A model for cardiac conduction. More...

#include <MMFDiffusion.h>

Inheritance diagram for Nektar::MMFDiffusion:

Public Member Functions
	~MMFDiffusion () override
	Desctructor. More...

Public Member Functions inherited from Nektar::SolverUtils::MMFSystem
SOLVER_UTILS_EXPORT	MMFSystem (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)

SOLVER_UTILS_EXPORT	~MMFSystem () override

SOLVER_UTILS_EXPORT void	v_GenerateSummary (SummaryList &s) override
	Virtual function for generating summary information. More...

SOLVER_UTILS_EXPORT void	MMFInitObject (const Array< OneD, const Array< OneD, NekDouble > > &Anisotropy, const int TangentXelem=-1)

SOLVER_UTILS_EXPORT void	CopyBoundaryTrace (const Array< OneD, const NekDouble > &Fwd, Array< OneD, NekDouble > &Bwd, const BoundaryCopyType BDCopyType, const int var=0, const std::string btype="NoUserDefined")

Public Member Functions inherited from Nektar::SolverUtils::UnsteadySystem
SOLVER_UTILS_EXPORT	~UnsteadySystem () override
	Destructor. More...

SOLVER_UTILS_EXPORT NekDouble	GetTimeStep (const Array< OneD, const Array< OneD, NekDouble > > &inarray)
	Calculate the larger time-step mantaining the problem stable. More...

SOLVER_UTILS_EXPORT NekDouble	GetTimeStep ()

SOLVER_UTILS_EXPORT void	SetTimeStep (const NekDouble timestep)

SOLVER_UTILS_EXPORT void	SteadyStateResidual (int step, Array< OneD, NekDouble > &L2)

SOLVER_UTILS_EXPORT LibUtilities::TimeIntegrationSchemeSharedPtr &	GetTimeIntegrationScheme ()
	Returns the time integration scheme. More...

SOLVER_UTILS_EXPORT LibUtilities::TimeIntegrationSchemeOperators &	GetTimeIntegrationSchemeOperators ()
	Returns the time integration scheme operators. More...

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

SOLVER_UTILS_EXPORT void	InitObject (bool DeclareField=true)
	Initialises the members of this object. More...

SOLVER_UTILS_EXPORT void	DoInitialise (bool dumpInitialConditions=true)
	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 std::string	GetSessionName ()
	Get Session name. More...

template<class T >
std::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	ExtraFldOutput (std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)

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 SessionFunctionSharedPtr	GetFunction (std::string name, const MultiRegions::ExpListSharedPtr &field=MultiRegions::NullExpListSharedPtr, bool cache=false)
	Get a SessionFunction by name. 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 NekDouble	LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Linf error computation. 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	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	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	GetTime ()
	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	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, const Array< OneD, const NekDouble > &input)

SOLVER_UTILS_EXPORT Array< OneD, NekDouble > &	UpdatePhysField (const int i)

SOLVER_UTILS_EXPORT void	SetSteps (const int steps)

SOLVER_UTILS_EXPORT void	ZeroPhysFields ()

SOLVER_UTILS_EXPORT void	FwdTransFields ()

SOLVER_UTILS_EXPORT void	SetModifiedBasis (const bool modbasis)

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 int	GetInfoSteps ()

SOLVER_UTILS_EXPORT void	SetInfoSteps (int num)

SOLVER_UTILS_EXPORT void	SetIterationNumberPIT (int num)

SOLVER_UTILS_EXPORT void	SetWindowNumberPIT (int num)

SOLVER_UTILS_EXPORT Array< OneD, const Array< OneD, NekDouble > >	GetTraceNormals ()

SOLVER_UTILS_EXPORT void	SetTime (const NekDouble time)

SOLVER_UTILS_EXPORT void	SetTimeStep (const NekDouble timestep)

SOLVER_UTILS_EXPORT void	SetInitialStep (const int step)

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

SOLVER_UTILS_EXPORT bool	NegatedOp ()
	Identify if operator is negated in DoSolve. More...

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

Public Attributes
TestType	m_TestType

Public Attributes inherited from Nektar::SolverUtils::MMFSystem
NekDouble	m_pi

int	m_shapedim

SurfaceType	m_surfaceType

UpwindType	m_upwindType

TestMaxwellType	m_TestMaxwellType

PolType	m_PolType

IncType	m_IncType

Array< OneD, NekDouble >	m_MMFfactors

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

Static Public Attributes inherited from Nektar::SolverUtils::UnsteadySystem
static std::string	cmdSetStartTime

static std::string	cmdSetStartChkNum

Protected Member Functions
	MMFDiffusion (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
	Constructor. More...

void	v_InitObject (bool DeclareField=true) override
	Init object for UnsteadySystem class. More...

void	DoImplicitSolve (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, NekDouble time, NekDouble lambda)
	Solve for the diffusion term. More...

void	DoOdeRhs (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, const NekDouble time)
	Computes the reaction terms \(f(u,v)\) and \(g(u,v)\). More...

void	TestPlaneProblem (const NekDouble time, Array< OneD, NekDouble > &outfield)

void	TestCubeProblem (const NekDouble time, Array< OneD, NekDouble > &outfield)

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

Array< OneD, NekDouble >	PlanePhiWave ()

void	v_SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0) override
	Sets a custom initial condition. More...

void	v_GenerateSummary (SolverUtils::SummaryList &s) override
	Prints a summary of the model parameters. More...

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

Protected Member Functions inherited from Nektar::SolverUtils::MMFSystem
void	SetUpMovingFrames (const Array< OneD, const Array< OneD, NekDouble > > &Anisotropy, const int TangentXelem)

void	CheckMovingFrames (const Array< OneD, const Array< OneD, NekDouble > > &movingframes)

SOLVER_UTILS_EXPORT void	ComputencdotMF ()

SOLVER_UTILS_EXPORT void	ComputeDivCurlMF ()

SOLVER_UTILS_EXPORT void	ComputeMFtrace ()

SOLVER_UTILS_EXPORT void	VectorDotProd (const Array< OneD, const Array< OneD, NekDouble > > &v1, const Array< OneD, const Array< OneD, NekDouble > > &v2, Array< OneD, NekDouble > &v3)

SOLVER_UTILS_EXPORT void	VectorCrossProd (const Array< OneD, const Array< OneD, NekDouble > > &v1, const Array< OneD, const Array< OneD, NekDouble > > &v2, Array< OneD, Array< OneD, NekDouble > > &v3)

SOLVER_UTILS_EXPORT void	VectorCrossProd (const Array< OneD, NekDouble > &v1, const Array< OneD, NekDouble > &v2, Array< OneD, NekDouble > &v3)

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

SOLVER_UTILS_EXPORT Array< OneD, NekDouble >	CartesianToMovingframes (const Array< OneD, const Array< OneD, NekDouble > > &uvec, unsigned int field)

SOLVER_UTILS_EXPORT void	DeriveCrossProductMF (Array< OneD, Array< OneD, NekDouble > > &CrossProductMF)

SOLVER_UTILS_EXPORT void	ComputeNtimesMF ()

SOLVER_UTILS_EXPORT void	ComputeNtimesFz (const int dir, const Array< OneD, Array< OneD, NekDouble > > &Fwd, const Array< OneD, Array< OneD, NekDouble > > &Bwd, const Array< OneD, const NekDouble > &imFwd, const Array< OneD, const NekDouble > &imBwd, Array< OneD, NekDouble > &outarrayFwd, Array< OneD, NekDouble > &outarrayBwd)

