Abstraction of a global continuous one-dimensional spectral/hp element expansion which approximates the solution of a set of partial differential equations. More...

#include <ContField1D.h>

Inheritance diagram for Nektar::MultiRegions::ContField1D:

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Collaboration diagram for Nektar::MultiRegions::ContField1D:

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Public Member Functions
	ContField1D ()
	Default constructor. More...

	ContField1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const std::string &variable)
	Set up global continuous field based on an input mesh and boundary conditions. More...

	ContField1D (const ContField1D &In)
	Copy constructor. More...

	ContField1D (const LibUtilities::SessionReaderSharedPtr &pSession, const ExpList1D &In)
	Copy constructor. More...

virtual	~ContField1D ()
	Destructor. More...

void	FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
	Perform global forward transformation of a function ,. More...

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

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

const Array< OneD, const MultiRegions::ExpListSharedPtr > &	GetBndCondExpansions ()
	Return the boundary conditions expansion. More...

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

void	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...

void	LocalToGlobal ()
	Gathers the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$ . 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)
	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 with respect to all global expansion modes $\phi_n^e(x)$ . More...

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

Public Member Functions inherited from Nektar::MultiRegions::DisContField1D
	DisContField1D ()
	Default constructor. More...

	DisContField1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const std::string &variable, const bool SetUpJustDG=true)
	Constructs a 1D discontinuous field based on a mesh and boundary conditions. More...

	DisContField1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::CompositeMap &domain, const SpatialDomains::BoundaryConditions &Allbcs, const std::string &variable, bool SetToOneSpaceDimensions=false)
	Constructor for a DisContField1D from a List of subdomains New Constructor for arterial network. More...

	DisContField1D (const DisContField1D &In)
	Constructs a 1D discontinuous field based on an existing field. More...

	DisContField1D (const ExpList1D &In)
	Constructs a 1D discontinuous field based on an existing field. (needed in order to use ContField( const ExpList1D &In) constructor. More...

virtual	~DisContField1D ()
	Destructor. More...

GlobalLinSysSharedPtr	GetGlobalBndLinSys (const GlobalLinSysKey &mkey)
	For a given key, returns the associated global linear system. More...

std::vector< bool > &	GetNegatedFluxNormal (void)

Public Member Functions inherited from Nektar::MultiRegions::ExpList1D
	ExpList1D ()
	The default constructor. More...

	ExpList1D (const ExpList1D &In, const bool DeclareCoeffPhysArrays=true)
	The copy constructor. More...

	ExpList1D (const ExpList1D &In, const std::vector< unsigned int > &eIDs, const bool DeclareCoeffPhysArrays=true)
	Constructor copying only elements defined in eIds. More...

	ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const LibUtilities::BasisKey &Ba, const SpatialDomains::MeshGraphSharedPtr &graph1D)
	Construct an ExpList1D from a given graph. More...

	ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const bool DeclareCoeffPhysArrays=true)
	This constructor sets up a list of local expansions based on an input graph1D. More...

	ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::CompositeMap &domain, const bool DeclareCoeffPhysArrays=true, const std::string var="DefaultVar", bool SetToOneSpaceDimension=false)
	This constructor sets up a list of local expansions based on an input compositeMap. More...

	ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::CompositeMap &domain, const SpatialDomains::MeshGraphSharedPtr &graph2D, const bool DeclareCoeffPhysArrays=true, const std::string variable="DefaultVar")
	Specialised constructor for Neumann boundary conditions in DisContField2D and ContField2D. More...

	ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::CompositeMap &domain, const SpatialDomains::MeshGraphSharedPtr &graph1D, int i, const bool DeclareCoeffPhysArrays=true)

	ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const Array< OneD, const ExpListSharedPtr > &bndConstraint, const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > &bndCond, const LocalRegions::ExpansionVector &locexp, const SpatialDomains::MeshGraphSharedPtr &graph2D, const PeriodicMap &periodicEdges, const bool DeclareCoeffPhysArrays=true, const std::string variable="DefaultVar")
	Specialised constructor for trace expansions. More...

virtual	~ExpList1D ()
	Destructor. More...

void	PostProcess (LibUtilities::KernelSharedPtr kernel, Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray, NekDouble h, int elmId=0)
	Performs the post-processing on a specified element. More...

void	PeriodicEval (Array< OneD, NekDouble > &inarray1, Array< OneD, NekDouble > &inarray2, NekDouble h, int nmodes, Array< OneD, NekDouble > &outarray)
	Evaluates the global spectral/hp expansion at some arbitray set of points. More...

void	ParNormalSign (Array< OneD, NekDouble > &normsign)
	Set up the normals on each expansion. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	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)
	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	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	LocalToGlobal (void)
	Put the coefficients into global ordering using m_coeffs. More...

void	GlobalToLocal (void)
	Put the coefficients into local ordering and place in m_coeffs. More...

