Base class for linear elastic system. More...

#include <LinearElasticSystem.h>

Inheritance diagram for Nektar::LinearElasticSystem:

Collaboration diagram for Nektar::LinearElasticSystem:

Public Member Functions
void	BuildMatrixSystem ()
	Build matrix system for linear elasticity equations. More...

void	SetStaticCondBlock (const int n, const LocalRegions::ExpansionSharedPtr exp, Array< TwoD, DNekMatSharedPtr > &mat)
	Given a block matrix for an element, construct its static condensation matrices. More...

DNekMatSharedPtr	BuildLaplacianIJMatrix (const int k1, const int k2, const NekDouble scale, LocalRegions::ExpansionSharedPtr exp)
	Construct a LaplacianIJ matrix for a given expansion. More...

Public Member Functions inherited from Nektar::SolverUtils::EquationSystem
virtual SOLVER_UTILS_EXPORT	~EquationSystem ()
	Destructor. More...

SOLVER_UTILS_EXPORT void	SetUpTraceNormals (void)

SOLVER_UTILS_EXPORT void	InitObject ()
	Initialises the members of this object. More...

SOLVER_UTILS_EXPORT void	DoInitialise ()
	Perform any initialisation necessary before solving the problem. More...

SOLVER_UTILS_EXPORT void	DoSolve ()
	Solve the problem. More...

SOLVER_UTILS_EXPORT void	TransCoeffToPhys ()
	Transform from coefficient to physical space. More...

SOLVER_UTILS_EXPORT void	TransPhysToCoeff ()
	Transform from physical to coefficient space. More...

SOLVER_UTILS_EXPORT void	Output ()
	Perform output operations after solve. More...

SOLVER_UTILS_EXPORT NekDouble	LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Linf error computation. More...

SOLVER_UTILS_EXPORT std::string	GetSessionName ()
	Get Session name. More...

template<class T >
boost::shared_ptr< T >	as ()

SOLVER_UTILS_EXPORT void	ResetSessionName (std::string newname)
	Reset Session name. More...

SOLVER_UTILS_EXPORT LibUtilities::SessionReaderSharedPtr	GetSession ()
	Get Session name. More...

SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	GetPressure ()
	Get pressure field if available. More...

SOLVER_UTILS_EXPORT void	PrintSummary (std::ostream &out)
	Print a summary of parameters and solver characteristics. More...

SOLVER_UTILS_EXPORT void	SetLambda (NekDouble lambda)
	Set parameter m_lambda. More...

SOLVER_UTILS_EXPORT void	EvaluateFunction (Array< OneD, Array< OneD, NekDouble > > &pArray, std::string pFunctionName, const NekDouble pTime=0.0, const int domain=0)
	Evaluates a function as specified in the session file. More...

SOLVER_UTILS_EXPORT void	EvaluateFunction (std::vector< std::string > pFieldNames, Array< OneD, Array< OneD, NekDouble > > &pFields, const std::string &pName, const NekDouble &pTime=0.0, const int domain=0)
	Populate given fields with the function from session. More...

SOLVER_UTILS_EXPORT void	EvaluateFunction (std::vector< std::string > pFieldNames, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields, const std::string &pName, const NekDouble &pTime=0.0, const int domain=0)
	Populate given fields with the function from session. More...

SOLVER_UTILS_EXPORT void	EvaluateFunction (std::string pFieldName, Array< OneD, NekDouble > &pArray, const std::string &pFunctionName, const NekDouble &pTime=0.0, const int domain=0)

SOLVER_UTILS_EXPORT std::string	DescribeFunction (std::string pFieldName, const std::string &pFunctionName, const int domain)
	Provide a description of a function for a given field name. More...

SOLVER_UTILS_EXPORT void	InitialiseBaseFlow (Array< OneD, Array< OneD, NekDouble > > &base)
	Perform initialisation of the base flow. More...

SOLVER_UTILS_EXPORT void	SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)
	Initialise the data in the dependent fields. More...

SOLVER_UTILS_EXPORT void	EvaluateExactSolution (int field, Array< OneD, NekDouble > &outfield, const NekDouble time)
	Evaluates an exact solution. More...

SOLVER_UTILS_EXPORT NekDouble	L2Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln, bool Normalised=false)
	Compute the L2 error between fields and a given exact solution. More...

SOLVER_UTILS_EXPORT NekDouble	L2Error (unsigned int field, bool Normalised=false)
	Compute the L2 error of the fields. More...

SOLVER_UTILS_EXPORT Array < OneD, NekDouble >	ErrorExtraPoints (unsigned int field)
	Compute error (L2 and L_inf) over an larger set of quadrature points return [L2 Linf]. More...

SOLVER_UTILS_EXPORT void	WeakAdvectionGreensDivergenceForm (const Array< OneD, Array< OneD, NekDouble > > &F, Array< OneD, NekDouble > &outarray)
	Compute the inner product $(\nabla \phi \cdot F)$ . More...

SOLVER_UTILS_EXPORT void	WeakAdvectionDivergenceForm (const Array< OneD, Array< OneD, NekDouble > > &F, Array< OneD, NekDouble > &outarray)
	Compute the inner product $(\phi, \nabla \cdot F)$ . More...

SOLVER_UTILS_EXPORT void	WeakAdvectionNonConservativeForm (const Array< OneD, Array< OneD, NekDouble > > &V, const Array< OneD, const NekDouble > &u, Array< OneD, NekDouble > &outarray, bool UseContCoeffs=false)
	Compute the inner product $(\phi, V\cdot \nabla u)$ . More...

f SOLVER_UTILS_EXPORT void	AdvectionNonConservativeForm (const Array< OneD, Array< OneD, NekDouble > > &V, const Array< OneD, const NekDouble > &u, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wk=NullNekDouble1DArray)
	Compute the non-conservative advection. More...

SOLVER_UTILS_EXPORT void	WeakDGAdvection (const Array< OneD, Array< OneD, NekDouble > > &InField, Array< OneD, Array< OneD, NekDouble > > &OutField, bool NumericalFluxIncludesNormal=true, bool InFieldIsInPhysSpace=false, int nvariables=0)
	Calculate the weak discontinuous Galerkin advection. More...

SOLVER_UTILS_EXPORT void	WeakDGDiffusion (const Array< OneD, Array< OneD, NekDouble > > &InField, Array< OneD, Array< OneD, NekDouble > > &OutField, bool NumericalFluxIncludesNormal=true, bool InFieldIsInPhysSpace=false)
	Calculate weak DG Diffusion in the LDG form. More...

SOLVER_UTILS_EXPORT void	Checkpoint_Output (const int n)
	Write checkpoint file of m_fields. More...

SOLVER_UTILS_EXPORT void	Checkpoint_Output (const int n, MultiRegions::ExpListSharedPtr &field, std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)
	Write checkpoint file of custom data fields. More...

SOLVER_UTILS_EXPORT void	Checkpoint_BaseFlow (const int n)
	Write base flow file of m_fields. More...

SOLVER_UTILS_EXPORT void	WriteFld (const std::string &outname)
	Write field data to the given filename. More...

SOLVER_UTILS_EXPORT void	WriteFld (const std::string &outname, MultiRegions::ExpListSharedPtr &field, std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)
	Write input fields to the given filename. More...

SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields)
	Input field data from the given file. More...

SOLVER_UTILS_EXPORT void	ImportFldToMultiDomains (const std::string &infile, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields, const int ndomains)
	Input field data from the given file to multiple domains. More...

SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, std::vector< std::string > &fieldStr, Array< OneD, Array< OneD, NekDouble > > &coeffs)
	Output a field. Input field data into array from the given file. More...

SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, MultiRegions::ExpListSharedPtr &pField, std::string &pFieldName)
	Output a field. Input field data into ExpList from the given file. More...

SOLVER_UTILS_EXPORT void	ScanForHistoryPoints ()
	Builds map of which element holds each history point. More...

SOLVER_UTILS_EXPORT void	WriteHistoryData (std::ostream &out)
	Probe each history point and write to file. More...

SOLVER_UTILS_EXPORT void	SessionSummary (SummaryList &vSummary)
	Write out a session summary. More...

SOLVER_UTILS_EXPORT Array < OneD, MultiRegions::ExpListSharedPtr > &	UpdateFields ()

SOLVER_UTILS_EXPORT LibUtilities::FieldMetaDataMap &	UpdateFieldMetaDataMap ()
	Get hold of FieldInfoMap so it can be updated. More...

SOLVER_UTILS_EXPORT NekDouble	GetFinalTime ()
	Return final time. More...

SOLVER_UTILS_EXPORT int	GetNcoeffs ()

SOLVER_UTILS_EXPORT int	GetNcoeffs (const int eid)

SOLVER_UTILS_EXPORT int	GetNumExpModes ()

SOLVER_UTILS_EXPORT const Array< OneD, int >	GetNumExpModesPerExp ()

SOLVER_UTILS_EXPORT int	GetNvariables ()

SOLVER_UTILS_EXPORT const std::string	GetVariable (unsigned int i)

SOLVER_UTILS_EXPORT int	GetTraceTotPoints ()

SOLVER_UTILS_EXPORT int	GetTraceNpoints ()

SOLVER_UTILS_EXPORT int	GetExpSize ()

SOLVER_UTILS_EXPORT int	GetPhys_Offset (int n)

SOLVER_UTILS_EXPORT int	GetCoeff_Offset (int n)

SOLVER_UTILS_EXPORT int	GetTotPoints ()

SOLVER_UTILS_EXPORT int	GetTotPoints (int n)

SOLVER_UTILS_EXPORT int	GetNpoints ()

SOLVER_UTILS_EXPORT int	GetNumElmVelocity ()

SOLVER_UTILS_EXPORT int	GetSteps ()

SOLVER_UTILS_EXPORT NekDouble	GetTimeStep ()

SOLVER_UTILS_EXPORT void	CopyFromPhysField (const int i, Array< OneD, NekDouble > &output)

SOLVER_UTILS_EXPORT void	CopyToPhysField (const int i, Array< OneD, NekDouble > &output)

SOLVER_UTILS_EXPORT void	SetSteps (const int steps)

SOLVER_UTILS_EXPORT void	ZeroPhysFields ()

SOLVER_UTILS_EXPORT void	FwdTransFields ()

SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &fluxX, Array< OneD, Array< OneD, NekDouble > > &fluxY)

SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, const int j, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numflux)

SOLVER_UTILS_EXPORT void	NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxX, Array< OneD, Array< OneD, NekDouble > > &numfluxY)

SOLVER_UTILS_EXPORT void	NumFluxforScalar (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &uflux)

SOLVER_UTILS_EXPORT void	NumFluxforVector (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &qfield, Array< OneD, Array< OneD, NekDouble > > &qflux)

SOLVER_UTILS_EXPORT void	SetModifiedBasis (const bool modbasis)

SOLVER_UTILS_EXPORT int	NoCaseStringCompare (const std::string &s1, const std::string &s2)
	Perform a case-insensitive string comparison. More...

SOLVER_UTILS_EXPORT int	GetCheckpointNumber ()

SOLVER_UTILS_EXPORT void	SetCheckpointNumber (int num)

SOLVER_UTILS_EXPORT int	GetCheckpointSteps ()

SOLVER_UTILS_EXPORT void	SetCheckpointSteps (int num)

SOLVER_UTILS_EXPORT void	SetTime (const NekDouble time)

SOLVER_UTILS_EXPORT void	SetInitialStep (const int step)

SOLVER_UTILS_EXPORT void	SetBoundaryConditions (NekDouble time)
	Evaluates the boundary conditions at the given time. More...

virtual SOLVER_UTILS_EXPORT bool	v_NegatedOp ()
	Virtual function to identify if operator is negated in DoSolve. More...

Static Public Member Functions
static EquationSystemSharedPtr	create (const LibUtilities::SessionReaderSharedPtr &pSession)
	Creates an instance of this class. More...

Static Public Attributes
static std::string	className
	Name of class. More...

Protected Member Functions
	LinearElasticSystem (const LibUtilities::SessionReaderSharedPtr &pSession)
	Default constructor. More...

virtual void	v_InitObject ()
	Set up the linear elasticity system. More...

virtual void	v_GenerateSummary (SolverUtils::SummaryList &s)
	Generate summary at runtime. More...

virtual void	v_DoSolve ()
	Solve elliptic linear elastic system. More...

virtual void	v_ExtraFldOutput (std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)

Protected Member Functions inherited from Nektar::SolverUtils::EquationSystem
SOLVER_UTILS_EXPORT	EquationSystem (const LibUtilities::SessionReaderSharedPtr &pSession)
	Initialises EquationSystem class members. More...

int	nocase_cmp (const std::string &s1, const std::string &s2)

virtual SOLVER_UTILS_EXPORT void	v_DoInitialise ()
	Virtual function for initialisation implementation. More...

virtual SOLVER_UTILS_EXPORT NekDouble	v_LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Virtual function for the L_inf error computation between fields and a given exact solution. More...

virtual SOLVER_UTILS_EXPORT NekDouble	v_L2Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray, bool Normalised=false)
	Virtual function for the L_2 error computation between fields and a given exact solution. More...

virtual SOLVER_UTILS_EXPORT void	v_TransCoeffToPhys ()
	Virtual function for transformation to physical space. More...

virtual SOLVER_UTILS_EXPORT void	v_TransPhysToCoeff ()
	Virtual function for transformation to coefficient space. More...

virtual SOLVER_UTILS_EXPORT void	v_SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)

virtual SOLVER_UTILS_EXPORT void	v_EvaluateExactSolution (unsigned int field, Array< OneD, NekDouble > &outfield, const NekDouble time)

SOLVER_UTILS_EXPORT void	SetUpBaseFields (SpatialDomains::MeshGraphSharedPtr &mesh)

SOLVER_UTILS_EXPORT void	ImportFldBase (std::string pInfile, SpatialDomains::MeshGraphSharedPtr pGraph)

virtual SOLVER_UTILS_EXPORT void	v_Output (void)

virtual SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	v_GetPressure (void)

Protected Attributes
NekDouble	m_nu
	Poisson ratio. More...

NekDouble	m_E
	Young's modulus. More...

NekDouble	m_beta
	Parameter dictating amount of thermal stress to add. More...

CoupledAssemblyMapSharedPtr	m_assemblyMap
	Assembly map for the coupled (u,v,w) system. More...

DNekScalBlkMatSharedPtr	m_schurCompl
	Schur complement boundary-boundary matrix. More...

DNekScalBlkMatSharedPtr	m_BinvD
	Matrix of elemental $B^{-1}D$ components. More...

DNekScalBlkMatSharedPtr	m_C
	Matrix of elemental components. More...

DNekScalBlkMatSharedPtr	m_Dinv
	Matrix of elemental $D^{-1}$ components. More...