SOLVER_UTILS_EXPORT void	ComputeNtimesF12 (const Array< OneD, Array< OneD, NekDouble > > &Fwd, const Array< OneD, Array< OneD, NekDouble > > &Bwd, const Array< OneD, const NekDouble > &im1Fwd, const Array< OneD, const NekDouble > &im1Bwd, const Array< OneD, const NekDouble > &im2Fwd, const Array< OneD, const NekDouble > &im2Bwd, Array< OneD, NekDouble > &outarrayFwd, Array< OneD, NekDouble > &outarrayBwd)

SOLVER_UTILS_EXPORT void	ComputeNtimestimesdFz (const int dir, const Array< OneD, Array< OneD, NekDouble > > &Fwd, const Array< OneD, Array< OneD, NekDouble > > &Bwd, const Array< OneD, const NekDouble > &imFwd, const Array< OneD, const NekDouble > &imBwd, Array< OneD, NekDouble > &outarrayFwd, Array< OneD, NekDouble > &outarrayBwd)

SOLVER_UTILS_EXPORT void	ComputeNtimestimesdF12 (const Array< OneD, Array< OneD, NekDouble > > &Fwd, const Array< OneD, Array< OneD, NekDouble > > &Bwd, const Array< OneD, const NekDouble > &im1Fwd, const Array< OneD, const NekDouble > &im1Bwd, const Array< OneD, const NekDouble > &im2Fwd, const Array< OneD, const NekDouble > &im2Bwd, Array< OneD, NekDouble > &outarrayFwd, Array< OneD, NekDouble > &outarrayBwd)

SOLVER_UTILS_EXPORT void	CartesianToSpherical (const NekDouble x0j, const NekDouble x1j, const NekDouble x2j, NekDouble &sin_varphi, NekDouble &cos_varphi, NekDouble &sin_theta, NekDouble &cos_theta)

SOLVER_UTILS_EXPORT void	ComputeZimYim (Array< OneD, Array< OneD, NekDouble > > &epsvec, Array< OneD, Array< OneD, NekDouble > > &muvec)

SOLVER_UTILS_EXPORT void	AdddedtMaxwell (const Array< OneD, const Array< OneD, NekDouble > > &physarray, Array< OneD, Array< OneD, NekDouble > > &outarray)

SOLVER_UTILS_EXPORT void	GetMaxwellFluxVector (const int var, const Array< OneD, const Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	GetMaxwellFlux1D (const int var, const Array< OneD, const Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	GetMaxwellFlux2D (const int var, const Array< OneD, const Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)

SOLVER_UTILS_EXPORT void	LaxFriedrichMaxwellFlux1D (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd)

SOLVER_UTILS_EXPORT void	UpwindMaxwellFlux1D (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd)

SOLVER_UTILS_EXPORT void	AverageMaxwellFlux1D (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd)

SOLVER_UTILS_EXPORT void	NumericalMaxwellFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd, const NekDouble time=0.0)

SOLVER_UTILS_EXPORT void	NumericalMaxwellFluxTM (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd, const NekDouble time)

SOLVER_UTILS_EXPORT void	NumericalMaxwellFluxTE (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxFwd, Array< OneD, Array< OneD, NekDouble > > &numfluxBwd, const NekDouble time)

SOLVER_UTILS_EXPORT Array< OneD, NekDouble >	GetIncidentField (const int var, const NekDouble time)

SOLVER_UTILS_EXPORT void	Computedemdxicdote ()

SOLVER_UTILS_EXPORT NekDouble	AvgInt (const Array< OneD, const NekDouble > &inarray)

SOLVER_UTILS_EXPORT NekDouble	AvgAbsInt (const Array< OneD, const NekDouble > &inarray)

SOLVER_UTILS_EXPORT NekDouble	AbsIntegral (const Array< OneD, const NekDouble > &inarray)

SOLVER_UTILS_EXPORT NekDouble	RootMeanSquare (const Array< OneD, const NekDouble > &inarray)

SOLVER_UTILS_EXPORT NekDouble	VectorAvgMagnitude (const Array< OneD, const Array< OneD, NekDouble > > &inarray)

SOLVER_UTILS_EXPORT void	GramSchumitz (const Array< OneD, const Array< OneD, NekDouble > > &v1, const Array< OneD, const Array< OneD, NekDouble > > &v2, Array< OneD, Array< OneD, NekDouble > > &outarray, bool KeepTheMagnitude=true)

SOLVER_UTILS_EXPORT void	BubbleSort (Array< OneD, NekDouble > &refarray, Array< OneD, NekDouble > &sortarray)

Protected Member Functions inherited from Nektar::SolverUtils::UnsteadySystem
SOLVER_UTILS_EXPORT	UnsteadySystem (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
	Initialises UnsteadySystem class members. More...

SOLVER_UTILS_EXPORT void	v_InitObject (bool DeclareField=true) override
	Init object for UnsteadySystem class. More...

SOLVER_UTILS_EXPORT void	v_DoSolve () override
	Solves an unsteady problem. More...

virtual SOLVER_UTILS_EXPORT void	v_PrintStatusInformation (const int step, const NekDouble cpuTime)
	Print Status Information. More...

virtual SOLVER_UTILS_EXPORT void	v_PrintSummaryStatistics (const NekDouble intTime)
	Print Summary Statistics. More...

SOLVER_UTILS_EXPORT void	v_DoInitialise (bool dumpInitialConditions=true) override
	Sets up initial conditions. More...

SOLVER_UTILS_EXPORT void	v_GenerateSummary (SummaryList &s) override
	Print a summary of time stepping parameters. More...

virtual SOLVER_UTILS_EXPORT NekDouble	v_GetTimeStep (const Array< OneD, const Array< OneD, NekDouble > > &inarray)
	Return the timestep to be used for the next step in the time-marching loop. More...

virtual SOLVER_UTILS_EXPORT bool	v_PreIntegrate (int step)

virtual SOLVER_UTILS_EXPORT bool	v_PostIntegrate (int step)

virtual SOLVER_UTILS_EXPORT bool	v_RequireFwdTrans ()

virtual SOLVER_UTILS_EXPORT void	v_SteadyStateResidual (int step, Array< OneD, NekDouble > &L2)

virtual SOLVER_UTILS_EXPORT bool	v_UpdateTimeStepCheck ()

SOLVER_UTILS_EXPORT NekDouble	MaxTimeStepEstimator ()
	Get the maximum timestep estimator for cfl control. More...

SOLVER_UTILS_EXPORT void	CheckForRestartTime (NekDouble &time, int &nchk)

SOLVER_UTILS_EXPORT void	SVVVarDiffCoeff (const Array< OneD, Array< OneD, NekDouble > > vel, StdRegions::VarCoeffMap &varCoeffMap)
	Evaluate the SVV diffusion coefficient according to Moura's paper where it should proportional to h time velocity. More...

SOLVER_UTILS_EXPORT void	DoDummyProjection (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, const NekDouble time)
	Perform dummy projection. More...