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...

int	GetOffset_Elmt_Id (int n) const
	Get the element id associated with the n th consecutive block of data in m_phys and m_coeffs. 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)

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)

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	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 ()
	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)

Protected Attributes
AssemblyMapCGSharedPtr	m_locToGloMap
	(A shared pointer to) the object which contains all the required information for the transformation from local to global degrees of freedom. More...

CoeffState	m_coeffState
	A enum list declaring how to interpret coeffs, i.e. eLocal, eHybrid or eGlobal. More...

GlobalMatrixMapShPtr	m_globalMat
	(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once. More...

LibUtilities::NekManager < GlobalLinSysKey, GlobalLinSys >	m_globalLinSysManager
	A manager which collects all the global linear systems being assembled, such that they should be constructed only once. More...

Protected Attributes inherited from Nektar::MultiRegions::DisContField1D
int	m_numDirBndCondExpansions
	The number of boundary segments on which Dirichlet boundary conditions are imposed. More...

Array< OneD, MultiRegions::ExpListSharedPtr >	m_bndCondExpansions
	Discretised boundary conditions. More...

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

GlobalLinSysMapShPtr	m_globalBndMat
	Global boundary matrix. More...

ExpListSharedPtr	m_trace
	Trace space storage for points between elements. More...

AssemblyMapDGSharedPtr	m_traceMap
	Local to global DG mapping for trace space. More...

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

PeriodicMap	m_periodicVerts
	A map which identifies groups of periodic vertices. More...

std::vector< int >	m_periodicFwdCopy
	A vector indicating degress of freedom which need to be copied from forwards to backwards space in case of a periodic boundary condition. More...

std::vector< int >	m_periodicBwdCopy

std::vector< bool >	m_leftAdjacentVerts

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

LibUtilities::SessionReaderSharedPtr	m_session
	Session. More...

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

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

int	m_npoints

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

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

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

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...

Array< OneD, int >	m_offset_elmt_id
	Array containing the element id m_offset_elmt_id[n] that the n^th consecutive block of data in m_coeffs and m_phys is associated, i.e. for an array of constant expansion size and single shape elements m_phys[n*m_npoints] is the data related to m_exp[m_offset_elmt_id[n]];. More...

NekOptimize::GlobalOptParamSharedPtr	m_globalOptParam

BlockMatrixMapShPtr	m_blockMat

bool	m_WaveSpace

Private Member Functions
GlobalLinSysSharedPtr	GetGlobalLinSys (const GlobalLinSysKey &mkey)
	Returns the linear system specified by mkey. More...

GlobalLinSysSharedPtr	GenGlobalLinSys (const GlobalLinSysKey &mkey)

void	GlobalSolve (const GlobalLinSysKey &key, const Array< OneD, const NekDouble > &rhs, Array< OneD, NekDouble > &inout, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)
	Solve the linear system specified by the key key. More...

virtual void	v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
	Perform a forward transform. More...

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

virtual void	v_ImposeDirichletConditions (Array< OneD, NekDouble > &outarray)
	Impose the Dirichlet Boundary Conditions on outarray. More...

virtual void	v_GlobalToLocal (void)
	Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$ . More...

virtual void	v_LocalToGlobal (void)
	Gathers the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$ . 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)

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

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

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

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

virtual void	v_ClearGlobalLinSysManager (void)

Additional Inherited Members
Public Attributes inherited from Nektar::MultiRegions::ExpList
ExpansionType	m_expType

Protected Member Functions inherited from Nektar::MultiRegions::DisContField1D
void	GenerateBoundaryConditionExpansion (const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::BoundaryConditions &bcs, const std::string variable)
	Discretises the boundary conditions. More...

void	FindPeriodicVertices (const SpatialDomains::BoundaryConditions &bcs, const std::string variable)
	Generate a associative map of periodic vertices in a mesh. More...

virtual ExpListSharedPtr &	v_GetTrace ()

virtual AssemblyMapDGSharedPtr &	v_GetTraceMap (void)

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

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

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

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

virtual void	v_ExtractTracePhys (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
	This method extracts the trace (verts in 1D) from the field inarray and puts the values in outarray. More...

void	SetBoundaryConditionExpansion (const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::BoundaryConditions &bcs, const std::string variable, Array< OneD, MultiRegions::ExpListSharedPtr > &bndCondExpansions, Array< OneD, SpatialDomains::BoundaryConditionShPtr > &bndConditions)
	Populates the list of boundary condition expansions. More...

void	SetMultiDomainBoundaryConditionExpansion (const SpatialDomains::MeshGraphSharedPtr &graph1D, const SpatialDomains::BoundaryConditions &bcs, const std::string variable, Array< OneD, MultiRegions::ExpListSharedPtr > &bndCondExpansions, Array< OneD, SpatialDomains::BoundaryConditionShPtr > &bndConditions, int subdomain)
	Populates the list of boundary condition expansions in multidomain case. More...

void	GenerateFieldBnd1D (SpatialDomains::BoundaryConditions &bcs, const std::string variable)

virtual std::map< int, RobinBCInfoSharedPtr >	v_GetRobinBCInfo ()

virtual const Array< OneD, const MultiRegions::ExpListSharedPtr > &	v_GetBndCondExpansions ()

virtual MultiRegions::ExpListSharedPtr &	v_UpdateBndCondExpansion (int i)

virtual Array< OneD, SpatialDomains::BoundaryConditionShPtr > &	v_UpdateBndConditions ()

virtual void	v_GetBoundaryToElmtMap (Array< OneD, int > &ElmtID, Array< OneD, int > &VertID)

virtual void	v_GetBndElmtExpansion (int i, boost::shared_ptr< ExpList > &result)

virtual void	v_Reset ()
	Reset this field, so that geometry information can be updated. More...

virtual void	v_EvaluateBoundaryConditions (const NekDouble time=0.0, const std::string varName="", const NekDouble x2_in=NekConstants::kNekUnsetDouble, const NekDouble x3_in=NekConstants::kNekUnsetDouble)
	Evaluate all boundary conditions at a given time.. More...

Protected Member Functions inherited from Nektar::MultiRegions::ExpList1D
void	v_Upwind (const Array< OneD, const Array< OneD, NekDouble > > &Vec, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)
	Upwind the Fwd and Bwd states based on the velocity field given by Vec. More...

void	v_Upwind (const Array< OneD, const NekDouble > &Vn, const Array< OneD, const NekDouble > &Fwd, const Array< OneD, const NekDouble > &Bwd, Array< OneD, NekDouble > &Upwind)
	Upwind the Fwd and Bwd states based on the one- dimensional normal velocity field given by Vn. More...

void	v_GetNormals (Array< OneD, Array< OneD, NekDouble > > &normals)
	Populate normals with the normals of all expansions. More...

Protected Member Functions inherited from Nektar::MultiRegions::ExpList
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 const Array< OneD, const int > &	v_GetTraceBndMap ()

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

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

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

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

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

virtual void	v_FillBndCondFromField ()

virtual void	v_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_SmoothField (Array< OneD, NekDouble > &field)

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

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

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

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

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

virtual void	v_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_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_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)

virtual void	v_PhysInterp1DScaled (const NekDouble scale, const Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

virtual void	v_PhysGalerkinProjection1DScaled (const NekDouble scale, const Array< OneD, NekDouble > &inarray, Array< OneD, NekDouble > &outarray)

void	ExtractFileBCs (const std::string &fileName, 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)

Detailed Description

Abstraction of a global continuous one-dimensional spectral/hp element expansion which approximates the solution of a set of partial differential equations.

As opposed to the class #ContExpList1D, the class ContField1D is able to incorporate the boundary conditions imposed to the problem to be solved. Therefore, the class is equipped with three additional data members:

m_bndCondExpansions
#m_bndTypes
#m_bndCondEquations

The first data structure, m_bndCondExpansions, contains the point Expansion on the boundary, #m_bndTypes stores information about the type of boundary condition on the different parts of the boundary while #m_bndCondEquations holds the equation of the imposed boundary conditions.

Furthermore, in case of Dirichlet boundary conditions, this class is capable of lifting a known solution satisfying these boundary conditions. If we denote the unknown solution by $u^{\mathcal{H}}(\boldsymbol{x})$ and the known Dirichlet boundary conditions by $u^{\mathcal{D}}(\boldsymbol{x})$ , the expansion then can be decomposed as

$u^{\delta}(\boldsymbol{x}_i)=u^{\mathcal{D}}(\boldsymbol{x}_i)+ u^{\mathcal{H}}(\boldsymbol{x}_i)=\sum_{n=0}^{N^{\mathcal{D}}-1} \hat{u}_n^{\mathcal{D}}\Phi_n(\boldsymbol{x}_i)+ \sum_{n={N^{\mathcal{D}}}}^{N_{\mathrm{dof}} -1}\hat{u}_n^{\mathcal{H}} \Phi_n(\boldsymbol{x}_i).$

This lifting is accomplished by ordering the known global degrees of freedom, prescribed by the Dirichlet boundary conditions, first in the global array $\boldsymbol{\hat{u}}$ , that is,

$\boldsymbol{\hat{u}}=\left[ \begin{array}{c} \boldsymbol{\hat{u}}^{\mathcal{D}}\\ \boldsymbol{\hat{u}}^{\mathcal{H}} \end{array} \right].$

Such kind of expansions are also referred to as continuoous fields. This class should be used when solving 2D problems using a standard Galerkin approach.

Definition at line 56 of file ContField1D.h.

Constructor & Destructor Documentation

Nektar::MultiRegions::ContField1D::ContField1D ( )

Default constructor.

Constructs an empty 1D continuous field.

Definition at line 86 of file ContField1D.cpp.

                                 :
             DisContField1D(),
             m_locToGloMap(),
             m_globalLinSysManager(
                     boost::bind(&ContField1D::GenGlobalLinSys, this, _1),
                     std::string("GlobalLinSys"))
         {
         }

Nektar::MultiRegions::ContField1D::ContField1D	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const SpatialDomains::MeshGraphSharedPtr &	graph1D,
		const std::string &	variable
	)

Set up global continuous field based on an input mesh and boundary conditions.

Given a mesh graph1D, containing information about the domain and the spectral/hp element expansion, this constructor fills the list of local expansions m_exp with the proper expansions, calculates the total number of quadrature points $\boldsymbol{x}_i$ and local expansion coefficients $\hat{u}^e_n$ and allocates memory for the arrays m_coeffs and m_phys. Furthermore, it constructs the mapping array (contained in m_locToGloMap) for the transformation between local elemental level and global level, it calculates the total number global expansion coefficients $\hat{u}_n$ . The constructor also discretises the boundary conditions, specified by the argument bcs, by expressing them in terms of the coefficient of the expansion on the boundary.

Parameters

graph1D	A 1D mesh, containing information about the domain and the spectral/hp element expansion.
bcs	The boundary conditions.
variable	An optional parameter to indicate for which variable the field should be constructed.

Definition at line 117 of file ContField1D.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::MultiRegions::DisContField1D::m_bndCondExpansions, Nektar::MultiRegions::DisContField1D::m_bndConditions, m_locToGloMap, Nektar::MultiRegions::ExpList::m_ncoeffs, Nektar::MultiRegions::DisContField1D::m_periodicVerts, and Nektar::MultiRegions::ExpList::m_session.

                                                            :
             DisContField1D(pSession,graph1D,variable,false),
             m_locToGloMap(),
             m_globalLinSysManager(
                     boost::bind(&ContField1D::GenGlobalLinSys, this, _1),
                     std::string("GlobalLinSys"))
         {
             SpatialDomains::BoundaryConditions bcs(pSession, graph1D);
 
             m_locToGloMap = MemoryManager<AssemblyMapCG>
                 ::AllocateSharedPtr(m_session,m_ncoeffs,*this,
                                     m_bndCondExpansions,
                                     m_bndConditions,
                                     false,
                                     variable,
                                     m_periodicVerts);
         }

Nektar::MultiRegions::ContField1D::ContField1D ( const ContField1D & In )

Copy constructor.

Constructs a 1D continuous field as a copy of an existing field including all boundary conditions.

Parameters

In	Existing continuous field to duplicate.

Definition at line 143 of file ContField1D.cpp.

                                                      :
             DisContField1D(In),
             m_locToGloMap(In.m_locToGloMap),
             m_globalLinSysManager(
                     boost::bind(&ContField1D::GenGlobalLinSys, this, _1),
                     std::string("GlobalLinSys"))
         {
         }

Nektar::MultiRegions::ContField1D::ContField1D	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const ExpList1D &	In
	)

Copy constructor.

Constructs a 1D continuous field as a copy of an existing explist 1D field and adding all the boundary conditions.

Parameters

In	Existing explist1D field .

Definition at line 157 of file ContField1D.cpp.

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

                                                                                                          :
             DisContField1D(In),
             m_locToGloMap(),
             m_globalLinSysManager(
                     boost::bind(&ContField1D::GenGlobalLinSys, this, _1),
                     std::string("GlobalLinSys"))
         {
             m_locToGloMap = MemoryManager<AssemblyMapCG>
                 ::AllocateSharedPtr(pSession, m_ncoeffs, In);
 
         }

Nektar::MultiRegions::ContField1D::~ContField1D ( )

virtual

Destructor.

Definition at line 172 of file ContField1D.cpp.

173 {

174 }

Member Function Documentation

void Nektar::MultiRegions::ContField1D::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.

Definition at line 309 of file ContField1D.h.

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

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

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

void Nektar::MultiRegions::ContField1D::Assemble	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

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 341 of file ContField1D.h.

References m_locToGloMap.

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

void Nektar::MultiRegions::ContField1D::BwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate = `eLocal`
	)

This function performs the backward transformation of the spectral/hp element expansion.

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

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

Parameters

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

Definition at line 228 of file ContField1D.cpp.

References Nektar::MultiRegions::ExpList::BwdTrans_IterPerExp(), Nektar::MultiRegions::eLocal, and Nektar::MultiRegions::ExpList::GlobalToLocal().

Referenced by v_BwdTrans().

         {
             Array<OneD, NekDouble> tmpinarray;
             if(coeffstate != eLocal)
             {
                 tmpinarray = Array<OneD, NekDouble>(inarray);
                 GlobalToLocal(inarray,tmpinarray);
             }
             else
             {
                 tmpinarray = inarray;
             }
 
             BwdTrans_IterPerExp(tmpinarray,outarray);
         }

void Nektar::MultiRegions::ContField1D::FwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate = `eLocal`
	)

Perform global forward transformation of a function $f(x)$ ,.

Given a function $f(x)$ defined at the quadrature points, this function determines the unknown global coefficients $\boldsymbol{\hat{u}}^{\mathcal{H}}$ employing a discrete Galerkin projection from physical space to coefficient space. The operation is evaluated by the function GlobalSolve using the global mass matrix.

The values of the function $f(x)$ evaluated at the quadrature points $x_i$ should be contained in the variable m_phys of the ExpList object Sin. The resulting global coefficients $\hat{u}_g$ are stored in the array m_coeffs.

Parameters

inarray	Discrete .
outarray	Storage for result.
coeffstate

Definition at line 194 of file ContField1D.cpp.

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

Referenced by v_FwdTrans().

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

void Nektar::MultiRegions::ContField1D::GeneralMatrixOp	(	const GlobalMatrixKey &	gkey,
		const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate = `eLocal`
	)

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

GlobalLinSysSharedPtr Nektar::MultiRegions::ContField1D::GenGlobalLinSys ( const GlobalLinSysKey & mkey )

private

Definition at line 371 of file ContField1D.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::ContField1D::GetBndCondExpansions ( )

inline

Return the boundary conditions expansion.

Definition at line 242 of file ContField1D.h.

References Nektar::MultiRegions::DisContField1D::m_bndCondExpansions.

         {
             return m_bndCondExpansions;
         }

const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField1D::GetBndConditions ( )

inline

Definition at line 248 of file ContField1D.h.

References Nektar::MultiRegions::DisContField1D::m_bndConditions.

Referenced by v_GetBndConditions().

         {
             return m_bndConditions;
         }

GlobalLinSysSharedPtr Nektar::MultiRegions::ContField1D::GetGlobalLinSys ( const GlobalLinSysKey & mkey )

private

Returns the linear system specified by mkey.

The function searches the map #m_globalLinSys to see if the global matrix has been created before. If not, it calls the function #GenglobalLinSys to generate the requested global system.

Parameters

mkey	Key specifying the linear system.

Returns: Pointer to the required linear system.

Definition at line 365 of file ContField1D.cpp.

References m_globalLinSysManager.

Referenced by GlobalSolve().

         {
             return m_globalLinSysManager[mkey];
         }

const AssemblyMapCGSharedPtr & Nektar::MultiRegions::ContField1D::GetLocalToGlobalMap ( ) const

inline

Returns the map from local to global level.

Definition at line 349 of file ContField1D.h.

References m_locToGloMap.

         {
             return  m_locToGloMap;
         }

void Nektar::MultiRegions::ContField1D::GlobalSolve	(	const GlobalLinSysKey &	key,
		const Array< OneD, const NekDouble > &	rhs,
		Array< OneD, NekDouble > &	inout,
		const Array< OneD, const NekDouble > &	dirForcing = `NullNekDouble1DArray`
	)

private

Solve the linear system specified by the key key.

Given a linear system specified by the key key,

$\boldsymbol{M}\boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}},$

this function solves this linear system taking into account the boundary conditions specified in the data member m_bndCondExpansions. Therefore, it adds an array $\boldsymbol{\hat{g}}$ which represents the non-zero surface integral resulting from the weak boundary conditions (e.g. Neumann boundary conditions) to the right hand side, that is,

$\boldsymbol{M}\boldsymbol{\hat{u}}_g=\boldsymbol{\hat{f}}+ \boldsymbol{\hat{g}}.$

Furthermore, it lifts the known degrees of freedom which are prescribed by the Dirichlet boundary conditions. As these known coefficients $\boldsymbol{\hat{u}}^{\mathcal{D}}$ are numbered first in the global coefficient array $\boldsymbol{\hat{u}}_g$ , the linear system can be decomposed as,

$\left[\begin{array}{cc} \boldsymbol{M}^{\mathcal{DD}}&\boldsymbol{M}^{\mathcal{DH}}\\ \boldsymbol{M}^{\mathcal{HD}}&\boldsymbol{M}^{\mathcal{HH}} \end{array}\right] \left[\begin{array}{c} \boldsymbol{\hat{u}}^{\mathcal{D}}\\ \boldsymbol{\hat{u}}^{\mathcal{H}} \end{array}\right]= \left[\begin{array}{c} \boldsymbol{\hat{f}}^{\mathcal{D}}\\ \boldsymbol{\hat{f}}^{\mathcal{H}} \end{array}\right]+ \left[\begin{array}{c} \boldsymbol{\hat{g}}^{\mathcal{D}}\\ \boldsymbol{\hat{g}}^{\mathcal{H}} \end{array}\right]$

which will then be solved for the unknown coefficients $\boldsymbol{\hat{u}}^{\mathcal{H}}$ as,

$\boldsymbol{M}^{\mathcal{HH}}\boldsymbol{\hat{u}}^{\mathcal{H}} = \boldsymbol{\hat{f}}^{\mathcal{H}} +\boldsymbol{\hat{g}}^{\mathcal{H}} -\boldsymbol{M}^{\mathcal{HD}}\boldsymbol{\hat{u}}^{\mathcal{D}}$

Parameters

key	Specifes the linear system to solve.
rhs	Forcing term $\boldsymbol{f}$ .
inout	Solution vector $\boldsymbol{\hat{u}}$ .
dirForcing	.

Definition at line 336 of file ContField1D.cpp.

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

Referenced by FwdTrans(), MultiplyByInvMassMatrix(), and v_HelmSolve().

         {
             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::ContField1D::GlobalToLocal	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray
	)

inline

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.

Parameters

inarray	An array of size $N_\mathrm{dof}$ containing the global degrees of freedom $\boldsymbol{x}_g$ .
outarray	The resulting local degrees of freedom $\boldsymbol{x}_l$ will be stored in this array of size $N_\mathrm{eof}$ .

Definition at line 280 of file ContField1D.h.

References m_locToGloMap.

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

void Nektar::MultiRegions::ContField1D::IProductWRTBase	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate = `eLocal`
	)

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

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

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

Parameters

In	An ExpList, containing the discrete evaluation of at the quadrature points in its array m_phys.

Definition at line 396 of file ContField1D.cpp.

References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::MultiRegions::ExpList::IProductWRTBase_IterPerExp(), and Nektar::MultiRegions::ExpList::m_ncoeffs.

Referenced by FwdTrans(), v_HelmSolve(), and v_IProductWRTBase().

         {
             if(coeffstate == eGlobal)
             {
                 Array<OneD, NekDouble> wsp(m_ncoeffs);
                 IProductWRTBase_IterPerExp(inarray,wsp);
                 Assemble(wsp,outarray);
             }
             else
             {
                 IProductWRTBase_IterPerExp(inarray,outarray);
             }
         }

void Nektar::MultiRegions::ContField1D::LocalToGlobal ( )

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

void Nektar::MultiRegions::ContField1D::MultiplyByInvMassMatrix	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate = `eLocal`
	)

Definition at line 251 of file ContField1D.cpp.

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

Referenced by v_MultiplyByInvMassMatrix().

         {
             GlobalLinSysKey key(StdRegions::eMass, m_locToGloMap);
             if(coeffstate == eGlobal)
             {
                 if(inarray.data() == outarray.data())
                 {
                     Array<OneD, NekDouble> tmp(inarray);
                     GlobalSolve(key,tmp,outarray);
                 }
                 else
                 {
                     GlobalSolve(key,inarray,outarray);
                 }
             }
             else
             {
                 Array<OneD, NekDouble> globaltmp(m_ncoeffs,0.0);
 
                 if(inarray.data() == outarray.data())
                 {
                     Array<OneD,NekDouble> tmp(inarray);
                     Assemble(tmp,outarray);
                 }
                 else
                 {
                     Assemble(inarray,outarray);
                 }
 
                 GlobalSolve(key,outarray,globaltmp);
                 GlobalToLocal(globaltmp,outarray);
             }
         }

void Nektar::MultiRegions::ContField1D::v_BwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate
	)

privatevirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 571 of file ContField1D.cpp.

References BwdTrans().

         {
             BwdTrans(inarray,outarray,coeffstate);
         }

void Nektar::MultiRegions::ContField1D::v_ClearGlobalLinSysManager ( void )

privatevirtual

Reset the GlobalLinSys Manager

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 628 of file ContField1D.cpp.

References m_globalLinSysManager.

         {
             m_globalLinSysManager.ClearManager("GlobalLinSys");
         }

void Nektar::MultiRegions::ContField1D::v_FwdTrans	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate
	)

privatevirtual

Perform a forward transform.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 414 of file ContField1D.cpp.

References FwdTrans().

         {
             FwdTrans(inarray,outarray,coeffstate);
         }

void Nektar::MultiRegions::ContField1D::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::ExpList.

Definition at line 603 of file ContField1D.cpp.

References Assemble(), Nektar::MultiRegions::eGlobal, Nektar::MultiRegions::ExpList::GeneralMatrixOp_IterPerExp(), Nektar::MultiRegions::ExpList::GlobalToLocal(), and Nektar::MultiRegions::ExpList::m_ncoeffs.

         {
             if(coeffstate == eGlobal)
             {
                 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::ContField1D::v_GetBndConditions ( void )

privatevirtual

Reimplemented from Nektar::MultiRegions::DisContField1D.

Definition at line 566 of file ContField1D.cpp.

References GetBndConditions().

         {
             return GetBndConditions();
         }

void Nektar::MultiRegions::ContField1D::v_GlobalToLocal ( void )

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.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 487 of file ContField1D.cpp.

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

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

void Nektar::MultiRegions::ContField1D::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
	)

privatevirtual

Consider the one dimensional Helmholtz equation,

$\frac{d^2u}{dx^2}-\lambda u(x) = f(x),$

supplemented with appropriate boundary conditions (which are contained in the data member m_bndCondExpansions). Applying a $C^0$ continuous Galerkin discretisation, this equation leads to the following linear system:

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

where $\boldsymbol{M}$ and $\boldsymbol{L}$ are the mass and Laplacian matrix respectively. This function solves the system above for the global coefficients $\boldsymbol{\hat{u}}$ by a call to the function GlobalSolve.

The values of the function $f(x)$ evaluated at the quadrature points $\boldsymbol{x}_i$ should be contained in the variable m_phys of the ExpList object inarray. The resulting global coefficients $\boldsymbol{\hat{u}}_g$ are stored in the array m_coeffs.

Parameters

inarray	Input containing forcing function $\boldsymbol{f}$ at the quadrature points.
outarray	Output containing the coefficients $\boldsymbol{u}_g$
lambda	Parameter value.
Sigma	Coefficients of lambda.
varcoeff	Variable diffusivity coefficients.
coeffstate
dirForcing	Dirichlet Forcing.

Reimplemented from Nektar::MultiRegions::DisContField1D.

Definition at line 522 of file ContField1D.cpp.

References Nektar::SpatialDomains::eDirichlet, Nektar::MultiRegions::eGlobal, Nektar::StdRegions::eHelmholtz, Nektar::eUseGlobal, GlobalSolve(), Nektar::MultiRegions::ExpList::GlobalToLocal(), IProductWRTBase(), Nektar::FlagList::isSet(), Nektar::MultiRegions::DisContField1D::m_bndCondExpansions, Nektar::MultiRegions::DisContField1D::m_bndConditions, m_locToGloMap, and Vmath::Neg().

         {
             // 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;
             for(i = 0; i < m_bndCondExpansions.num_elements(); ++i)
             {
                 if(m_bndConditions[i]->GetBoundaryConditionType() != SpatialDomains::eDirichlet)
                 {
                     wsp[m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap(i)]
                         += m_bndCondExpansions[i]->GetCoeff(0);
                 }
             }
 
             // Solve the system
             GlobalLinSysKey key(StdRegions::eHelmholtz,
                                 m_locToGloMap,factors,varcoeff);
 
             if(flags.isSet(eUseGlobal))
             {
                 GlobalSolve(key,wsp,outarray,dirForcing);
             }
             else
             {
                 Array<OneD,NekDouble> tmp(contNcoeffs,0.0);
                 GlobalSolve(key,wsp,tmp,dirForcing);
                 GlobalToLocal(tmp,outarray);
             }
         }

void Nektar::MultiRegions::ContField1D::v_ImposeDirichletConditions ( Array< OneD, NekDouble > & outarray )

privatevirtual

Impose the Dirichlet Boundary Conditions on outarray.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 430 of file ContField1D.cpp.

References Nektar::SpatialDomains::eDirichlet, Nektar::MultiRegions::DisContField1D::m_bndCondExpansions, Nektar::MultiRegions::DisContField1D::m_bndConditions, and m_locToGloMap.

Referenced by GlobalSolve().

         {
             for(int i = 0; i < m_bndCondExpansions.num_elements(); ++i)
             {
                 if(m_bndConditions[i]->GetBoundaryConditionType() == SpatialDomains::eDirichlet)
                 {
                     outarray[m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap(i)]
                         = m_bndCondExpansions[i]->GetCoeff(0);
                 }
             }            
         }

void Nektar::MultiRegions::ContField1D::v_IProductWRTBase	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate
	)

privatevirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 579 of file ContField1D.cpp.

References IProductWRTBase().

         {
             IProductWRTBase(inarray,outarray,coeffstate);
         }

void Nektar::MultiRegions::ContField1D::v_LocalToGlobal ( void )

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.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 462 of file ContField1D.cpp.

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

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

void Nektar::MultiRegions::ContField1D::v_MultiplyByInvMassMatrix	(	const Array< OneD, const NekDouble > &	inarray,
		Array< OneD, NekDouble > &	outarray,
		CoeffState	coeffstate
	)

privatevirtual

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 422 of file ContField1D.cpp.

References MultiplyByInvMassMatrix().

         {
             MultiplyByInvMassMatrix(inarray,outarray,coeffstate);
         }

Member Data Documentation

CoeffState Nektar::MultiRegions::ContField1D::m_coeffState

protected

A enum list declaring how to interpret coeffs, i.e. eLocal, eHybrid or eGlobal.

Definition at line 154 of file ContField1D.h.

LibUtilities::NekManager<GlobalLinSysKey, GlobalLinSys> Nektar::MultiRegions::ContField1D::m_globalLinSysManager

protected

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

Definition at line 164 of file ContField1D.h.

Referenced by GetGlobalLinSys(), and v_ClearGlobalLinSysManager().

GlobalMatrixMapShPtr Nektar::MultiRegions::ContField1D::m_globalMat

protected

(A shared pointer to) a list which collects all the global matrices being assembled, such that they should be constructed only once.

Definition at line 159 of file ContField1D.h.

AssemblyMapCGSharedPtr Nektar::MultiRegions::ContField1D::m_locToGloMap

protected

(A shared pointer to) the object which contains all the required information for the transformation from local to global degrees of freedom.

Definition at line 149 of file ContField1D.h.

Referenced by Assemble(), ContField1D(), FwdTrans(), GenGlobalLinSys(), GetLocalToGlobalMap(), GlobalSolve(), GlobalToLocal(), MultiplyByInvMassMatrix(), v_GlobalToLocal(), v_HelmSolve(), v_ImposeDirichletConditions(), and v_LocalToGlobal().

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Protected Attributes

Private Member Functions

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Constructor & Destructor Documentation

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Member Data Documentation