Array< OneD, Array< OneD, unsigned int > >	m_bmap
	Boundary maps for each of the fields. More...

Array< OneD, Array< OneD, unsigned int > >	m_imap
	Interior maps for each of the fields. More...

Array< OneD, Array< OneD, NekDouble > >	m_temperature
	Storage for the temperature terms. More...

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_stress
	Storage for the thermal stress terms. More...

Protected Attributes inherited from Nektar::SolverUtils::EquationSystem
LibUtilities::CommSharedPtr	m_comm
	Communicator. More...

LibUtilities::SessionReaderSharedPtr	m_session
	The session reader. More...

LibUtilities::FieldIOSharedPtr	m_fld
	Field input/output. More...

std::map< std::string, Array < OneD, Array< OneD, float > > >	m_interpWeights
	Map of the interpolation weights for a specific filename. More...

std::map< std::string, Array < OneD, Array< OneD, unsigned int > > >	m_interpInds
	Map of the interpolation indices for a specific filename. More...

Array< OneD, MultiRegions::ExpListSharedPtr >	m_fields
	Array holding all dependent variables. More...

Array< OneD, MultiRegions::ExpListSharedPtr >	m_base
	Base fields. More...

Array< OneD, MultiRegions::ExpListSharedPtr >	m_derivedfields
	Array holding all dependent variables. More...

SpatialDomains::BoundaryConditionsSharedPtr	m_boundaryConditions
	Pointer to boundary conditions object. More...

SpatialDomains::MeshGraphSharedPtr	m_graph
	Pointer to graph defining mesh. More...

std::string	m_sessionName
	Name of the session. More...

NekDouble	m_time
	Current time of simulation. More...

int	m_initialStep
	Number of the step where the simulation should begin. More...

NekDouble	m_fintime
	Finish time of the simulation. More...

NekDouble	m_timestep
	Time step size. More...

NekDouble	m_lambda
	Lambda constant in real system if one required. More...

std::set< std::string >	m_loadedFields

NekDouble	m_checktime
	Time between checkpoints. More...

int	m_nchk
	Number of checkpoints written so far. More...

int	m_steps
	Number of steps to take. More...

int	m_checksteps
	Number of steps between checkpoints. More...

int	m_spacedim
	Spatial dimension (>= expansion dim). More...

int	m_expdim
	Expansion dimension. More...

bool	m_singleMode
	Flag to determine if single homogeneous mode is used. More...

bool	m_halfMode
	Flag to determine if half homogeneous mode is used. More...

bool	m_multipleModes
	Flag to determine if use multiple homogenenous modes are used. More...

bool	m_useFFT
	Flag to determine if FFT is used for homogeneous transform. More...

bool	m_homogen_dealiasing
	Flag to determine if dealiasing is used for homogeneous simulations. More...

bool	m_specHP_dealiasing
	Flag to determine if dealisising is usde for the Spectral/hp element discretisation. More...

enum MultiRegions::ProjectionType	m_projectionType
	Type of projection; e.g continuous or discontinuous. More...

Array< OneD, Array< OneD, NekDouble > >	m_traceNormals
	Array holding trace normals for DG simulations in the forwards direction. More...

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_gradtan
	1 x nvariable x nq More...

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_tanbasis
	2 x m_spacedim x nq More...

Array< OneD, bool >	m_checkIfSystemSingular
	Flag to indicate if the fields should be checked for singularity. More...

LibUtilities::FieldMetaDataMap	m_fieldMetaDataMap
	Map to identify relevant solver info to dump in output fields. More...

int	m_NumQuadPointsError
	Number of Quadrature points used to work out the error. More...

enum HomogeneousType	m_HomogeneousType

NekDouble	m_LhomX
	physical length in X direction (if homogeneous) More...

NekDouble	m_LhomY
	physical length in Y direction (if homogeneous) More...

NekDouble	m_LhomZ
	physical length in Z direction (if homogeneous) More...

int	m_npointsX
	number of points in X direction (if homogeneous) More...

int	m_npointsY
	number of points in Y direction (if homogeneous) More...

int	m_npointsZ
	number of points in Z direction (if homogeneous) More...

int	m_HomoDirec
	number of homogenous directions More...

Friends
class	MemoryManager< LinearElasticSystem >
	Class may only be instantiated through the MemoryManager. More...

Additional Inherited Members
Protected Types inherited from Nektar::SolverUtils::EquationSystem
enum	HomogeneousType { eHomogeneous1D, eHomogeneous2D, eHomogeneous3D, eNotHomogeneous }
	Parameter for homogeneous expansions. More...

Detailed Description

Base class for linear elastic system.

Definition at line 50 of file LinearElasticSystem.h.

Constructor & Destructor Documentation

Nektar::LinearElasticSystem::LinearElasticSystem ( const LibUtilities::SessionReaderSharedPtr & pSession )

protected

Default constructor.

Definition at line 129 of file LinearElasticSystem.cpp.

     : EquationSystem(pSession)
 {
 }

Member Function Documentation

DNekMatSharedPtr Nektar::LinearElasticSystem::BuildLaplacianIJMatrix	(	const int	k1,
		const int	k2,
		const NekDouble	scale,
		LocalRegions::ExpansionSharedPtr	exp
	)

Construct a LaplacianIJ matrix for a given expansion.

This routine constructs matrices whose entries contain the evaluation of

$\partial_{\tt k1} \phi_i \partial_{\tt k2} \phi_j \,dx$

Definition at line 880 of file LinearElasticSystem.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::eFULL, and Vmath::Smul().

Referenced by BuildMatrixSystem().

 {
     const int nCoeffs = exp->GetNcoeffs();
     const int nPhys   = exp->GetTotPoints();
     int i;
 
     DNekMatSharedPtr ret = MemoryManager<DNekMat>::AllocateSharedPtr(
         nCoeffs, nCoeffs, 0.0, eFULL);
 
     Array<OneD, NekDouble> tmp2(nPhys);
     Array<OneD, NekDouble> tmp3(nPhys);
 
     for (i = 0; i < nCoeffs; ++i)
     {
         Array<OneD, NekDouble> tmp1(nCoeffs, 0.0);
         tmp1[i] = 1.0;
 
         exp->BwdTrans            (    tmp1, tmp2);
         exp->PhysDeriv           (k1, tmp2, tmp3);
         exp->IProductWRTDerivBase(k2, tmp3, tmp1);
 
         Vmath::Smul(
             nCoeffs, scale, &tmp1[0], 1, &(ret->GetPtr())[0]+i*nCoeffs, 1);
     }
 
     return ret;
 }

void Nektar::LinearElasticSystem::BuildMatrixSystem ( )

Build matrix system for linear elasticity equations.

This routine constructs the matrix discretisation arising from the weak formulation of the linear elasticity equations. The resulting matrix system is then passed to LinearElasticSystem::SetStaticCondBlock in order to construct the statically condensed system.

All of the matrices involved in the construction of the divergence of the stress tensor are Laplacian-like. We use the variable coefficient functionality within the library to multiply the Laplacian by the appropriate constants for all diagonal terms, and off-diagonal terms use LinearElasticSystem::BuildLaplacianIJMatrix to construct matrices containing

$\int \partial_{x_i} \phi_k \partial_{x_j} \phi_l$

where mixed derivative terms are present. Symmetry (in terms of k,l) is exploited to avoid constructing this matrix repeatedly.

Todo:: Make static condensation optional and construct full system instead.