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

virtual SOLVER_UTILS_EXPORT void	v_InitObject (bool DeclareFeld=true)
	Initialisation object for EquationSystem. More...

virtual SOLVER_UTILS_EXPORT void	v_DoInitialise (bool dumpInitialConditions=true)
	Virtual function for initialisation implementation. More...

virtual SOLVER_UTILS_EXPORT void	v_DoSolve ()
	Virtual function for solve 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_GenerateSummary (SummaryList &l)
	Virtual function for generating summary information. 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)

virtual SOLVER_UTILS_EXPORT void	v_Output (void)

virtual SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	v_GetPressure (void)

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

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

Protected Attributes
InitWaveType	m_InitWaveType

NekDouble	m_InitPtx

NekDouble	m_InitPty

NekDouble	m_InitPtz

Protected Attributes inherited from Nektar::SolverUtils::MMFSystem
NekDouble	m_alpha

NekDouble	m_Incfreq

int	m_SmoothFactor

NekDouble	m_SFinit

Array< OneD, Array< OneD, NekDouble > >	m_movingframes

Array< OneD, Array< OneD, NekDouble > >	m_surfaceNormal

Array< OneD, Array< OneD, NekDouble > >	m_ncdotMFFwd

Array< OneD, Array< OneD, NekDouble > >	m_ncdotMFBwd

Array< OneD, Array< OneD, NekDouble > >	m_nperpcdotMFFwd

Array< OneD, Array< OneD, NekDouble > >	m_nperpcdotMFBwd

Array< OneD, Array< OneD, NekDouble > >	m_DivMF

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_CurlMF

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_MFtraceFwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_MFtraceBwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_ntimesMFFwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_ntimesMFBwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_ntimes_ntimesMFFwd

Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_ntimes_ntimesMFBwd

Array< OneD, Array< OneD, NekDouble > >	m_ZimFwd

Array< OneD, Array< OneD, NekDouble > >	m_ZimBwd

Array< OneD, Array< OneD, NekDouble > >	m_YimFwd

Array< OneD, Array< OneD, NekDouble > >	m_YimBwd

Array< OneD, Array< OneD, NekDouble > >	m_epsvec

Array< OneD, Array< OneD, NekDouble > >	m_muvec

Array< OneD, Array< OneD, NekDouble > >	m_negepsvecminus1

Array< OneD, Array< OneD, NekDouble > >	m_negmuvecminus1

Array< OneD, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > >	m_dedxi_cdot_e

SpatialDomains::GeomMMF	m_MMFdir

Protected Attributes inherited from Nektar::SolverUtils::UnsteadySystem
LibUtilities::TimeIntegrationSchemeSharedPtr	m_intScheme
	Wrapper to the time integration scheme. More...

LibUtilities::TimeIntegrationSchemeOperators	m_ode
	The time integration scheme operators to use. More...

Array< OneD, Array< OneD, NekDouble > >	m_previousSolution
	Storage for previous solution for steady-state check. More...

std::vector< int >	m_intVariables

NekDouble	m_cflSafetyFactor
	CFL safety factor (comprise between 0 to 1). More...

NekDouble	m_CFLGrowth
	CFL growth rate. More...

NekDouble	m_CFLEnd
	Maximun cfl in cfl growth. More...

int	m_abortSteps
	Number of steps between checks for abort conditions. More...

bool	m_explicitDiffusion
	Indicates if explicit or implicit treatment of diffusion is used. More...

bool	m_explicitAdvection
	Indicates if explicit or implicit treatment of advection is used. More...

bool	m_explicitReaction
	Indicates if explicit or implicit treatment of reaction is used. More...

int	m_steadyStateSteps
	Check for steady state at step interval. More...

NekDouble	m_steadyStateTol
	Tolerance to which steady state should be evaluated at. More...

int	m_filtersInfosteps
	Number of time steps between outputting filters information. More...

std::vector< std::pair< std::string, FilterSharedPtr > >	m_filters

bool	m_homoInitialFwd
	Flag to determine if simulation should start in homogeneous forward transformed state. More...

std::ofstream	m_errFile

NekDouble	m_epsilon
	Diffusion coefficient. More...

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

bool	m_verbose

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

std::map< std::string, SolverUtils::SessionFunctionSharedPtr >	m_sessionFunctions
	Map of known SessionFunctions. More...

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

Array< OneD, MultiRegions::ExpListSharedPtr >	m_fields
	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...

NekDouble	m_checktime
	Time between checkpoints. More...

NekDouble	m_lastCheckTime

NekDouble	m_TimeIncrementFactor

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_infosteps
	Number of time steps between outputting status information. More...

int	m_iterPIT = 0
	Number of parallel-in-time time iteration. More...

int	m_windowPIT = 0
	Index of windows for parallel-in-time time iteration. 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, 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...

Array< OneD, NekDouble >	m_movingFrameVelsxyz
	Moving frame of reference velocities (u, v, w, omega_x, omega_y, omega_z, a_x, a_y, a_z, domega_x, domega_y, domega_z) More...

Array< OneD, NekDouble >	m_movingFrameData
	Moving frame of reference angles with respect to the. More...

boost::numeric::ublas::matrix< NekDouble >	m_movingFrameProjMat
	Projection matrix for transformation between inertial and moving. 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...

Private Attributes
StdRegions::VarCoeffMap	m_varcoeff
	Variable diffusivity. More...

Array< OneD, NekDouble >	m_epsilon

Array< OneD, NekDouble >	m_epsu

Friends
class	MemoryManager< MMFDiffusion >

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

Static Protected Attributes inherited from Nektar::SolverUtils::EquationSystem
static std::string	equationSystemTypeLookupIds []

static std::string	projectionTypeLookupIds []

Detailed Description

A model for cardiac conduction.

Definition at line 79 of file MMFDiffusion.h.

Constructor & Destructor Documentation

◆ ~MMFDiffusion()

Nektar::MMFDiffusion::~MMFDiffusion ( )

override

Desctructor.

Definition at line 180 of file MMFDiffusion.cpp.

181{

182}

◆ MMFDiffusion()

Nektar::MMFDiffusion::MMFDiffusion	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const SpatialDomains::MeshGraphSharedPtr &	pGraph
	)

protected

Constructor.

Definition at line 56 of file MMFDiffusion.cpp.

    : UnsteadySystem(pSession, pGraph), MMFSystem(pSession, pGraph)
{
}

Member Function Documentation

◆ create()

static SolverUtils::EquationSystemSharedPtr Nektar::MMFDiffusion::create	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const SpatialDomains::MeshGraphSharedPtr &	pGraph
	)

inlinestatic

Creates an instance of this class.

Definition at line 85 of file MMFDiffusion.h.

    {
        SolverUtils::EquationSystemSharedPtr p =
            MemoryManager<MMFDiffusion>::AllocateSharedPtr(pSession, pGraph);
        p->InitObject();
        return p;
    }

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and CellMLToNektar.cellml_metadata::p.

◆ DoImplicitSolve()

void Nektar::MMFDiffusion::DoImplicitSolve	(	const Array< OneD, const Array< OneD, NekDouble > > &	inarray,
		Array< OneD, Array< OneD, NekDouble > > &	outarray,
		NekDouble	time,
		NekDouble	lambda
	)

protected

Solve for the diffusion term.

OdeRhs

Parameters

inarray	Input array.
outarray	Output array.
time	Current simulation time.
lambda	Timestep.

Definition at line 190 of file MMFDiffusion.cpp.

{
    int nvariables = inarray.size();
    int nq         = m_fields[0]->GetNpoints();
 
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorTau] = 1.0;
 
    Array<OneD, Array<OneD, NekDouble>> F(nvariables);
    factors[StdRegions::eFactorLambda] = 1.0 / lambda;
    F[0] = Array<OneD, NekDouble>(nq * nvariables);
 
    for (int n = 1; n < nvariables; ++n)
    {
        F[n] = F[n - 1] + nq;
    }
 
    // We solve ( \nabla^2 - HHlambda ) Y[i] = rhs [i]
    // inarray = input: \hat{rhs} -> output: \hat{Y}
    // outarray = output: nabla^2 \hat{Y}
    // where \hat = modal coeffs
    SetBoundaryConditions(time);
 
    for (int i = 0; i < nvariables; ++i)
    {
        factors[StdRegions::eFactorLambda] = 1.0 / lambda / m_epsu[i];
 
        // Multiply 1.0/timestep
        Vmath::Smul(nq, -factors[StdRegions::eFactorLambda], inarray[i], 1,
                    F[i], 1);
 
        // Solve a system of equations with Helmholtz solver and transform
        // back into physical space.
        m_fields[i]->HelmSolve(F[i], m_fields[i]->UpdateCoeffs(), factors,
                               m_varcoeff);
 
        m_fields[i]->BwdTrans(m_fields[i]->GetCoeffs(), outarray[i]);
    }
}

References Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eFactorTau, Nektar::VarcoeffHashingTest::factors, m_epsu, Nektar::SolverUtils::EquationSystem::m_fields, m_varcoeff, Nektar::SolverUtils::EquationSystem::SetBoundaryConditions(), and Vmath::Smul().

Referenced by v_InitObject().

◆ DoOdeRhs()

void Nektar::MMFDiffusion::DoOdeRhs	(	const Array< OneD, const Array< OneD, NekDouble > > &	inarray,
		Array< OneD, Array< OneD, NekDouble > > &	outarray,
		const NekDouble	time
	)

protected

Computes the reaction terms \(f(u,v)\) and \(g(u,v)\).

Definition at line 236 of file MMFDiffusion.cpp.

{
    int nq = GetTotPoints();
 
    switch (m_TestType)
    {
        case eTestPlane:
        {
 
            Array<OneD, NekDouble> x(nq);
            Array<OneD, NekDouble> y(nq);
            Array<OneD, NekDouble> z(nq);
 
            m_fields[0]->GetCoords(x, y, z);
 
            for (int k = 0; k < nq; k++)
            {
                outarray[0][k] = (m_epsilon[0] + m_epsilon[1] - 1.0) * m_pi *
                                 m_pi * exp(-1.0 * m_pi * m_pi * time) *
                                 sin(m_pi * x[k]) * cos(m_pi * y[k]);
            }
        }
        break;
 
        case eTestCube:
        {
 
            Array<OneD, NekDouble> x(nq);
            Array<OneD, NekDouble> y(nq);
            Array<OneD, NekDouble> z(nq);
 
            m_fields[0]->GetCoords(x, y, z);
 
            for (int k = 0; k < nq; k++)
            {
                outarray[0][k] =
                    (m_epsilon[0] + m_epsilon[1] + m_epsilon[2] - 1.0) * m_pi *
                    m_pi * exp(-1.0 * m_pi * m_pi * time) * sin(m_pi * x[k]) *
                    sin(m_pi * y[k]) * sin(m_pi * z[k]);
            }
        }
        break;
 
        case eTestLinearSphere:
        {
            Array<OneD, NekDouble> temp(nq);
 
            NekDouble A = 2.0;
            NekDouble B = 5.0;
 
            NekDouble m_a, m_b, m_c, m_d;
            m_a = B - 1.0;
            m_b = A * A;
            m_c = -1.0 * B;
            m_d = -1.0 * A * A;
 
            temp = Array<OneD, NekDouble>(nq, 0.0);
            Vmath::Svtvp(nq, m_a, &inarray[0][0], 1, &temp[0], 1, &temp[0], 1);
            Vmath::Svtvp(nq, m_b, &inarray[1][0], 1, &temp[0], 1,
                         &outarray[0][0], 1);
 
            temp = Array<OneD, NekDouble>(nq, 0.0);
            Vmath::Svtvp(nq, m_c, &inarray[0][0], 1, &temp[0], 1, &temp[0], 1);
            Vmath::Svtvp(nq, m_d, &inarray[1][0], 1, &temp[0], 1,
                         &outarray[1][0], 1);
        }
        break;
 
        case eTestNonlinearSphere:
        {
            NekDouble A = 2.0;
            NekDouble B = 5.0;
 
            Array<OneD, NekDouble> Aonevec(nq, A);
 
            // cube = phys0*phys0*phy1
            Array<OneD, NekDouble> cube(nq);
            Vmath::Vmul(nq, &inarray[0][0], 1, &inarray[0][0], 1, &cube[0], 1);
            Vmath::Vmul(nq, &inarray[1][0], 1, &cube[0], 1, &cube[0], 1);
 
            // outarray[0] = A - B*phy0 + phy0*phy0*phy1 - phy0
            NekDouble coeff = -1.0 * B - 1.0;
            Array<OneD, NekDouble> tmp(nq);
            Vmath::Svtvp(nq, coeff, &inarray[0][0], 1, &cube[0], 1, &tmp[0], 1);
            Vmath::Vadd(nq, &Aonevec[0], 1, &tmp[0], 1, &outarray[0][0], 1);
 
            // outarray[1] = B*phys0 - phy0*phy0*phy1
            Vmath::Svtvm(nq, B, &inarray[0][0], 1, &cube[0], 1, &outarray[1][0],
                         1);
        }
        break;
 
        case eFHNStandard:
        {
            // \phi - \phi^3/3 - \psi
            NekDouble a  = 0.12;
            NekDouble b  = 0.011;
            NekDouble c1 = 0.175;
            NekDouble c2 = 0.03;
            NekDouble d  = 0.55;
 
            Array<OneD, NekDouble> tmp(nq);
 
            // Reaction for \phi = c1 \phi ( \phi - a)*(1 - \phi) - c2 v
            Vmath::Smul(nq, -1.0 * c1, inarray[0], 1, outarray[0], 1);
            Vmath::Sadd(nq, -1.0 * a, inarray[0], 1, tmp, 1);
            Vmath::Vmul(nq, tmp, 1, inarray[0], 1, outarray[0], 1);
            Vmath::Sadd(nq, -1.0, inarray[0], 1, tmp, 1);
            Vmath::Vmul(nq, tmp, 1, outarray[0], 1, outarray[0], 1);
 
            Vmath::Smul(nq, -1.0 * c2, inarray[1], 1, tmp, 1);
            Vmath::Vadd(nq, tmp, 1, outarray[0], 1, outarray[0], 1);
 
            // Reaction for \psi = b (\phi - d \psi )
            Vmath::Svtvp(nq, -1.0 * d, inarray[1], 1, inarray[0], 1,
                         outarray[1], 1);
            Vmath::Smul(nq, b, outarray[1], 1, outarray[1], 1);
        }
        break;
 
        case eFHNRogers:
        {
            NekDouble a  = 0.13;
            NekDouble b  = 0.013;
            NekDouble c1 = 0.26;
            NekDouble c2 = 0.1;
            NekDouble d  = 1.0;
 
            Array<OneD, NekDouble> tmp(nq);
 
            // Reaction for \phi = c1 \phi ( \phi - a)*(1 - \phi) - c2 u v
            Vmath::Smul(nq, -1.0 * c1, inarray[0], 1, outarray[0], 1);
            Vmath::Sadd(nq, -1.0 * a, inarray[0], 1, tmp, 1);
            Vmath::Vmul(nq, tmp, 1, outarray[0], 1, outarray[0], 1);
            Vmath::Sadd(nq, -1.0, inarray[0], 1, tmp, 1);
            Vmath::Vmul(nq, tmp, 1, outarray[0], 1, outarray[0], 1);
 
            Vmath::Vmul(nq, inarray[0], 1, inarray[1], 1, tmp, 1);
            Vmath::Smul(nq, -1.0 * c2, tmp, 1, tmp, 1);
            Vmath::Vadd(nq, tmp, 1, outarray[0], 1, outarray[0], 1);
 
            // Reaction for \psi = b (\phi - d \psi )
            Vmath::Svtvp(nq, -1.0 * d, inarray[1], 1, inarray[0], 1,
                         outarray[1], 1);
            Vmath::Smul(nq, b, outarray[1], 1, outarray[1], 1);
        }
        break;
 
        case eFHNAlievPanf:
        {
 
            NekDouble a   = 0.15;
            NekDouble c1  = 8.0;
            NekDouble c2  = 1.0;
            NekDouble c0  = 0.002;
            NekDouble mu1 = 0.2;
            NekDouble mu2 = 0.3;
 
            Array<OneD, NekDouble> tmp(nq);
 
            // Reaction for \phi = c1 \phi ( \phi - a)*(1 - \phi) - c2 u v
            Vmath::Smul(nq, -1.0 * c1, inarray[0], 1, outarray[0], 1);
            Vmath::Sadd(nq, -1.0 * a, inarray[0], 1, tmp, 1);
            Vmath::Vmul(nq, tmp, 1, outarray[0], 1, outarray[0], 1);
            Vmath::Sadd(nq, -1.0, inarray[0], 1, tmp, 1);
            Vmath::Vmul(nq, tmp, 1, outarray[0], 1, outarray[0], 1);
 
            Vmath::Vmul(nq, inarray[0], 1, inarray[1], 1, tmp, 1);
            Vmath::Smul(nq, -1.0 * c2, tmp, 1, tmp, 1);
            Vmath::Vadd(nq, tmp, 1, outarray[0], 1, outarray[0], 1);
 
            // Reaction for \psi = (c0 + (\mu1 \psi/(\mu2+\phi) ) )*(-\psi - c1
            // * \phi*(\phi - a - 1) )
 
            Vmath::Smul(nq, mu1, inarray[1], 1, outarray[1], 1);
            Vmath::Sadd(nq, mu2, inarray[0], 1, tmp, 1);
            Vmath::Vdiv(nq, outarray[1], 1, tmp, 1, outarray[1], 1);
            Vmath::Sadd(nq, c0, outarray[1], 1, outarray[1], 1);
 
            Vmath::Sadd(nq, (-a - 1.0), inarray[0], 1, tmp, 1);
            Vmath::Vmul(nq, inarray[0], 1, tmp, 1, tmp, 1);
            Vmath::Smul(nq, c1, tmp, 1, tmp, 1);
            Vmath::Vadd(nq, inarray[1], 1, tmp, 1, tmp, 1);
            Vmath::Neg(nq, tmp, 1);
 
            Vmath::Vmul(nq, tmp, 1, outarray[1], 1, outarray[1], 1);
        }
        break;
 
        default:
            break;
    }
}

References Nektar::UnitTests::d(), Nektar::eFHNAlievPanf, Nektar::eFHNRogers, Nektar::eFHNStandard, Nektar::eTestCube, Nektar::eTestLinearSphere, Nektar::eTestNonlinearSphere, Nektar::eTestPlane, Nektar::SolverUtils::EquationSystem::GetTotPoints(), m_epsilon, Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::MMFSystem::m_pi, m_TestType, Vmath::Neg(), Vmath::Sadd(), Vmath::Smul(), Vmath::Svtvm(), Vmath::Svtvp(), Vmath::Vadd(), Vmath::Vdiv(), Vmath::Vmul(), and Nektar::UnitTests::z().

Referenced by v_InitObject().

◆ Morphogenesis()

void Nektar::MMFDiffusion::Morphogenesis	(	const NekDouble	time,
		unsigned int	field,
		Array< OneD, NekDouble > &	outfield
	)

protected

Definition at line 547 of file MMFDiffusion.cpp.

{
    int nq = GetTotPoints();
 
    int i, m, n, ind;
    NekDouble a_n, d_n, gamma_n;
    NekDouble A_mn, C_mn, theta, phi, radius;
 
    std::complex<double> Spericharmonic, delta_n, temp;
    std::complex<double> varphi0, varphi1;
    std::complex<double> B_mn, D_mn;
 
    // Set some parameter values
    int Maxn = 6;
    int Maxm = 2 * Maxn - 1;
 
    NekDouble A = 2.0;
    NekDouble B = 5.0;
 
    NekDouble m_mu = 0.001;
    NekDouble m_nu = 0.002;
 
    NekDouble m_a, m_b, m_c, m_d;
 
    m_a = B - 1.0;
    m_b = A * A;
    m_c = -1.0 * B;
    m_d = -1.0 * A * A;
 
    Array<OneD, Array<OneD, NekDouble>> Ainit(Maxn);
    Array<OneD, Array<OneD, NekDouble>> Binit(Maxn);
 
    for (i = 0; i < Maxn; ++i)
    {
        Ainit[i] = Array<OneD, NekDouble>(Maxm, 0.0);
        Binit[i] = Array<OneD, NekDouble>(Maxm, 0.0);
    }
 
    Ainit[5][0]  = -0.5839;
    Ainit[5][1]  = -0.8436;
    Ainit[5][2]  = -0.4764;
    Ainit[5][3]  = 0.6475;
    Ainit[5][4]  = 0.1886;
    Ainit[5][5]  = 0.8709;
    Ainit[5][6]  = -0.8338;
    Ainit[5][7]  = 0.1795;
    Ainit[5][8]  = -0.7873;
    Ainit[5][9]  = 0.8842;
    Ainit[5][10] = 0.2943;
 
    Binit[5][0]  = -0.6263;
    Binit[5][1]  = 0.9803;
    Binit[5][2]  = 0.7222;
    Binit[5][3]  = 0.5945;
    Binit[5][4]  = 0.6026;
    Binit[5][5]  = -0.2076;
    Binit[5][6]  = 0.4556;
    Binit[5][7]  = 0.6024;
    Binit[5][8]  = 0.9695;
    Binit[5][9]  = -0.4936;
    Binit[5][10] = 0.1098;
 
    Array<OneD, NekDouble> u(nq);
    Array<OneD, NekDouble> v(nq);
    Array<OneD, NekDouble> x(nq);
    Array<OneD, NekDouble> y(nq);
    Array<OneD, NekDouble> z(nq);
 
    m_fields[0]->GetCoords(x, y, z);
    for (int i = 0; i < nq; ++i)
    {
        radius = sqrt(x[i] * x[i] + y[i] * y[i] + z[i] * z[i]);
 
        // theta is in [0, pi]
        theta = asin(z[i] / radius) + 0.5 * m_pi;
 
        // phi is in [0, 2*pi]
        phi = atan2(y[i], x[i]) + m_pi;
 
        varphi0 = 0.0 * varphi0;
        varphi1 = 0.0 * varphi1;
        for (n = 0; n < Maxn; ++n)
        {
            // Set up parameters
            a_n = m_a - m_mu * (n * (n + 1) / radius / radius);
            d_n = m_d - m_nu * (n * (n + 1) / radius / radius);
 
            gamma_n = 0.5 * (a_n + d_n);
 
            temp    = (a_n + d_n) * (a_n + d_n) - 4.0 * (a_n * d_n - m_b * m_c);
            delta_n = 0.5 * sqrt(temp);
 
            for (m = -n; m <= n; ++m)
            {
                ind  = m + n;
                A_mn = Ainit[n][ind];
                C_mn = Binit[n][ind];
 
                B_mn = ((a_n - gamma_n) * Ainit[n][ind] + m_b * Binit[n][ind]) /
                       delta_n;
                D_mn = (m_c * Ainit[n][ind] + (d_n - gamma_n) * Binit[n][ind]) /
                       delta_n;
 
                Spericharmonic =
                    boost::math::spherical_harmonic(n, m, theta, phi);
                varphi0 += exp(gamma_n * time) *
                           (A_mn * cosh(delta_n * time) +
                            B_mn * sinh(delta_n * time)) *
                           Spericharmonic;
                varphi1 += exp(gamma_n * time) *
                           (C_mn * cosh(delta_n * time) +
                            D_mn * sinh(delta_n * time)) *
                           Spericharmonic;
            }
        }
 
        u[i] = varphi0.real();
        v[i] = varphi1.real();
    }
 
    switch (field)
    {
        case 0:
        {
            outfield = u;
        }
        break;
 
        case 1:
        {
            outfield = v;
        }
        break;
    }
}

References Nektar::SolverUtils::EquationSystem::GetTotPoints(), Nektar::SolverUtils::EquationSystem::m_fields, m_mu, Nektar::SolverUtils::MMFSystem::m_pi, tinysimd::sqrt(), and Nektar::UnitTests::z().

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ PlanePhiWave()

Array< OneD, NekDouble > Nektar::MMFDiffusion::PlanePhiWave ( )

protected

Definition at line 684 of file MMFDiffusion.cpp.

{
    int nq = GetTotPoints();
    Array<OneD, NekDouble> outarray(nq, 0.0);
 
    Array<OneD, NekDouble> x(nq);
    Array<OneD, NekDouble> y(nq);
    Array<OneD, NekDouble> z(nq);
 
    m_fields[0]->GetCoords(x, y, z);
 
    NekDouble xmin, ymin, xmax;
 
    xmin = Vmath::Vmin(nq, x, 1);
    xmax = Vmath::Vmax(nq, x, 1);
    ymin = Vmath::Vmin(nq, y, 1);
 
    NekDouble xp, yp, xp2;
    for (int i = 0; i < nq; i++)
    {
        switch (m_InitWaveType)
        {
            case eLeft:
            {
                NekDouble radiusofinit = 4.0;
                NekDouble frontstiff   = 0.1;
 
                xp = x[i] - xmin;
                outarray[i] =
                    1.0 / (1.0 + exp((xp - radiusofinit) / frontstiff));
            }
            break;
 
            case eBothEnds:
            {
                NekDouble radiusofinit = 3.0;
                NekDouble frontstiff   = 0.1;
 
                xp  = x[i] - xmin;
                xp2 = x[i] - xmax;
 
                outarray[i] =
                    1.0 / (1.0 +
                           exp((sqrt(xp * xp) - radiusofinit) / frontstiff)) +
                    1.0 / (1.0 +
                           exp((sqrt(xp2 * xp2) - radiusofinit) / frontstiff));
            }
            break;
 
            case eCenter:
            {
                NekDouble radiusofinit = 6.0;
                NekDouble frontstiff   = 0.1;
 
                xp = x[i] - xmin;
                outarray[i] =
                    1.0 / (1.0 + exp((xp - radiusofinit) / frontstiff));
            }
            break;
 
            case eLeftBottomCorner:
            {
                NekDouble radiusofinit = 6.0;
                NekDouble frontstiff   = 0.1;
                NekDouble bs           = 2.0;
 
                xp = x[i] - xmin;
                yp = y[i] - ymin;
                outarray[i] =
                    1.0 /
                    (1.0 + exp((sqrt(xp * xp + yp * yp) / bs - radiusofinit) /
                               frontstiff));
            }
            break;
 
            case ePoint:
            {
                NekDouble xloc, yloc, zloc, rad;
                NekDouble radiusofinit = 10.0;
 
                xloc = x[i] - m_InitPtx;
                yloc = y[i] - m_InitPty;
                zloc = z[i] - m_InitPtz;
 
                rad = sqrt(xloc * xloc + yloc * yloc + zloc * zloc);
 
                xloc = xloc / radiusofinit;
                yloc = yloc / radiusofinit;
                zloc = zloc / radiusofinit;
 
                if (rad < radiusofinit)
                {
                    outarray[i] =
                        exp(-(1.0 / 2.0) *
                            (xloc * xloc + yloc * yloc + zloc * zloc));
                }
 
                else
                {
                    outarray[i] = 0.0;
                }
            }
            break;
 
            case eSpiralDock:
            {
                NekDouble radiusofinit = 3.0;
                NekDouble frontstiff   = 0.1;
                xp                     = x[i] - 4.0;
                yp                     = y[i];
                outarray[i] =
                    (1.0 / (1.0 + exp(2.0 * yp))) *
                    (1.0 / (1.0 + exp(-2.0 * xp))) *
                    (1.0 / (1.0 + exp((xp - radiusofinit) / frontstiff)));
            }
            break;
 
            default:
                break;
        }
    }
 
    return outarray;
}

References Nektar::eBothEnds, Nektar::eCenter, Nektar::eLeft, Nektar::eLeftBottomCorner, Nektar::ePoint, Nektar::eSpiralDock, Nektar::SolverUtils::EquationSystem::GetTotPoints(), Nektar::SolverUtils::EquationSystem::m_fields, m_InitPtx, m_InitPty, m_InitPtz, m_InitWaveType, Nektar::LibUtilities::rad(), tinysimd::sqrt(), Vmath::Vmax(), Vmath::Vmin(), and Nektar::UnitTests::z().

Referenced by v_SetInitialConditions().

◆ TestCubeProblem()

void Nektar::MMFDiffusion::TestCubeProblem	(	const NekDouble	time,
		Array< OneD, NekDouble > &	outfield
	)

protected

Definition at line 527 of file MMFDiffusion.cpp.

{
    int nq = GetTotPoints();
 
    Array<OneD, NekDouble> x(nq);
    Array<OneD, NekDouble> y(nq);
    Array<OneD, NekDouble> z(nq);
 
    m_fields[0]->GetCoords(x, y, z);
 
    outfield = Array<OneD, NekDouble>(nq);
    for (int k = 0; k < nq; k++)
    {
        outfield[k] = exp(-1.0 * m_pi * m_pi * time) * sin(m_pi * x[k]) *
                      sin(m_pi * y[k]) * sin(m_pi * z[k]);
    }
}

References Nektar::SolverUtils::EquationSystem::GetTotPoints(), Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::MMFSystem::m_pi, and Nektar::UnitTests::z().

