamma[m_locToGloMap
                             ->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
                             += (m_bndCondExpansions[i]->GetCoeffs())[j];
                     }
                 }
                 else
                 {
                     bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
                 }
             }
             
             m_locToGloMap->UniversalAssemble(gamma);
 
             // Add weak boundary conditions to forcing
             Vmath::Vadd(contNcoeffs, wsp, 1, gamma, 1, wsp, 1);
 
             GlobalLinSysKey key(StdRegions::eHelmholtz,m_locToGloMap,factors,varcoeff);
             
             if(flags.isSet(eUseGlobal))
             {
                 GlobalSolve(key,wsp,outarray,dirForcing);
             }
             else
             {
                 Array<OneD,NekDouble> tmp(contNcoeffs);
                 LocalToGlobal(outarray,tmp);
                 GlobalSolve(key,wsp,tmp,dirForcing);
                 GlobalToLocal(tmp,outarray);
             }
         }

void Nektar::MultiRegions::ContField2D::v_ImposeDirichletConditions ( Array< OneD, NekDouble > & outarray )

privatevirtual

Impose the Dirichlet Boundary Conditions on outarray.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 636 of file ContField2D.cpp.

References Nektar::SpatialDomains::eDirichlet, Nektar::MultiRegions::ExpList::GetNcoeffs(), Nektar::iterator, Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, sign, and Vmath::Vcopy().

Referenced by GlobalSolve().

         {
             int i,j;
             int bndcnt=0;
             int nDir        = m_locToGloMap->GetNumGlobalDirBndCoeffs();
 
             // STEP 1: SET THE DIRICHLET DOFS TO THE RIGHT VALUE IN THE SOLUTION
             // ARRAY
             NekDouble sign;
             const Array<OneD,const int> &bndMap = 
                 m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap();
           
             Array<OneD, NekDouble> tmp(
                 m_locToGloMap->GetNumGlobalBndCoeffs(), 0.0);
 
             // Fill in Dirichlet coefficients that are to be sent to
             // other processors.  This code block uses a
             // tuple<int,int.NekDouble> which stores the local id of
             // coefficent the global id of the data location and the
             // inverse of the values of the data (arising from
             // periodic boundary conditiosn)
             map<int, vector<ExtraDirDof> > &extraDirDofs =
                 m_locToGloMap->GetExtraDirDofs();
             map<int, vector<ExtraDirDof> >::iterator it;
             for (it = extraDirDofs.begin(); it != extraDirDofs.end(); ++it)
             {
                 for (i = 0; i < it->second.size(); ++i)
                 {
                     tmp[it->second.at(i).get<1>()] = 
                         m_bndCondExpansions[it->first]->GetCoeffs()[
                             it->second.at(i).get<0>()]*it->second.at(i).get<2>(); 
                 }
             }
             m_locToGloMap->UniversalAssembleBnd(tmp);
 
             // Now fill in all other Dirichlet coefficients.
             for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
             {
                 if(m_bndConditions[i]->GetBoundaryConditionType() ==
                    SpatialDomains::eDirichlet)
                 {
                     const Array<OneD,const NekDouble>& coeffs =
                         m_bndCondExpansions[i]->GetCoeffs();
                     for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); ++j)
                     {
                         sign = m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsSign(
                             bndcnt);
                         tmp[bndMap[bndcnt++]] = sign * coeffs[j];
                     }
                 }
                 else
                 {
                     bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
                 }
             }
 
             Vmath::Vcopy(nDir, tmp, 1, outarray, 1);
         }

void Nektar::MultiRegions::ContField2D::v_LinearAdvectionDiffusionReactionSolve	(	const Array< OneD, Array< OneD, NekDouble > > &	velocity,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const NekDouble	lambda,
		CoeffState	coeffstate = `eLocal`,
		const Array< OneD, const NekDouble > &	dirForcing = `NullNekDouble1DArray`
	)

privatevirtual

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
coeffstate	State of Coefficients, Local or Global
dirForcing	Dirichlet Forcing.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 1002 of file ContField2D.cpp.

References Nektar::SpatialDomains::eDirichlet, Nektar::StdRegions::eFactorLambda, Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eLinearAdvectionDiffusionReaction, Nektar::StdRegions::eVarCoeffVelX, Nektar::StdRegions::eVarCoeffVelY, Nektar::MultiRegions::ExpList::GetNcoeffs(), GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), Nektar::MultiRegions::DisContField2D::m_bndCondExpansions, Nektar::MultiRegions::DisContField2D::m_bndConditions, m_locToGloMap, Vmath::Neg(), and Vmath::Vadd().