Definition at line 240 of file LinearElasticSystem.cpp.

References BuildLaplacianIJMatrix(), Nektar::StdRegions::eLaplacian, Nektar::StdRegions::eVarCoeffD00, Nektar::StdRegions::eVarCoeffD11, Nektar::StdRegions::eVarCoeffD22, m_E, Nektar::SolverUtils::EquationSystem::m_fields, m_nu, Nektar::SolverUtils::EquationSystem::m_session, and SetStaticCondBlock().

Referenced by v_DoSolve().

 {
     const int nEl = m_fields[0]->GetExpSize();
     const int nVel = m_fields[0]->GetCoordim(0);
 
     LocalRegions::ExpansionSharedPtr exp;
     int n;
 
     // Factors map for matrix keys.
     StdRegions::ConstFactorMap factors;
 
     // Calculate various constants
     NekDouble mu     = m_E * 0.5  / (1.0 + m_nu);
     NekDouble lambda = m_E * m_nu / (1.0 + m_nu) / (1.0 - 2.0*m_nu);
 
     bool verbose = m_session->DefinesCmdLineArgument("verbose");
     bool root    = m_session->GetComm()->GetRank() == 0;
 
     // Loop over each element and construct matrices.
     if (nVel == 2)
     {
         for (n = 0; n < nEl; ++n)
         {
             exp = m_fields[0]->GetExp(m_fields[0]->GetOffset_Elmt_Id(n));
             const int nPhys = exp->GetTotPoints();
             Array<OneD, NekDouble> aArr(nPhys, lambda + 2*mu);
             Array<OneD, NekDouble> bArr(nPhys, mu);
 
             StdRegions::VarCoeffMap varcoeffA, varcoeffD;
             varcoeffA[StdRegions::eVarCoeffD00] = aArr;
             varcoeffA[StdRegions::eVarCoeffD11] = bArr;
             varcoeffD[StdRegions::eVarCoeffD00] = bArr;
             varcoeffD[StdRegions::eVarCoeffD11] = aArr;
 
             LocalRegions::MatrixKey matkeyA(StdRegions::eLaplacian,
                                             exp->DetShapeType(),
                                             *exp, factors, varcoeffA);
             LocalRegions::MatrixKey matkeyD(StdRegions::eLaplacian,
                                             exp->DetShapeType(),
                                             *exp, factors, varcoeffD);
 
             /*
              * mat holds the linear operator [ A B ] acting on [ u ].
              *                               [ C D ]           [ v ]
              */
             Array<TwoD, DNekMatSharedPtr> mat(2,2);
             mat[0][0] = exp->GenMatrix(matkeyA);
             mat[0][1] = BuildLaplacianIJMatrix(1, 0, mu+lambda, exp);
             mat[1][0] = mat[0][1];
             mat[1][1] = exp->GenMatrix(matkeyD);
 
             // Set up the statically condensed block for this element.
             SetStaticCondBlock(n, exp, mat);
 
             if (verbose && root)
             {
                 cout << "\rBuilding matrix system: "
                      << (int)(100.0 * n / nEl) << "%" << flush;
             }
         }
     }
     else if (nVel == 3)
     {
         for (n = 0; n < nEl; ++n)
         {
             exp = m_fields[0]->GetExp(m_fields[0]->GetOffset_Elmt_Id(n));
             const int nPhys = exp->GetTotPoints();
             Array<OneD, NekDouble> aArr(nPhys, lambda + 2*mu);
             Array<OneD, NekDouble> bArr(nPhys, mu);
 
             StdRegions::VarCoeffMap varcoeffA, varcoeffE, varcoeffI;
             varcoeffA[StdRegions::eVarCoeffD00] = aArr;
             varcoeffA[StdRegions::eVarCoeffD11] = bArr;
             varcoeffA[StdRegions::eVarCoeffD22] = bArr;
             varcoeffE[StdRegions::eVarCoeffD00] = bArr;
             varcoeffE[StdRegions::eVarCoeffD11] = aArr;
             varcoeffE[StdRegions::eVarCoeffD22] = bArr;
             varcoeffI[StdRegions::eVarCoeffD00] = bArr;
             varcoeffI[StdRegions::eVarCoeffD11] = bArr;
             varcoeffI[StdRegions::eVarCoeffD22] = aArr;
 
             LocalRegions::MatrixKey matkeyA(StdRegions::eLaplacian,
                                             exp->DetShapeType(),
                                             *exp, factors, varcoeffA);
             LocalRegions::MatrixKey matkeyE(StdRegions::eLaplacian,
                                             exp->DetShapeType(),
                                             *exp, factors, varcoeffE);
             LocalRegions::MatrixKey matkeyI(StdRegions::eLaplacian,
                                             exp->DetShapeType(),
                                             *exp, factors, varcoeffI);
 
             /*
              * mat holds the linear operator [ A B C ] acting on [ u ].
              *                               [ D E F ]           [ v ]
              *                               [ G H I ]           [ w ]
              */
             Array<TwoD, DNekMatSharedPtr> mat(3,3);
             mat[0][0] = exp->GenMatrix(matkeyA);
             mat[0][1] = BuildLaplacianIJMatrix(1, 0, mu + lambda, exp);
             mat[0][2] = BuildLaplacianIJMatrix(2, 0, mu + lambda, exp);
 
             mat[1][0] = mat[0][1];
             mat[1][1] = exp->GenMatrix(matkeyE);
             mat[1][2] = BuildLaplacianIJMatrix(2, 1, mu + lambda, exp);
 
             mat[2][0] = mat[0][2];
             mat[2][1] = mat[1][2];
             mat[2][2] = exp->GenMatrix(matkeyI);
 
             // Set up the statically condensed block for this element.
             SetStaticCondBlock(n, exp, mat);
 
             if (verbose && root)
             {
                 cout << "\rBuilding matrix system: "
                      << (int)(100.0 * n / nEl) << "%" << flush;
             }
         }
     }
 
     if (verbose && root)
     {
         cout << "\rBuilding matrix system: done." << endl;
     }
 }

static EquationSystemSharedPtr Nektar::LinearElasticSystem::create ( const LibUtilities::SessionReaderSharedPtr & pSession )

inlinestatic

Creates an instance of this class.

Definition at line 57 of file LinearElasticSystem.h.

     {
         EquationSystemSharedPtr p = MemoryManager<
             LinearElasticSystem>::AllocateSharedPtr(pSession);
         p->InitObject();
         return p;
     }

void Nektar::LinearElasticSystem::SetStaticCondBlock	(	const int	n,
		const LocalRegions::ExpansionSharedPtr	exp,
		Array< TwoD, DNekMatSharedPtr > &	mat
	)

Given a block matrix for an element, construct its static condensation matrices.

This routine essentially duplicates the logic present in many of the LocalRegions matrix generation routines to construct the statically condensed equivalent of mat to pass to the GlobalLinSys solver.

Parameters

n	Element/block number.
exp	Pointer to expansion.
mat	Block matrix containing matrix operator.

Definition at line 792 of file LinearElasticSystem.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), Nektar::eFULL, m_BinvD, m_bmap, m_C, m_Dinv, m_imap, and m_schurCompl.

Referenced by BuildMatrixSystem().

 {
     int i, j, k, l;
     const int nVel = mat.GetRows();
     const int nB   = exp->NumBndryCoeffs();
     const int nI   = exp->GetNcoeffs() - nB;
     const int nBnd = exp->NumBndryCoeffs() * nVel;
     const int nInt = exp->GetNcoeffs() * nVel - nBnd;
     const MatrixStorage s = eFULL; // Maybe look into doing symmetric
     // version of this?
 