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ TestPlaneProblem()

void Nektar::MMFDiffusion::TestPlaneProblem	(	const NekDouble	time,
		Array< OneD, NekDouble > &	outfield
	)

protected

Definition at line 507 of file MMFDiffusion.cpp.

{
    int nq = GetTotPoints();
 
    Array<OneD, NekDouble> x(nq);
    Array<OneD, NekDouble> y(nq);
    Array<OneD, NekDouble> z(nq);
 
    m_fields[0]->GetCoords(x, y, z);
 
    outfield = Array<OneD, NekDouble>(nq);
    for (int k = 0; k < nq; k++)
    {
        outfield[k] = exp(-1.0 * m_pi * m_pi * time) * sin(m_pi * x[k]) *
                      cos(m_pi * y[k]);
    }
}

References Nektar::SolverUtils::EquationSystem::GetTotPoints(), Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::MMFSystem::m_pi, and Nektar::UnitTests::z().

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ v_EvaluateExactSolution()

void Nektar::MMFDiffusion::v_EvaluateExactSolution	(	unsigned int	field,
		Array< OneD, NekDouble > &	outfield,
		const NekDouble	time
	)

overrideprotectedvirtual

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 809 of file MMFDiffusion.cpp.

{
    switch (m_TestType)
    {
        case eTestPlane:
        {
            TestPlaneProblem(time, outfield);
        }
        break;
 
        case eTestCube:
        {
            TestCubeProblem(time, outfield);
        }
        break;
 
        case eTestLinearSphere:
        case eTestNonlinearSphere:
        {
            Morphogenesis(time, field, outfield);
        }
        break;
 
        case eFHNStandard:
        case eFHNRogers:
        case eFHNAlievPanf:
        {
            int nq   = GetTotPoints();
            outfield = Array<OneD, NekDouble>(nq, 0.0);
        }
            /* Falls through. */
        default:
        {
            EquationSystem::v_EvaluateExactSolution(field, outfield, time);
        }
        break;
    }
}

References Nektar::eFHNAlievPanf, Nektar::eFHNRogers, Nektar::eFHNStandard, Nektar::eTestCube, Nektar::eTestLinearSphere, Nektar::eTestNonlinearSphere, Nektar::eTestPlane, Nektar::SolverUtils::EquationSystem::GetTotPoints(), m_TestType, Morphogenesis(), TestCubeProblem(), TestPlaneProblem(), and Nektar::SolverUtils::EquationSystem::v_EvaluateExactSolution().

◆ v_GenerateSummary()

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

overrideprotectedvirtual

Prints a summary of the model parameters.

Reimplemented from Nektar::SolverUtils::MMFSystem.

Definition at line 850 of file MMFDiffusion.cpp.

{
    MMFSystem::v_GenerateSummary(s);
    SolverUtils::AddSummaryItem(s, "TestType", TestTypeMap[m_TestType]);
    SolverUtils::AddSummaryItem(s, "epsilon0", m_epsilon[0]);
    SolverUtils::AddSummaryItem(s, "epsilon1", m_epsilon[1]);
    SolverUtils::AddSummaryItem(s, "epsilon2", m_epsilon[2]);
    if (m_TestType == eTestLinearSphere)
    {
        SolverUtils::AddSummaryItem(s, "epsilon for u", m_epsu[0]);
        SolverUtils::AddSummaryItem(s, "epsilon for v", m_epsu[1]);
    }
}

References Nektar::SolverUtils::AddSummaryItem(), Nektar::eTestLinearSphere, m_epsilon, m_epsu, m_TestType, Nektar::TestTypeMap, and Nektar::SolverUtils::MMFSystem::v_GenerateSummary().

◆ v_InitObject()

void Nektar::MMFDiffusion::v_InitObject ( bool DeclareField = true )

overrideprotectedvirtual

Init object for UnsteadySystem class.

Initialization object for UnsteadySystem class.

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 62 of file MMFDiffusion.cpp.

{
    UnsteadySystem::v_InitObject(DeclareFields);
 
    int nq    = m_fields[0]->GetNpoints();
    int nvar  = m_fields.size();
    int MFdim = 3;
 
    // Diffusivity coefficient for e^j
    m_epsilon = Array<OneD, NekDouble>(MFdim);
    m_session->LoadParameter("epsilon0", m_epsilon[0], 1.0);
    m_session->LoadParameter("epsilon1", m_epsilon[1], 1.0);
    m_session->LoadParameter("epsilon2", m_epsilon[2], 1.0);
 
    // Diffusivity coefficient for u^j
    m_epsu = Array<OneD, NekDouble>(nvar + 1);
    m_session->LoadParameter("epsu0", m_epsu[0], 1.0);
    m_session->LoadParameter("epsu1", m_epsu[1], 1.0);
 
    m_session->LoadParameter("InitPtx", m_InitPtx, 0.0);
    m_session->LoadParameter("InitPty", m_InitPty, 0.0);
    m_session->LoadParameter("InitPtz", m_InitPtz, 0.0);
 
    int shapedim = m_fields[0]->GetShapeDimension();
    Array<OneD, Array<OneD, NekDouble>> Anisotropy(shapedim);
    for (int j = 0; j < shapedim; ++j)
    {
        Anisotropy[j] = Array<OneD, NekDouble>(nq, 1.0);
        Vmath::Fill(nq, sqrt(m_epsilon[j]), &Anisotropy[j][0], 1);
    }
 
    MMFSystem::MMFInitObject(Anisotropy);
 
    // Define ProblemType
    if (m_session->DefinesSolverInfo("TESTTYPE"))
    {
        std::string TestTypeStr = m_session->GetSolverInfo("TESTTYPE");
        int i;
        for (i = 0; i < (int)SIZE_TestType; ++i)
        {
            if (boost::iequals(TestTypeMap[i], TestTypeStr))
            {
                m_TestType = (TestType)i;
                break;
            }
        }
    }
    else
    {
        m_TestType = (TestType)0;
    }
 
    if (m_session->DefinesSolverInfo("INITWAVETYPE"))
    {
        std::string InitWaveTypeStr = m_session->GetSolverInfo("INITWAVETYPE");
        for (int i = 0; i < (int)SIZE_TestType; ++i)
        {
            if (boost::iequals(InitWaveTypeMap[i], InitWaveTypeStr))
            {
                m_InitWaveType = (InitWaveType)i;
                break;
            }
        }
    }
    else
    {
        m_InitWaveType = (InitWaveType)0;
    }
 
    StdRegions::VarCoeffType MMFCoeffs[15] = {
        StdRegions::eVarCoeffMF1x,   StdRegions::eVarCoeffMF1y,
        StdRegions::eVarCoeffMF1z,   StdRegions::eVarCoeffMF1Div,
        StdRegions::eVarCoeffMF1Mag, StdRegions::eVarCoeffMF2x,
        StdRegions::eVarCoeffMF2y,   StdRegions::eVarCoeffMF2z,
        StdRegions::eVarCoeffMF2Div, StdRegions::eVarCoeffMF2Mag,
        StdRegions::eVarCoeffMF3x,   StdRegions::eVarCoeffMF3y,
        StdRegions::eVarCoeffMF3z,   StdRegions::eVarCoeffMF3Div,
        StdRegions::eVarCoeffMF3Mag};
 
    int indx;
    Array<OneD, NekDouble> tmp(nq);
    for (int k = 0; k < MFdim; ++k)
    {
        // For Moving Frames
        indx = 5 * k;
 
        for (int j = 0; j < m_spacedim; ++j)
        {
            Vmath::Vcopy(nq, &m_movingframes[k][j * nq], 1, &tmp[0], 1);
            m_varcoeff[MMFCoeffs[indx + j]] = tmp;
        }
 
        // m_DivMF
        Vmath::Vcopy(nq, &m_DivMF[k][0], 1, &tmp[0], 1);
        m_varcoeff[MMFCoeffs[indx + 3]] = tmp;
 
        // \| e^k \|
        tmp = Array<OneD, NekDouble>(nq, 0.0);
        for (int i = 0; i < m_spacedim; ++i)
        {
            Vmath::Vvtvp(nq, &m_movingframes[k][i * nq], 1,
                         &m_movingframes[k][i * nq], 1, &tmp[0], 1, &tmp[0], 1);
        }
 
        m_varcoeff[MMFCoeffs[indx + 4]] = tmp;
    }
 
    if (!m_explicitDiffusion)
    {
        m_ode.DefineImplicitSolve(&MMFDiffusion::DoImplicitSolve, this);
    }
 
    m_ode.DefineOdeRhs(&MMFDiffusion::DoOdeRhs, this);
}

◆ v_SetInitialConditions()

void Nektar::MMFDiffusion::v_SetInitialConditions	(	NekDouble	initialtime = `0.0`,
		bool	dumpInitialConditions = `true`,
		const int	domain = `0`
	)

overrideprotectedvirtual

Sets a custom initial condition.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 435 of file MMFDiffusion.cpp.

{
    int nq = GetTotPoints();
 
    switch (m_TestType)
    {
        case eTestPlane:
        {
            Array<OneD, NekDouble> u(nq);
 
            TestPlaneProblem(initialtime, u);
            m_fields[0]->SetPhys(u);
        }
        break;
 
        case eTestCube:
        {
            Array<OneD, NekDouble> u(nq);
 
            TestCubeProblem(initialtime, u);
            m_fields[0]->SetPhys(u);
        }
        break;
 
        case eTestLinearSphere:
        case eTestNonlinearSphere:
        {
            Array<OneD, NekDouble> u(nq);
            Array<OneD, NekDouble> v(nq);
 
            Morphogenesis(initialtime, 0, u);
            Morphogenesis(initialtime, 1, v);
 
            m_fields[0]->SetPhys(u);
            m_fields[1]->SetPhys(v);
        }
        break;
 
        case eFHNStandard:
        case eFHNRogers:
        case eFHNAlievPanf:
        {
            Array<OneD, NekDouble> Zero(nq, 0.0);
            m_fields[0]->SetPhys(PlanePhiWave());
            m_fields[1]->SetPhys(Zero);
        }
        break;
 
        default:
        {
            EquationSystem::v_SetInitialConditions(initialtime, false);
        }
        break;
    }
 
    // forward transform to fill the modal coeffs
    for (int i = 0; i < m_fields.size(); ++i)
    {
        m_fields[i]->SetPhysState(true);
        m_fields[i]->FwdTrans(m_fields[i]->GetPhys(),
                              m_fields[i]->UpdateCoeffs());
    }
 
    if (dumpInitialConditions)
    {
        std::string outname = m_sessionName + "_initial.chk";
        WriteFld(outname);
    }
}

References Nektar::eFHNAlievPanf, Nektar::eFHNRogers, Nektar::eFHNStandard, Nektar::eTestCube, Nektar::eTestLinearSphere, Nektar::eTestNonlinearSphere, Nektar::eTestPlane, Nektar::SolverUtils::EquationSystem::GetTotPoints(), Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::EquationSystem::m_sessionName, m_TestType, Morphogenesis(), PlanePhiWave(), TestCubeProblem(), TestPlaneProblem(), Nektar::SolverUtils::EquationSystem::v_SetInitialConditions(), Nektar::SolverUtils::EquationSystem::WriteFld(), and Vmath::Zero().

Friends And Related Function Documentation

◆ MemoryManager< MMFDiffusion >

friend class MemoryManager< MMFDiffusion >

friend

Definition at line 74 of file MMFDiffusion.h.

Member Data Documentation

◆ className

string Nektar::MMFDiffusion::className

static

Initial value:

=
    SolverUtils::GetEquationSystemFactory().RegisterCreatorFunction(
        "MMFDiffusion", MMFDiffusion::create, "MMFDiffusion equation.")

Name of class.

Definition at line 96 of file MMFDiffusion.h.

◆ m_epsilon

Array<OneD, NekDouble> Nektar::MMFDiffusion::m_epsilon

private

Definition at line 152 of file MMFDiffusion.h.

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

◆ m_epsu

Array<OneD, NekDouble> Nektar::MMFDiffusion::m_epsu

private

Definition at line 153 of file MMFDiffusion.h.

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

◆ m_InitPtx

NekDouble Nektar::MMFDiffusion::m_InitPtx

protected

Definition at line 146 of file MMFDiffusion.h.

Referenced by PlanePhiWave(), and v_InitObject().

◆ m_InitPty

NekDouble Nektar::MMFDiffusion::m_InitPty

protected

Definition at line 146 of file MMFDiffusion.h.

Referenced by PlanePhiWave(), and v_InitObject().

◆ m_InitPtz

NekDouble Nektar::MMFDiffusion::m_InitPtz

protected

Definition at line 146 of file MMFDiffusion.h.

Referenced by PlanePhiWave(), and v_InitObject().

◆ m_InitWaveType

InitWaveType Nektar::MMFDiffusion::m_InitWaveType

protected

Definition at line 108 of file MMFDiffusion.h.

Referenced by PlanePhiWave(), and v_InitObject().

◆ m_TestType

TestType Nektar::MMFDiffusion::m_TestType

Definition at line 98 of file MMFDiffusion.h.

Referenced by DoOdeRhs(), v_EvaluateExactSolution(), v_GenerateSummary(), v_InitObject(), and v_SetInitialConditions().

◆ m_varcoeff

StdRegions::VarCoeffMap Nektar::MMFDiffusion::m_varcoeff

private

Variable diffusivity.

Definition at line 150 of file MMFDiffusion.h.

Referenced by DoImplicitSolve(), and v_InitObject().

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ~MMFDiffusion()

◆ MMFDiffusion()

Member Function Documentation

◆ create()

◆ DoImplicitSolve()

◆ DoOdeRhs()

◆ Morphogenesis()

◆ PlanePhiWave()

◆ TestCubeProblem()

◆ TestPlaneProblem()

◆ v_EvaluateExactSolution()

◆ v_GenerateSummary()

◆ v_InitObject()

◆ v_SetInitialConditions()

Friends And Related Function Documentation

◆ MemoryManager< MMFDiffusion >

Member Data Documentation

◆ className

◆ m_epsilon

◆ m_epsu

◆ m_InitPtx

◆ m_InitPty

◆ m_InitPtz

◆ m_InitWaveType

◆ m_TestType

◆ m_varcoeff