         {
             // Inner product of forcing
             int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
             Array<OneD,NekDouble> wsp(contNcoeffs);
             IProductWRTBase(inarray,wsp,eGlobal);
             // Note -1.0 term necessary to invert forcing function to
             // be consistent with matrix definition
             Vmath::Neg(contNcoeffs, wsp, 1);
 
             // Forcing function with weak boundary conditions
             int i,j;
             int bndcnt=0;
             Array<OneD, NekDouble> gamma(contNcoeffs, 0.0);
             for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
             {
                 if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
                 {
                     for(j = 0; j < (m_bndCondExpansions[i])->GetNcoeffs(); j++)
                     {
                         gamma[m_locToGloMap
                             ->GetBndCondCoeffsToGlobalCoeffsMap(bndcnt++)]
                             += (m_bndCondExpansions[i]->GetCoeffs())[j];
                     }
                 }
                 else
                 {
                     bndcnt += m_bndCondExpansions[i]->GetNcoeffs();
                 }
             }
             m_locToGloMap->UniversalAssemble(gamma);
             // Add weak boundary conditions to forcing
             Vmath::Vadd(contNcoeffs, wsp, 1, gamma, 1, wsp, 1);
 
             // 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::eLinearAdvectionDiffusionReaction,m_locToGloMap,factors,varcoeffs);
 
             if(coeffstate == eGlobal)
             {
                 GlobalSolve(key,wsp,outarray,dirForcing);
             }
             else
             {
                 Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
                 GlobalSolve(key,wsp,tmp,dirForcing);
                 GlobalToLocal(tmp,outarray);
             }
         }

void Nektar::MultiRegions::ContField2D::v_LinearAdvectionReactionSolve	(	const Array< OneD, Array< OneD, NekDouble > > &	velocity,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		const NekDouble	lambda,
		CoeffState	coeffstate = `eLocal`,
		const Array< OneD, const NekDouble > &	dirForcing = `NullNekDouble1DArray`
	)

privatevirtual

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
coeffstate	State of Coefficients, Local or Global
dirForcing	Dirichlet Forcing.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 1071 of file ContField2D.cpp.

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

         {
             // Inner product of forcing
             int contNcoeffs = m_locToGloMap->GetNumGlobalCoeffs();
             Array<OneD,NekDouble> wsp(contNcoeffs);
             IProductWRTBase(inarray,wsp,eGlobal);
 
             // 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);
 
             if(coeffstate == eGlobal)
             {
                 GlobalSolve(key,wsp,outarray,dirForcing);
             }
             else
             {
                 Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
                 GlobalSolve(key,wsp,tmp,dirForcing);
                 GlobalToLocal(tmp,outarray);
             }
         }

void Nektar::MultiRegions::ContField2D::v_LocalToGlobal	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		bool	useComm
	)

privatevirtual

Gathers the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$ .

This operation is evaluated as:

$\begin{tabbing} \hspace{1cm} \= Do \= $e=$ $1, N_{\mathrm{el}}$ \\ \> \> Do \= $i=$ $0,N_m^e-1$ \\ \> \> \> $\boldsymbol{\hat{u}}_g[\mbox{map}[e][i]] = \mbox{sign}[e][i] \cdot \boldsymbol{\hat{u}}^{e}[i]$\\ \> \> continue\\ \> continue \end{tabbing}$

where map $[e][i]$ is the mapping array and sign 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 815 of file ContField2D.cpp.

References m_locToGloMap.

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

void Nektar::MultiRegions::ContField2D::v_LocalToGlobal ( bool useComm )

privatevirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 824 of file ContField2D.cpp.

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

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

void Nektar::MultiRegions::ContField2D::v_MultiplyByInvMassMatrix	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate
	)

privatevirtual

Template method virtual forwarder for MultiplyByInvMassMatrix().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 833 of file ContField2D.cpp.

References MultiplyByInvMassMatrix().

         {
             MultiplyByInvMassMatrix(inarray,outarray,coeffstate);
         }

void Nektar::MultiRegions::ContField2D::v_SmoothField ( Array< OneD, NekDouble > & field )

privatevirtual

Template method virtual forwarded for SmoothField().

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 274 of file ContField2D.cpp.

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

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

Member Data Documentation

LibUtilities::NekManager<GlobalLinSysKey, GlobalLinSys> Nektar::MultiRegions::ContField2D::m_globalLinSysManager

private

A manager which collects all the global linear systems being assembled, such that they should be constructed only once.

Definition at line 177 of file ContField2D.h.

Referenced by GetGlobalLinSys(), and v_ClearGlobalLinSysManager().

GlobalMatrixMapShPtr Nektar::MultiRegions::ContField2D::m_globalMat

private

(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 172 of file ContField2D.h.

Referenced by GetGlobalMatrix(), and GetGlobalMatrixNnz().

AssemblyMapCGSharedPtr Nektar::MultiRegions::ContField2D::m_locToGloMap

private

(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 167 of file ContField2D.h.

Referenced by Assemble(), BwdTrans(), ContField2D(), FwdTrans(), GenGlobalLinSys(), GetGlobalMatrix(), GetLocalToGlobalMap(), GlobalSolve(), IProductWRTBase(), LaplaceSolve(), LinearAdvectionEigs(), MultiplyByInvMassMatrix(), v_FillBndCondFromField(), v_GeneralMatrixOp(), v_GlobalToLocal(), v_HelmSolve(), v_ImposeDirichletConditions(), v_LinearAdvectionDiffusionReactionSolve(), v_LinearAdvectionReactionSolve(), v_LocalToGlobal(), and v_SmoothField().

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation