A model for cardiac conduction. More...

#include <MMFDiffusion.h>

Inheritance diagram for Nektar::MMFDiffusion:

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

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

virtual SOLVER_UTILS_EXPORT	~MMFSystem ()

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

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 (bool DeclareField=true)
	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 >
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 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	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	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	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 Array< OneD, const Array< OneD, NekDouble > >	GetTraceNormals ()

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 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

Public Attributes inherited from Nektar::SolverUtils::UnsteadySystem
NekDouble	m_cflSafetyFactor
	CFL safety factor (comprise between 0 to 1). More...

NekDouble	m_cflNonAcoustic

NekDouble	m_CFLGrowth
	CFL growth rate. More...

NekDouble	m_CFLEnd
	maximun cfl in cfl growth More...

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...

virtual void	v_InitObject (bool DeclareField=true)
	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 ()

virtual void	v_SetInitialConditions (NekDouble initialtime, bool dumpInitialConditions, const int domain)
	Sets a custom initial condition. More...

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

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

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

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

virtual SOLVER_UTILS_EXPORT void	v_DoInitialise ()
	Sets up initial conditions. More...

virtual SOLVER_UTILS_EXPORT void	v_AppendOutput1D (Array< OneD, Array< OneD, NekDouble >> &solution1D)
	Print the solution at each solution point in a txt file. 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)

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...

virtual SOLVER_UTILS_EXPORT bool	UpdateTimeStepCheck ()

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 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_Output (void)

virtual SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	v_GetPressure (void)

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

Array< OneD, NekDouble >	m_MFlength

Protected Attributes inherited from Nektar::SolverUtils::UnsteadySystem
int	m_infosteps
	Number of time steps between outputting status information. More...

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

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

int	m_nanSteps

LibUtilities::TimeIntegrationSchemeSharedPtr	m_intScheme
	Wrapper to the time integration scheme. More...

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

NekDouble	m_epsilon

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...

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

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

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

NekDouble	m_steadyStateRes = 1.0

NekDouble	m_steadyStateRes0 = 1.0

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

std::ofstream	m_errFile

std::vector< int >	m_intVariables

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

NekDouble	m_filterTimeWarning
	Number of time steps between outputting status information. More...

NekDouble	m_TimeIntegLambda = 0.0
	coefff of spacial derivatives(rhs or m_F in GLM) in calculating the residual of the whole equation(used in unsteady time integrations) More...

bool	m_flagImplicitItsStatistics

bool	m_flagImplicitSolver = false

Array< OneD, NekDouble >	m_magnitdEstimat
	estimate the magnitude of each conserved varibles More...

Array< OneD, NekDouble >	m_locTimeStep
	local time step(notice only for jfnk other see m_cflSafetyFactor) More...

NekDouble	m_inArrayNorm = -1.0

int	m_TotLinItePerStep = 0

int	m_StagesPerStep = 1

bool	m_flagUpdatePreconMat

int	m_maxLinItePerNewton

int	m_TotNewtonIts = 0

int	m_TotLinIts = 0

int	m_TotImpStages = 0

bool	m_CalcPhysicalAV = true
	flag to update artificial viscosity More...

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

bool	m_verbose

bool	m_root

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_timestepMax = -1.0
	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_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. More...

Array< OneD, NekDouble >	m_movingFrameTheta
	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 []

Detailed Description

A model for cardiac conduction.

Definition at line 79 of file MMFDiffusion.h.

Constructor & Destructor Documentation

◆ ~MMFDiffusion()

Nektar::MMFDiffusion::~MMFDiffusion ( )

virtual

Desctructor.

Definition at line 184 of file MMFDiffusion.cpp.

185 {

186 }

◆ MMFDiffusion()

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

protected

Constructor.

Definition at line 57 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 194 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;
         // cout << "F["<< n<<"=" << F[n][1] <<endl;
     }
  
     // 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);
  
         /* for (int k = 0; k < 15; ++k)
              cout << "inarray["<<i << "]"<< k<<"=" << inarray[i][k]<<endl;*/
         // 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]);
         /* Array<OneD, NekDouble> coefarray = m_fields[i]->GetCoeffs();
          for (int k = 0; k < 15; ++k)
              cout << "inarray["<< k<<"=" << coefarray[k]<<endl;*/
     }
     /* for (int kk = 0; kk < 15; ++kk)
          cout << "inarray["<< kk<<"=" <<
        m_varcoeff[StdRegions::eVarCoeffMF3Mag][kk]<<endl;*/
 }

References Nektar::StdRegions::eFactorLambda, Nektar::StdRegions::eFactorTau, 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 249 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::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(), and Vmath::Vmul().

Referenced by v_InitObject().

◆ Morphogenesis()

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

protected

Definition at line 569 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, and tinysimd::sqrt().

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ PlanePhiWave()

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

protected

Definition at line 706 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;
  
                 // NekDouble xc = 0.5*(Vmath::Vmax(nq, x, 1) + Vmath::Vmin(nq,
                 // x, 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(), and Vmath::Vmin().

Referenced by v_SetInitialConditions().

◆ TestCubeProblem()

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

protected

Definition at line 549 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, and Nektar::SolverUtils::MMFSystem::m_pi.

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ TestPlaneProblem()

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

protected

Definition at line 529 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, and Nektar::SolverUtils::MMFSystem::m_pi.

Referenced by v_EvaluateExactSolution(), and v_SetInitialConditions().

◆ v_EvaluateExactSolution()

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

protectedvirtual

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 834 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 )

protectedvirtual

Prints a summary of the model parameters.

Reimplemented from Nektar::SolverUtils::MMFSystem.

Definition at line 875 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 )

protectedvirtual

Init object for UnsteadySystem class.

Initialization object for UnsteadySystem class.

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 63 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)
         {
             m_varcoeff[MMFCoeffs[indx + j]] = Array<OneD, NekDouble>(nq, 0.0);
             Vmath::Vcopy(nq, &m_movingframes[k][j * nq], 1,
                          &m_varcoeff[MMFCoeffs[indx + j]][0], 1);
         }
  
         // m_DivMF
         m_varcoeff[MMFCoeffs[indx + 3]] = Array<OneD, NekDouble>(nq, 0.0);
         Vmath::Vcopy(nq, &m_DivMF[k][0], 1, &m_varcoeff[MMFCoeffs[indx + 3]][0],
                      1);
  
         // \| e^k \|
         m_varcoeff[MMFCoeffs[indx + 4]] = Array<OneD, NekDouble>(nq, 0.0);
         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);
         }
  
         Vmath::Vcopy(nq, &tmp[0], 1, &m_varcoeff[MMFCoeffs[indx + 4]][0], 1);
     }
  
     if (!m_explicitDiffusion)
     {
         m_ode.DefineImplicitSolve(&MMFDiffusion::DoImplicitSolve, this);
     }
  
     m_ode.DefineOdeRhs(&MMFDiffusion::DoOdeRhs, this);
 }

◆ v_SetInitialConditions()

void Nektar::MMFDiffusion::v_SetInitialConditions	(	NekDouble	initialtime,
		bool	dumpInitialConditions,
		const int	domain
	)

protectedvirtual

Sets a custom initial condition.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 448 of file MMFDiffusion.cpp.

 {
     boost::ignore_unused(domain);
  
     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);
             /*for (int k=0; k<nq; ++k)
             {
                 //for (int j=0; j<m_spacedim; ++j)
                 //{
                 cout << "_varcoeff" << u[k] <<endl;
                 // }
             }*/
         }
         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