     DNekMatSharedPtr A =
         MemoryManager<DNekMat>::AllocateSharedPtr(nBnd, nBnd, 0.0, s);
     DNekMatSharedPtr B =
         MemoryManager<DNekMat>::AllocateSharedPtr(nBnd, nInt, 0.0, s);
     DNekMatSharedPtr C =
         MemoryManager<DNekMat>::AllocateSharedPtr(nInt, nBnd, 0.0, s);
     DNekMatSharedPtr D =
         MemoryManager<DNekMat>::AllocateSharedPtr(nInt, nInt, 0.0, s);
 
     for (i = 0; i < nVel; ++i)
     {
         for (j = 0; j < nVel; ++j)
         {
             // Boundary-boundary and boundary-interior
             for (k = 0; k < nB; ++k)
             {
                 for (l = 0; l < nB; ++l)
                 {
                     (*A)(k + i*nB, l + j*nB) =
                         (*mat[i][j])(m_bmap[n][k], m_bmap[n][l]);
                 }
 
                 for (l = 0; l < nI; ++l)
                 {
                     (*B)(k + i*nB, l + j*nI) =
                         (*mat[i][j])(m_bmap[n][k], m_imap[n][l]);
                 }
             }
 
             // Interior-boundary / interior-interior
             for (k = 0; k < nI; ++k)
             {
                 for (l = 0; l < nB; ++l)
                 {
                     (*C)(k + i*nI, l + j*nB) =
                         (*mat[i][j])(m_imap[n][k], m_bmap[n][l]);
                 }
 
                 for (l = 0; l < nI; ++l)
                 {
                     (*D)(k + i*nI, l + j*nI) =
                         (*mat[i][j])(m_imap[n][k], m_imap[n][l]);
                 }
             }
         }
     }
 
     // Construct static condensation matrices.
     D->Invert();
     (*B) = (*B)*(*D);
     (*A) = (*A) - (*B)*(*C);
 
     DNekScalMatSharedPtr tmp_mat;
     m_schurCompl->SetBlock(
         n, n, tmp_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(
             1.0, A));
     m_BinvD     ->SetBlock(
         n, n, tmp_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(
             1.0, B));
     m_C         ->SetBlock(
         n, n, tmp_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(
             1.0, C));
     m_Dinv      ->SetBlock(
         n, n, tmp_mat = MemoryManager<DNekScalMat>::AllocateSharedPtr(
             1.0, D));
 }

void Nektar::LinearElasticSystem::v_DoSolve ( void )

protectedvirtual

Solve elliptic linear elastic system.

The solve proceeds as follows:

Create a MultiRegions::GlobalLinSys object.
Evaluate a forcing function from the session file.
If the temperature term is enabled, evaluate this and add to forcing.
Apply Dirichlet boundary conditions.
Scatter forcing into the correct ordering according to the coupled assembly map.
Do the solve.
Scatter solution back to fields and backwards transform to physical space.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Reimplemented in Nektar::IterativeElasticSystem.

Definition at line 391 of file LinearElasticSystem.cpp.

References ASSERTL0, BuildMatrixSystem(), Nektar::SpatialDomains::eDeformed, Nektar::eDIAGONAL, Nektar::MultiRegions::eDirectStaticCond, Nektar::SpatialDomains::eDirichlet, Nektar::eFULL, Nektar::MultiRegions::eIterativeStaticCond, Nektar::StdRegions::eLinearAdvectionReaction, Nektar::MultiRegions::ePETScStaticCond, Nektar::SolverUtils::EquationSystem::EvaluateFunction(), Nektar::MultiRegions::eXxtStaticCond, Vmath::Fill(), Nektar::SolverUtils::EquationSystem::GetNpoints(), Nektar::iterator, m_assemblyMap, m_beta, m_BinvD, m_bmap, m_C, m_Dinv, Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::EquationSystem::m_graph, m_imap, m_schurCompl, Nektar::SolverUtils::EquationSystem::m_session, m_stress, m_temperature, Nektar::MappingIdealToRef(), Vmath::Neg(), Nektar::MultiRegions::NullPreconditionerSharedPtr, sign, Vmath::Smul(), Nektar::Transpose(), Vmath::Vadd(), and Vmath::Vcopy().

Referenced by Nektar::IterativeElasticSystem::v_DoSolve().

 {
 
     int i, j, k, l, nv;
     const int nVel = m_fields[0]->GetCoordim(0);
 
     // Build initial matrix system.
     BuildMatrixSystem();
 
     // Now we've got the matrix system set up, create a GlobalLinSys
     // object. We mask ourselves as LinearAdvectionReaction to create a full
     // matrix instead of symmetric storage.
     MultiRegions::GlobalLinSysKey key(
         StdRegions::eLinearAdvectionReaction, m_assemblyMap);
     MultiRegions::GlobalLinSysSharedPtr linSys;
 
     // Currently either direct or iterative static condensation is
     // supported.
     if (m_assemblyMap->GetGlobalSysSolnType() == MultiRegions::eDirectStaticCond)
     {
         linSys = MemoryManager<
             MultiRegions::GlobalLinSysDirectStaticCond>::AllocateSharedPtr(
                 key, m_fields[0], m_schurCompl, m_BinvD, m_C, m_Dinv,
                 m_assemblyMap);
     }
     else if (m_assemblyMap->GetGlobalSysSolnType() ==
              MultiRegions::eIterativeStaticCond)
     {
         linSys = MemoryManager<
             MultiRegions::GlobalLinSysIterativeStaticCond>::AllocateSharedPtr(
                 key, m_fields[0], m_schurCompl, m_BinvD, m_C, m_Dinv,
                 m_assemblyMap, MultiRegions::NullPreconditionerSharedPtr);
     }
 #ifdef NEKTAR_USE_PETSC
     else if (m_assemblyMap->GetGlobalSysSolnType() ==
              MultiRegions::ePETScStaticCond)
     {
         linSys = MemoryManager<
             MultiRegions::GlobalLinSysPETScStaticCond>::AllocateSharedPtr(
                 key, m_fields[0], m_schurCompl, m_BinvD, m_C, m_Dinv,
                 m_assemblyMap);
     }
 #endif
 #ifdef NEKTAR_USE_MPI
     else if (m_assemblyMap->GetGlobalSysSolnType() ==
              MultiRegions::eXxtStaticCond)
     {
         linSys = MemoryManager<
             MultiRegions::GlobalLinSysXxtStaticCond>::AllocateSharedPtr(
                 key, m_fields[0], m_schurCompl, m_BinvD, m_C, m_Dinv,
                 m_assemblyMap);
     }
 #endif
 
     linSys->Initialise(m_assemblyMap);
 
     const int nCoeffs = m_fields[0]->GetNcoeffs();
     const int nGlobDofs = m_assemblyMap->GetNumGlobalCoeffs();
 
     //
     // -- Evaluate forcing functions
     //
 
     // Evaluate the forcing function from the XML file.
     Array<OneD, Array<OneD, NekDouble> > forcing(nVel);
     EvaluateFunction(forcing, "Forcing");
 
     // Add temperature term
     string tempEval;
     m_session->LoadSolverInfo("Temperature", tempEval, "None");
 
     if (tempEval == "Jacobian")
     {
         // Allocate storage
         m_temperature = Array<OneD, Array<OneD, NekDouble> >(nVel);
 
         for (nv = 0; nv < nVel; ++nv)
         {
             Array<OneD, NekDouble> tmp;
             m_temperature[nv] = Array<OneD, NekDouble>(
                 m_fields[nv]->GetNpoints());
 
             for (i = 0; i < m_fields[0]->GetExpSize(); ++i)
             {
                 // Calculate element area
                 LocalRegions::ExpansionSharedPtr exp =
                     m_fields[0]->GetExp(i);
                 LibUtilities::PointsKeyVector pkey =
                     exp->GetPointsKeys();
                 Array<OneD, NekDouble> jac =
                     exp->GetMetricInfo()->GetJac(pkey);
 
                 int offset = m_fields[0]->GetPhys_Offset(i);
 
                 if (exp->GetMetricInfo()->GetGtype() ==
                     SpatialDomains::eDeformed)
                 {
                     Vmath::Smul(exp->GetTotPoints(), m_beta, jac, 1,
                                 tmp = m_temperature[nv] + offset, 1);
                 }
                 else
                 {
                     Vmath::Fill(exp->GetTotPoints(), m_beta*jac[0],
                                 tmp = m_temperature[nv] + offset, 1);
                 }
             }
             m_fields[nv]->PhysDeriv(nv, m_temperature[nv], forcing[nv]);
         }
     }
     else if (tempEval == "Metric")
     {
         ASSERTL0((m_fields[0]->GetCoordim(0)         == 2 &&
                   m_graph->GetAllQuadGeoms().size() == 0) ||
                  (m_fields[0]->GetCoordim(0)         == 3 &&
                   m_graph->GetAllPrismGeoms().size() == 0 &&
                   m_graph->GetAllPyrGeoms  ().size() == 0 &&
                   m_graph->GetAllHexGeoms  ().size() == 0),
                  "LinearIdealMetric temperature only implemented for "
                  "two-dimensional triangular meshes or three-dimensional "
                  "tetrahedral meshes.");
 
         m_temperature = Array<OneD, Array<OneD, NekDouble> >(nVel);
         m_stress = Array<OneD, Array<OneD, Array<OneD, NekDouble> > >(nVel);
 
         for (nv = 0; nv < nVel; ++nv)
         {
             m_temperature[nv] = Array<OneD, NekDouble>(
                 m_fields[nv]->GetNpoints(), 0.0);
             m_stress[nv] = Array<OneD, Array<OneD, NekDouble> >(nVel);
 
             for (i = 0; i < nVel; ++i)
             {
                 m_stress[nv][i] = Array<OneD, NekDouble>(
                     m_fields[nv]->GetNpoints(), 0.0);
             }
         }
 
         for (i = 0; i < m_fields[0]->GetExpSize(); ++i)
         {
             // Calculate element area
             LocalRegions::ExpansionSharedPtr exp =
                 m_fields[0]->GetExp(i);
             LibUtilities::PointsKeyVector pkey = exp->GetPointsKeys();
             Array<OneD, Array<OneD, Array<OneD, NekDouble> > > deriv =
                 exp->GetMetricInfo()->GetDeriv(pkey);
             int offset = m_fields[0]->GetPhys_Offset(i);
 
             DNekMat i2rm = MappingIdealToRef(exp->GetGeom());
 
             // Compute metric tensor
             DNekMat jac     (nVel, nVel, 0.0, eFULL);
             DNekMat jacIdeal(nVel, nVel, 0.0, eFULL);
             DNekMat metric  (nVel, nVel, 0.0, eFULL);
 
             for (j = 0; j < deriv[0][0].num_elements(); ++j)
             {
                 for (k = 0; k < nVel; ++k)
                 {
                     for (l = 0; l < nVel; ++l)
                     {
                         jac(l,k) = deriv[k][l][j];
                     }
                 }
 
                 jacIdeal = jac * i2rm;
                 metric = Transpose(jacIdeal) * jacIdeal;
 
                 // Compute eigenvalues/eigenvectors of metric tensor using
                 // ideal mapping.
                 char jobvl = 'N', jobvr = 'V';
                 int worklen = 8*nVel, info;
 
                 DNekMat eval   (nVel, nVel, 0.0, eDIAGONAL);
                 DNekMat evec   (nVel, nVel, 0.0, eFULL);
                 DNekMat evecinv(nVel, nVel, 0.0, eFULL);
                 Array<OneD, NekDouble> vl  (nVel*nVel);
                 Array<OneD, NekDouble> work(worklen);
                 Array<OneD, NekDouble> wi  (nVel);
 
                 Lapack::Dgeev(jobvl, jobvr, nVel, metric.GetRawPtr(), nVel,
                               &(eval.GetPtr())[0], &wi[0], &vl[0], nVel,
                               &(evec.GetPtr())[0], nVel,
                               &work[0], worklen, info);
 
                 evecinv = evec;
                 evecinv.Invert();
 
                 // rescaling of the eigenvalues
                 for (nv = 0; nv < nVel; ++nv)
                 {
                     eval(nv,nv) = m_beta * (sqrt(eval(nv,nv)) - 1.0);
                 }
 
                 DNekMat beta = evec * eval * evecinv;
 
                 for (k = 0; k < nVel; ++k)
                 {
                     for (l = 0; l < nVel; ++l)
                     {
                         m_stress[k][l][offset+j] = beta(k,l);
                     }
                 }
             }
 
             if (deriv[0][0].num_elements() != exp->GetTotPoints())
             {
                 Array<OneD, NekDouble> tmp;
                 for (k = 0; k < nVel; ++k)
                 {
                     for (l = 0; l < nVel; ++l)
                     {
                         Vmath::Fill(
                             exp->GetTotPoints(), m_stress[k][l][offset],
                             tmp = m_stress[k][l] + offset, 1);
                     }
                 }
             }
         }
 
         // Calculate divergence of stress tensor.
         Array<OneD, NekDouble> tmpderiv(m_fields[0]->GetNpoints());
         for (i = 0; i < nVel; ++i)
         {
             for (j = 0; j < nVel; ++j)
             {
                 m_fields[i]->PhysDeriv(j, m_stress[i][j], tmpderiv);
                 Vmath::Vadd (m_fields[i]->GetNpoints(), tmpderiv, 1,
                              m_temperature[i], 1, m_temperature[i], 1);
             }
 
             Vmath::Vcopy(m_fields[i]->GetNpoints(),
                          m_temperature[i], 1, forcing[i], 1);
         }
     }
     else if (tempEval != "None")
     {
         ASSERTL0(false, "Unknown temperature form: " + tempEval);
     }
 
     // Set up some temporary storage.
     //
     // - forCoeffs holds the forcing coefficients in a local ordering;
     //   however note that the ordering is different and dictated by the
     //   assembly map. We loop over each element, then the boundary degrees of
     //   freedom for u, boundary for v, followed by the interior for u and then
     //   interior for v.
     // - rhs is the global assembly of forCoeffs.
     // - inout holds the Dirichlet degrees of freedom in the global ordering,
     //   which have been assembled from the boundary expansion.
     Array<OneD, NekDouble> forCoeffs(nVel * nCoeffs, 0.0);
     Array<OneD, NekDouble> inout    (nGlobDofs, 0.0);
     Array<OneD, NekDouble> rhs      (nGlobDofs, 0.0);
 
     for (nv = 0; nv < nVel; ++nv)
     {
         // Take the inner product of the forcing function.
         Array<OneD, NekDouble> tmp(nCoeffs);
         m_fields[nv]->IProductWRTBase_IterPerExp(forcing[nv], tmp);
 
         // Scatter forcing into RHS vector according to the ordering dictated in
         // the comment above.
         for (i = 0; i < m_fields[nv]->GetExpSize(); ++i)
         {
             int nBnd   = m_bmap[i].num_elements();
             int nInt   = m_imap[i].num_elements();
             int offset = m_fields[nv]->GetCoeff_Offset(i);
 
             for (j = 0; j < nBnd; ++j)
             {
                 forCoeffs[nVel*offset + nv*nBnd + j] =
                     tmp[offset+m_bmap[i][j]];
             }
             for (j = 0; j < nInt; ++j)
             {
                 forCoeffs[nVel*(offset + nBnd) + nv*nInt + j] =
                     tmp[offset+m_imap[i][j]];
             }
         }
     }
 
     // -- Impose Dirichlet boundary conditions.
 
     // First try to do parallel assembly: the intention here is that Dirichlet
     // values at some edges/vertices need to be communicated to processes which
     // don't contain the entire boundary region. See
     // ContField2D::v_ImposeDirichletConditions for more detail.
     map<int, vector<MultiRegions::ExtraDirDof> > &extraDirDofs =
         m_assemblyMap->GetExtraDirDofs();
     map<int, vector<MultiRegions::ExtraDirDof> >::iterator it;
 
     for (nv = 0; nv < nVel; ++nv)
     {
         const Array<OneD, const MultiRegions::ExpListSharedPtr> &bndCondExp
             = m_fields[nv]->GetBndCondExpansions();
 
         // First try to do parallel stuff
         for (it = extraDirDofs.begin(); it != extraDirDofs.end(); ++it)
         {
             for (i = 0; i < it->second.size(); ++i)
             {
                 inout[it->second.at(i).get<1>()*nVel + nv] =
                     bndCondExp[it->first]->GetCoeffs()[
                         it->second.at(i).get<0>()]*it->second.at(i).get<2>();
             }
         }
     }
 
     m_assemblyMap->UniversalAssemble(inout);
 
     // Counter for the local Dirichlet boundary to global ordering.
     int bndcnt = 0;
 
     // Now assemble local boundary contributions.
     for (nv = 0; nv < nVel; ++nv)
     {
         const Array<OneD, const MultiRegions::ExpListSharedPtr> &bndCondExp
             = m_fields[nv]->GetBndCondExpansions();
         const Array<OneD, const int> &bndMap
             = m_assemblyMap->GetBndCondCoeffsToGlobalCoeffsMap();
 
         for (i = 0; i < bndCondExp.num_elements(); ++i)
         {
             if (m_fields[nv]->GetBndConditions()[i]->GetBoundaryConditionType()
                 == SpatialDomains::eDirichlet)
             {
                 const Array<OneD,const NekDouble> &bndCoeffs =
                     bndCondExp[i]->GetCoeffs();
 
                 for (j = 0; j < bndCondExp[i]->GetNcoeffs(); ++j)
                 {
                     NekDouble sign =
                         m_assemblyMap->GetBndCondCoeffsToGlobalCoeffsSign(
                             bndcnt);
                     inout[bndMap[bndcnt++]] = sign * bndCoeffs[j];
                 }
             }
             else
             {
                 bndcnt += bndCondExp[i]->GetNcoeffs();
             }
         }
     }
 
     //
     // -- Perform solve
     //
 
     // Assemble forcing into the RHS.
     m_assemblyMap->Assemble(forCoeffs, rhs);
 
     // Negate RHS to be consistent with matrix definition.
     Vmath::Neg(rhs.num_elements(), rhs, 1);
 
     // Solve.
     linSys->Solve(rhs, inout, m_assemblyMap);
 
     // Scatter the global ordering back to the alternate local ordering.
     Array<OneD, NekDouble> tmp(nVel * nCoeffs);
     m_assemblyMap->GlobalToLocal(inout, tmp);
 
     //
     // -- Postprocess
     //
 
     // Scatter back to field degrees of freedom
     for (nv = 0; nv < nVel; ++nv)
     {
         for (i = 0; i < m_fields[nv]->GetExpSize(); ++i)
         {
             int nBnd   = m_bmap[i].num_elements();
             int nInt   = m_imap[i].num_elements();
             int offset = m_fields[nv]->GetCoeff_Offset(i);
 
             for (j = 0; j < nBnd; ++j)
             {
                 m_fields[nv]->UpdateCoeffs()[offset+m_bmap[i][j]] =
                     tmp[nVel*offset + nv*nBnd + j];
             }
             for (j = 0; j < nInt; ++j)
             {
                 m_fields[nv]->UpdateCoeffs()[offset+m_imap[i][j]] =
                     tmp[nVel*(offset + nBnd) + nv*nInt + j];
             }
         }
         m_fields[nv]->BwdTrans(m_fields[nv]->GetCoeffs(),
                                m_fields[nv]->UpdatePhys());
     }
 }

void Nektar::LinearElasticSystem::v_ExtraFldOutput	(	std::vector< Array< OneD, NekDouble > > &	fieldcoeffs,
		std::vector< std::string > &	variables
	)

protectedvirtual

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 912 of file LinearElasticSystem.cpp.

References Nektar::SolverUtils::EquationSystem::m_fields, m_stress, and m_temperature.

 {
     const int nVel    = m_fields[0]->GetCoordim(0);
     const int nCoeffs = m_fields[0]->GetNcoeffs();
 
     if (m_temperature.num_elements() == 0)
     {
         return;
     }
 
     for (int i = 0; i < nVel; ++i)
     {
         Array<OneD, NekDouble> tFwd(nCoeffs);
         m_fields[i]->FwdTrans(m_temperature[i], tFwd);
         fieldcoeffs.push_back(tFwd);
         variables.push_back(
             "ThermStressDiv" + boost::lexical_cast<std::string>(i));
     }
 
     if (m_stress.num_elements() == 0)
     {
         return;
     }
 
     for (int i = 0; i < nVel; ++i)
     {
         for (int j = 0; j < nVel; ++j)
         {
             Array<OneD, NekDouble> tFwd(nCoeffs);
             m_fields[i]->FwdTrans(m_stress[i][j], tFwd);
             fieldcoeffs.push_back(tFwd);
             variables.push_back(
                 "ThermStress"
                 + boost::lexical_cast<std::string>(i)
                 + boost::lexical_cast<std::string>(j));
         }
     }
 }

void Nektar::LinearElasticSystem::v_GenerateSummary ( SolverUtils::SummaryList & s )

protectedvirtual

Generate summary at runtime.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Reimplemented in Nektar::IterativeElasticSystem.

Definition at line 369 of file LinearElasticSystem.cpp.

References Nektar::SolverUtils::AddSummaryItem(), m_E, m_nu, and Nektar::SolverUtils::EquationSystem::SessionSummary().

Referenced by Nektar::IterativeElasticSystem::v_GenerateSummary().

 {
     EquationSystem::SessionSummary(s);
 
     AddSummaryItem(s, "Young's modulus", m_E);
     AddSummaryItem(s, "Poisson ratio", m_nu);
 }

void Nektar::LinearElasticSystem::v_InitObject ( )

protectedvirtual

Set up the linear elasticity system.

This routine loads the E and nu variables from the session file, creates a coupled assembly map and creates containers for the statically condensed block matrix system.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Reimplemented in Nektar::IterativeElasticSystem.

