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Nektar::MultiRegions::ContField1D Class Reference

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>

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Public Member Functions

 ContField1D ()
 Default constructor.
 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.
 ContField1D (const ContField1D &In)
 Copy constructor.
 ContField1D (const LibUtilities::SessionReaderSharedPtr &pSession, const ExpList1D &In)
 Copy constructor.
virtual ~ContField1D ()
 Destructor.
void FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 Perform global forward transformation of a function $f(x)$,.
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.
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.
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 $\boldsymbol{\hat{u}}_l$.
void LocalToGlobal ()
 Gathers the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$.
void Assemble ()
 Assembles the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$.
void Assemble (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
 Assembles the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$.
const AssemblyMapCGSharedPtr & GetLocalToGlobalMap () const
 Returns the map from local to global level.
void IProductWRTBase (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate=eLocal)
 Calculates the inner product of a function $f(x)$ with respect to all global expansion modes $\phi_n^e(x)$.
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.
- Public Member Functions inherited from Nektar::MultiRegions::DisContField1D
 DisContField1D ()
 Default constructor.
 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.
 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.
 DisContField1D (const DisContField1D &In)
 Constructs a 1D discontinuous field based on an existing field.
 DisContField1D (const ExpList1D &In)
 Constructs a 1D discontinuous field based on an existing field. (needed in order to use ContField( const ExpList1D &In) constructor.
virtual ~DisContField1D ()
 Destructor.
GlobalLinSysSharedPtr GetGlobalBndLinSys (const GlobalLinSysKey &mkey)
 For a given key, returns the associated global linear system.
vector< bool > & GetNegatedFluxNormal (void)
- Public Member Functions inherited from Nektar::MultiRegions::ExpList1D
 ExpList1D ()
 The default constructor.
 ExpList1D (const ExpList1D &In, const bool DeclareCoeffPhysArrays=true)
 The copy constructor.
 ExpList1D (const LibUtilities::SessionReaderSharedPtr &pSession, const LibUtilities::BasisKey &Ba, const SpatialDomains::MeshGraphSharedPtr &graph1D)
 Construct an ExpList1D from a given graph.
 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.
 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.
 ExpList1D (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.
 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.
virtual ~ExpList1D ()
 Destructor.
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.
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.
void ParNormalSign (Array< OneD, NekDouble > &normsign)
 Set up the normals on each expansion.
- Public Member Functions inherited from Nektar::MultiRegions::ExpList
 ExpList ()
 The default constructor.
 ExpList (const LibUtilities::SessionReaderSharedPtr &pSession)
 The default constructor.
 ExpList (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
 The default constructor.
 ExpList (const ExpList &in, const bool DeclareCoeffPhysArrays=true)
 The copy constructor.
virtual ~ExpList ()
 The default destructor.
int GetNcoeffs (void) const
 Returns the total number of local degrees of freedom $N_{\mathrm{eof}}=\sum_{e=1}^{{N_{\mathrm{el}}}}N^{e}_m$.
int GetNcoeffs (const int eid) const
 Returns the total number of local degrees of freedom for element eid.
ExpansionType GetExpType (void)
 Returns the type of the expansion.
void SetExpType (ExpansionType Type)
 Returns the type of the expansion.
int EvalBasisNumModesMax (void) const
 Evaulates the maximum number of modes in the elemental basis order over all elements.
const Array< OneD, int > EvalBasisNumModesMaxPerExp (void) const
 Returns the vector of the number of modes in the elemental basis order over all elements.
int GetTotPoints (void) const
 Returns the total number of quadrature points m_npoints $=Q_{\mathrm{tot}}$.
int GetTotPoints (const int eid) const
 Returns the total number of quadrature points for eid's element $=Q_{\mathrm{tot}}$.
int GetNpoints (void) const
 Returns the total number of quadrature points m_npoints $=Q_{\mathrm{tot}}$.
int Get1DScaledTotPoints (const NekDouble scale) const
 Returns the total number of qudature points scaled by the factor scale on each 1D direction.
void SetWaveSpace (const bool wavespace)
 Sets the wave space to the one of the possible configuration true or false.
void SetModifiedBasis (const bool modbasis)
 Set Modified Basis for the stability analysis.
void SetPhys (int i, NekDouble val)
 Set the i th value of m_phys to value val.
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.
void SetPhys (const Array< OneD, const NekDouble > &inarray)
 Fills the array m_phys.
void SetPhysArray (Array< OneD, NekDouble > &inarray)
 Sets the array m_phys.
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.
bool GetPhysState (void) const
 This function indicates whether the array of physical values $\boldsymbol{u}_l$ (implemented as m_phys) is filled or not.
NekDouble PhysIntegral (void)
 This function integrates a function $f(\boldsymbol{x})$ over the domain consisting of all the elements of the expansion.
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.
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 $\phi_n^e(\boldsymbol{x})$.
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.
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.
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.
void SmoothField (Array< OneD, NekDouble > &field)
 Smooth a field across elements.
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.
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.
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.
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.
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 $\boldsymbol{x}_i$.
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 ApplyGeomInfo ()
 Apply geometry information to each expansion.
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)
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.
void SetCoeff (int i, NekDouble val)
 Set the i th coefficiient in m_coeffs to value val.
void SetCoeffs (int i, NekDouble val)
 Set the i th coefficiient in m_coeffs to value val.
void SetCoeffsArray (Array< OneD, NekDouble > &inarray)
 Set the m_coeffs array to inarray.
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.
void ImposeDirichletConditions (Array< OneD, NekDouble > &outarray)
 Impose Dirichlet Boundary Conditions onto Array.
void FillBndCondFromField (void)
 Fill Bnd Condition expansion from the values stored in expansion.
void GlobalToLocal (void)
 Put the coefficients into local ordering and place in m_coeffs.
NekDouble GetCoeff (int i)
 Get the i th value (coefficient) of m_coeffs.
NekDouble GetCoeffs (int i)
 Get the i th value (coefficient) of m_coeffs.
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.
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.
NekDouble L2 (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray)
 This function calculates the $L_2$ error with respect to soln of the global spectral/hp element approximation.
NekDouble H1 (const Array< OneD, const NekDouble > &inarray, const Array< OneD, const NekDouble > &soln=NullNekDouble1DArray)
 Calculates the $H^1$ error of the global spectral/hp element approximation.
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.
void SetHomo1DSpecVanVisc (Array< OneD, NekDouble > visc)
 This function sets the Spectral Vanishing Viscosity in homogeneous1D expansion.
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.
LibUtilities::TranspositionSharedPtr GetTransposition (void)
 This function returns the transposition class associaed with the homogeneous expansion.
NekDouble GetHomoLen (void)
 This function returns the Width of homogeneous direction associaed with the homogeneous expansion.
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.
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.
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.
int GetExpSize (void)
 This function returns the number of elements in the expansion.
int GetNumElmts (void)
 This function returns the number of elements in the expansion which may be different for a homogeoenous extended expansionp.
const boost::shared_ptr
< LocalRegions::ExpansionVector > 		GetExp () const
 This function returns the vector of elements in the expansion.
LocalRegions::ExpansionSharedPtr & GetExp (int n) const
 This function returns (a shared pointer to) the local elemental expansion of the $n^{\mathrm{th}}$ element.
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.
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.
int GetPhys_Offset (int n) const
 Get the start offset position for a global list of m_phys correspoinding to element n.
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.
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.
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.
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.
void PhysDeriv (const int dir, const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &out_d)
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)
void ExtractTracePhys (Array< OneD, NekDouble > &outarray)
void ExtractTracePhys (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray)
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_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 GeneralGetFieldDefinitions (std::vector< LibUtilities::FieldDefinitionsSharedPtr > &fielddef, int NumHomoDir=0, Array< OneD, LibUtilities::BasisSharedPtr > &HomoBasis=LibUtilities::NullBasisSharedPtr1DArray, std::vector< NekDouble > &HomoLen=LibUtilities::NullNekDoubleVector, std::vector< unsigned int > &HomoZIDs=LibUtilities::NullUnsignedIntVector, std::vector< unsigned int > &HomoYIDs=LibUtilities::NullUnsignedIntVector)
const
NekOptimize::GlobalOptParamSharedPtr & 		GetGlobalOptParam (void)
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.
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.
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.
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.
void ExtractDataToCoeffs (LibUtilities::FieldDefinitionsSharedPtr &fielddef, std::vector< NekDouble > &fielddata, std::string &field, Array< OneD, NekDouble > &coeffs)
 Extract the data in fielddata into the coeffs.
boost::shared_ptr< ExpList > GetSharedThisPtr ()
 Returns a shared pointer to the current object.
boost::shared_ptr
< LibUtilities::SessionReader > 		GetSession ()
 Returns the session object.
boost::shared_ptr
< LibUtilities::Comm > 		GetComm ()
 Returns the comm object.
SpatialDomains::MeshGraphSharedPtr GetGraph ()
LibUtilities::BasisSharedPtr GetHomogeneousBasis (void)
boost::shared_ptr< ExpList > & GetPlane (int n)

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.
CoeffState m_coeffState
 A enum list declaring how to interpret coeffs, i.e. eLocal, eHybrid or eGlobal.
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.
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.
- Protected Attributes inherited from Nektar::MultiRegions::DisContField1D
int m_numDirBndCondExpansions
 The number of boundary segments on which Dirichlet boundary conditions are imposed.
Array< OneD,
MultiRegions::ExpListSharedPtr > 		m_bndCondExpansions
 Discretised boundary conditions.
Array< OneD,
SpatialDomains::BoundaryConditionShPtr > 		m_bndConditions
 An array which contains the information about the boundary condition on the different boundary regions.
GlobalLinSysMapShPtr m_globalBndMat
 Global boundary matrix.
ExpListSharedPtr m_trace
 Trace space storage for points between elements.
AssemblyMapDGSharedPtr m_traceMap
 Local to global DG mapping for trace space.
std::set< int > m_boundaryVerts
 A set storing the global IDs of any boundary edges.
PeriodicMap m_periodicVerts
 A map which identifies groups of periodic vertices.
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.
vector< int > m_periodicBwdCopy
vector< bool > m_leftAdjacentVerts

Private Member Functions

GlobalLinSysSharedPtr GetGlobalLinSys (const GlobalLinSysKey &mkey)
 Returns the linear system specified by mkey.
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.
virtual void v_FwdTrans (const Array< OneD, const NekDouble > &inarray, Array< OneD, NekDouble > &outarray, CoeffState coeffstate)
 Perform a forward transform.
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.
virtual void v_GlobalToLocal (void)
 Scatters from the global coefficients $\boldsymbol{\hat{u}}_g$ to the local coefficients $\boldsymbol{\hat{u}}_l$.
virtual void v_LocalToGlobal (void)
 Gathers the global coefficients $\boldsymbol{\hat{u}}_g$ from the local coefficients $\boldsymbol{\hat{u}}_l$.
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.

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.
void FindPeriodicVertices (const SpatialDomains::BoundaryConditions &bcs, const std::string variable)
 Generate a associative map of periodic vertices in a mesh.
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.
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.
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.
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.
void GenerateFieldBnd1D (SpatialDomains::BoundaryConditions &bcs, const std::string variable)
virtual map< int,
RobinBCInfoSharedPtr > 		v_GetRobinBCInfo ()
virtual const Array< OneD,
const
MultiRegions::ExpListSharedPtr > & 		v_GetBndCondExpansions ()
virtual const Array< OneD,
const
SpatialDomains::BoundaryConditionShPtr > & 		v_GetBndConditions ()
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_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..
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)
 Solve the Helmholtz equation.
- 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:

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
graph1DA 1D mesh, containing information about the domain and the spectral/hp element expansion.
bcsThe boundary conditions.
variableAn optional parameter to indicate for which variable the field should be constructed.

Definition at line 117 of file ContField1D.cpp.

References 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
InExisting 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
InExisting explist1D field .

Definition at line 157 of file ContField1D.cpp.

References 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.

{
}

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 $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the gather operation $\boldsymbol{\hat{u}}_g=\mathcal{A}^{T}\boldsymbol{\hat{u}}_l$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

Definition at line 307 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 $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the gather operation $\boldsymbol{\hat{u}}_g=\mathcal{A}^{T}\boldsymbol{\hat{u}}_l$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

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

Definition at line 339 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
InAn ExpList, containing the local coefficients $\hat{u}_n^e$ in its array m_coeffs.

Reimplemented from Nektar::MultiRegions::ExpList.

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
inarrayDiscrete $f(x)$.
outarrayStorage for result.
coeffstate

Reimplemented from Nektar::MultiRegions::ExpList.

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.

Reimplemented from Nektar::MultiRegions::ExpList.

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

Definition at line 380 of file ContField1D.cpp.

References ASSERTL1, 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.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 240 of file ContField1D.h.

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

{
return m_bndCondExpansions;
}
const Array< OneD, const SpatialDomains::BoundaryConditionShPtr > & Nektar::MultiRegions::ContField1D::GetBndConditions ( )
inline

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 246 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
mkeyKey specifying the linear system.
Returns
Pointer to the required linear system.

Definition at line 374 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 347 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
keySpecifes the linear system to solve.
rhsForcing term $\boldsymbol{f}$.
inoutSolution vector $\boldsymbol{\hat{u}}$.
dirForcing.

Definition at line 336 of file ContField1D.cpp.

References Nektar::SpatialDomains::eDirichlet, GetGlobalLinSys(), Nektar::MultiRegions::DisContField1D::m_bndCondExpansions, Nektar::MultiRegions::DisContField1D::m_bndConditions, 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);
for(int i = 0; i < m_bndCondExpansions.num_elements(); ++i)
{
if(m_bndConditions[i]->GetBoundaryConditionType() == SpatialDomains::eDirichlet)
{
inout[m_locToGloMap->GetBndCondCoeffsToGlobalCoeffsMap(i)]
= m_bndCondExpansions[i]->GetCoeff(0);
}
}
// 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 $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the scatter operation $\boldsymbol{\hat{u}}_l=\mathcal{A}\boldsymbol{\hat{u}}_g$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

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

Definition at line 278 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
InAn ExpList, containing the discrete evaluation of $f(x)$ at the quadrature points in its array m_phys.

Reimplemented from Nektar::MultiRegions::ExpList.

Definition at line 405 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 $\boldsymbol{\hat{u}}_l$.

Reimplemented from Nektar::MultiRegions::ExpList.

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

Reimplemented from Nektar::MultiRegions::ExpList.

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

Definition at line 580 of file ContField1D.cpp.

References BwdTrans().

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

Perform a forward transform.

Definition at line 423 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
mkeyThis key uniquely defines the type matrix required for the operation.
inarrayThe vector $\boldsymbol{\hat{u}}_g$ of size $N_{\mathrm{dof}}$.
outarrayThe resulting vector of size $N_{\mathrm{dof}}$.

Definition at line 612 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

Definition at line 575 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 $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the scatter operation $\boldsymbol{\hat{u}}_l=\mathcal{A}\boldsymbol{\hat{u}}_g$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

Definition at line 496 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
inarrayInput containing forcing function $\boldsymbol{f}$ at the quadrature points.
outarrayOutput containing the coefficients $\boldsymbol{u}_g$
lambdaParameter value.
SigmaCoefficients of lambda.
varcoeffVariable diffusivity coefficients.
coeffstate
dirForcingDirichlet Forcing.

Definition at line 531 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.

Definition at line 439 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

Definition at line 588 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 $[e][i]$ is an array of similar dimensions ensuring the correct modal connectivity between the different elements (both these arrays are contained in the data member m_locToGloMap). This operation is equivalent to the gather operation $\boldsymbol{\hat{u}}_g=\mathcal{A}^{-1}\boldsymbol{\hat{u}}_l$, where $\mathcal{A}$ is the $N_{\mathrm{eof}}\times N_{\mathrm{dof}}$ permutation matrix.

Definition at line 471 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

Definition at line 431 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().

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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