Definition at line 142 of file LinearElasticSystem.cpp.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), ASSERTL0, Nektar::eDIAGONAL, m_assemblyMap, m_beta, m_BinvD, m_bmap, m_C, m_Dinv, m_E, Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::EquationSystem::m_graph, m_imap, m_nu, m_schurCompl, Nektar::SolverUtils::EquationSystem::m_session, and Nektar::SolverUtils::EquationSystem::v_InitObject().

Referenced by Nektar::IterativeElasticSystem::v_InitObject().

 {
     EquationSystem::v_InitObject();
 
     const int nVel = m_fields[0]->GetCoordim(0);
     int n;
 
     ASSERTL0(nVel > 1, "Linear elastic solver not set up for"
              " this dimension (only 2D/3D supported).");
 
     // Make sure that we have Young's modulus and Poisson ratio set.
     m_session->LoadParameter("E",    m_E,    1.00);
     m_session->LoadParameter("nu",   m_nu,   0.25);
     m_session->LoadParameter("Beta", m_beta, 1.00);
 
     // Create a coupled assembly map which allows us to tie u, v and w
     // fields together.
     if (nVel == 2)
     {
         MultiRegions::ContField2DSharedPtr u = boost::dynamic_pointer_cast<
             MultiRegions::ContField2D>(m_fields[0]);
         m_assemblyMap = MemoryManager<CoupledAssemblyMap>
             ::AllocateSharedPtr(m_session,
                                 m_graph,
                                 u->GetLocalToGlobalMap(),
                                 m_fields[0]->GetBndConditions(),
                                 m_fields);
     }
 
     if (nVel == 3)
     {
         MultiRegions::ContField3DSharedPtr u = boost::dynamic_pointer_cast<
             MultiRegions::ContField3D>(m_fields[0]);
         m_assemblyMap = MemoryManager<CoupledAssemblyMap>
             ::AllocateSharedPtr(m_session,
                                 m_graph,
                                 u->GetLocalToGlobalMap(),
                                 m_fields[0]->GetBndConditions(),
                                 m_fields);
     }
 
     // Figure out size of our new matrix systems by looping over all expansions
     // and multiply number of coefficients by velocity components.
     const int nEl = m_fields[0]->GetExpSize();
     LocalRegions::ExpansionSharedPtr exp;
 
     Array<OneD, unsigned int> sizeBnd(nEl);
     Array<OneD, unsigned int> sizeInt(nEl);
 
     // Allocate storage for boundary and interior map caches.
     m_bmap = Array<OneD, Array<OneD, unsigned int> >(nEl);
     m_imap = Array<OneD, Array<OneD, unsigned int> >(nEl);
 
     // Cache interior and boundary maps to avoid recalculating
     // constantly. Should really be handled by manager in StdRegions but not
     // really working yet.
     for (n = 0; n < nEl; ++n)
     {
         exp = m_fields[0]->GetExp(m_fields[0]->GetOffset_Elmt_Id(n));
         sizeBnd[n] = nVel * exp->NumBndryCoeffs();
         sizeInt[n] = nVel * exp->GetNcoeffs() - sizeBnd[n];
         exp->GetBoundaryMap(m_bmap[n]);
         exp->GetInteriorMap(m_imap[n]);
     }
 
     // Create block matrix storage for the statically condensed system.
     MatrixStorage blkmatStorage = eDIAGONAL;
     m_schurCompl = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
         sizeBnd, sizeBnd, blkmatStorage);
     m_BinvD      = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
         sizeBnd, sizeInt, blkmatStorage);
     m_C          = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
         sizeInt, sizeBnd, blkmatStorage);
     m_Dinv       = MemoryManager<DNekScalBlkMat>::AllocateSharedPtr(
         sizeInt, sizeInt, blkmatStorage);
 }

Friends And Related Function Documentation

friend class MemoryManager< LinearElasticSystem >

friend

Class may only be instantiated through the MemoryManager.

Definition at line 54 of file LinearElasticSystem.h.

Member Data Documentation

string Nektar::LinearElasticSystem::className

static

Initial value:

= GetEquationSystemFactory().
    RegisterCreatorFunction("LinearElasticSystem",
                            LinearElasticSystem::create)

Name of class.

Definition at line 67 of file LinearElasticSystem.h.

CoupledAssemblyMapSharedPtr Nektar::LinearElasticSystem::m_assemblyMap

protected

Assembly map for the coupled (u,v,w) system.

Definition at line 93 of file LinearElasticSystem.h.

Referenced by v_DoSolve(), and v_InitObject().

NekDouble Nektar::LinearElasticSystem::m_beta

protected

Parameter dictating amount of thermal stress to add.

Definition at line 91 of file LinearElasticSystem.h.

Referenced by v_DoSolve(), and v_InitObject().

DNekScalBlkMatSharedPtr Nektar::LinearElasticSystem::m_BinvD

protected

Matrix of elemental $B^{-1}D$ components.

Definition at line 97 of file LinearElasticSystem.h.

Referenced by SetStaticCondBlock(), v_DoSolve(), and v_InitObject().

Array<OneD, Array<OneD, unsigned int> > Nektar::LinearElasticSystem::m_bmap

protected

Boundary maps for each of the fields.

Definition at line 103 of file LinearElasticSystem.h.

Referenced by SetStaticCondBlock(), v_DoSolve(), and v_InitObject().

DNekScalBlkMatSharedPtr Nektar::LinearElasticSystem::m_C

protected

Matrix of elemental $ C $ components.

Definition at line 99 of file LinearElasticSystem.h.

Referenced by SetStaticCondBlock(), v_DoSolve(), and v_InitObject().

DNekScalBlkMatSharedPtr Nektar::LinearElasticSystem::m_Dinv

protected

Matrix of elemental $D^{-1}$ components.

Definition at line 101 of file LinearElasticSystem.h.

Referenced by SetStaticCondBlock(), v_DoSolve(), and v_InitObject().

NekDouble Nektar::LinearElasticSystem::m_E

protected

Young's modulus.

Definition at line 89 of file LinearElasticSystem.h.

Referenced by BuildMatrixSystem(), v_GenerateSummary(), and v_InitObject().

Array<OneD, Array<OneD, unsigned int> > Nektar::LinearElasticSystem::m_imap

protected

Interior maps for each of the fields.

Definition at line 105 of file LinearElasticSystem.h.

Referenced by SetStaticCondBlock(), v_DoSolve(), and v_InitObject().

NekDouble Nektar::LinearElasticSystem::m_nu

protected

Poisson ratio.

Definition at line 87 of file LinearElasticSystem.h.

Referenced by BuildMatrixSystem(), v_GenerateSummary(), and v_InitObject().

DNekScalBlkMatSharedPtr Nektar::LinearElasticSystem::m_schurCompl

protected

Schur complement boundary-boundary matrix.

Definition at line 95 of file LinearElasticSystem.h.

Referenced by SetStaticCondBlock(), v_DoSolve(), and v_InitObject().

Array<OneD, Array<OneD, Array<OneD, NekDouble> > > Nektar::LinearElasticSystem::m_stress

protected

Storage for the thermal stress terms.

Definition at line 109 of file LinearElasticSystem.h.

Referenced by v_DoSolve(), and v_ExtraFldOutput().

Array<OneD, Array<OneD, NekDouble> > Nektar::LinearElasticSystem::m_temperature

protected

Storage for the temperature terms.

Definition at line 107 of file LinearElasticSystem.h.

Referenced by v_DoSolve(), and v_ExtraFldOutput().

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation