A model for cardiac conduction. More...

#include <Monodomain.h>

Inheritance diagram for Nektar::Monodomain:

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

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 EquationSystemSharedPtr	create (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
	Creates an instance of this class. 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
	Monodomain (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	v_SetInitialConditions (NekDouble initialtime, bool dumpInitialConditions, const int domain) override
	Sets a custom initial condition. More...

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

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)

Private Member Functions
void	LoadStimuli ()

Private Attributes
CellModelSharedPtr	m_cell
	Cell model. More...

std::vector< StimulusSharedPtr >	m_stimulus

StdRegions::VarCoeffMap	m_vardiff
	Variable diffusivity. More...

NekDouble	m_chi

NekDouble	m_capMembrane

NekDouble	m_stimDuration
	Stimulus current. More...

Friends
class	MemoryManager< Monodomain >

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

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...

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

static std::string	projectionTypeLookupIds []

Detailed Description

A model for cardiac conduction.

Base model of cardiac electrophysiology of the form

\begin{align*} \frac{\partial u}{\partial t} = \nabla^2 u + J_{ion}, \end{align*}

where the reaction term, \(J_{ion}\) is defined by a specific cell model.

This implementation, at present, treats the reaction terms explicitly and the diffusive element implicitly.

Definition at line 48 of file Monodomain.h.

Constructor & Destructor Documentation

◆ ~Monodomain()

Nektar::Monodomain::~Monodomain ( )

override

Desctructor.

Definition at line 302 of file Monodomain.cpp.

303{

304}

◆ Monodomain()

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

protected

Constructor.

Definition at line 70 of file Monodomain.cpp.

    : UnsteadySystem(pSession, pGraph)
{
}

Member Function Documentation

◆ create()

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

inlinestatic

Creates an instance of this class.

Definition at line 54 of file Monodomain.h.

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

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

◆ DoImplicitSolve()

void Nektar::Monodomain::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.

Parameters

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

Definition at line 312 of file Monodomain.cpp.

{
    int nvariables = inarray.size();
    int nq         = m_fields[0]->GetNpoints();
    StdRegions::ConstFactorMap factors;
    // lambda = \Delta t
    factors[StdRegions::eFactorLambda] = 1.0 / lambda * m_chi * m_capMembrane;
 
    // 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
    for (int i = 0; i < nvariables; ++i)
    {
        // Multiply 1.0/timestep
        Vmath::Smul(nq, -factors[StdRegions::eFactorLambda], inarray[i], 1,
                    m_fields[i]->UpdatePhys(), 1);
 
        // Solve a system of equations with Helmholtz solver and transform
        // back into physical space.
        m_fields[i]->HelmSolve(m_fields[i]->GetPhys(),
                               m_fields[i]->UpdateCoeffs(), factors, m_vardiff);
 
        m_fields[i]->BwdTrans(m_fields[i]->GetCoeffs(),
                              m_fields[i]->UpdatePhys());
        m_fields[i]->SetPhysState(true);
 
        // Copy the solution vector (required as m_fields must be set).
        outarray[i] = m_fields[i]->GetPhys();
    }
}

References Nektar::StdRegions::eFactorLambda, Nektar::VarcoeffHashingTest::factors, m_capMembrane, m_chi, Nektar::SolverUtils::EquationSystem::m_fields, m_vardiff, and Vmath::Smul().

Referenced by v_InitObject().

◆ DoOdeRhs()

void Nektar::Monodomain::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 350 of file Monodomain.cpp.

{
    // Compute I_ion
    m_cell->TimeIntegrate(inarray, outarray, time);
 
    // Compute I_stim
    for (unsigned int i = 0; i < m_stimulus.size(); ++i)
    {
        m_stimulus[i]->Update(outarray, time);
    }
}

References m_cell, and m_stimulus.

Referenced by v_InitObject().

◆ LoadStimuli()

void Nektar::Monodomain::LoadStimuli ( )

private

◆ v_GenerateSummary()

void Nektar::Monodomain::v_GenerateSummary ( SummaryList & s )

overrideprotectedvirtual

Prints a summary of the model parameters.

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 379 of file Monodomain.cpp.

{
    UnsteadySystem::v_GenerateSummary(s);
    if (m_session->DefinesFunction("d00") &&
        m_session->GetFunctionType("d00", "intensity") ==
            LibUtilities::eFunctionTypeExpression)
    {
        AddSummaryItem(
            s, "Diffusivity-x",
            m_session->GetFunction("d00", "intensity")->GetExpression());
    }
    if (m_session->DefinesFunction("d11") &&
        m_session->GetFunctionType("d11", "intensity") ==
            LibUtilities::eFunctionTypeExpression)
    {
        AddSummaryItem(
            s, "Diffusivity-y",
            m_session->GetFunction("d11", "intensity")->GetExpression());
    }
    if (m_session->DefinesFunction("d22") &&
        m_session->GetFunctionType("d22", "intensity") ==
            LibUtilities::eFunctionTypeExpression)
    {
        AddSummaryItem(
            s, "Diffusivity-z",
            m_session->GetFunction("d22", "intensity")->GetExpression());
    }
    m_cell->GenerateSummary(s);
}

References Nektar::SolverUtils::AddSummaryItem(), Nektar::LibUtilities::eFunctionTypeExpression, m_cell, Nektar::SolverUtils::EquationSystem::m_session, and Nektar::SolverUtils::UnsteadySystem::v_GenerateSummary().

◆ v_InitObject()

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

overrideprotectedvirtual

Init object for UnsteadySystem class.

Initialization object for UnsteadySystem class.

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 79 of file Monodomain.cpp.

{
    UnsteadySystem::v_InitObject(DeclareField);
 
    m_session->LoadParameter("Chi", m_chi);
    m_session->LoadParameter("Cm", m_capMembrane);
 
    std::string vCellModel;
    m_session->LoadSolverInfo("CELLMODEL", vCellModel, "");
 
    ASSERTL0(vCellModel != "", "Cell Model not specified.");
 
    m_cell = GetCellModelFactory().CreateInstance(vCellModel, m_session,
                                                  m_fields[0]);
 
    m_intVariables.push_back(0);
 
    // Load variable coefficients
    StdRegions::VarCoeffType varCoeffEnum[6] = {
        StdRegions::eVarCoeffD00, StdRegions::eVarCoeffD01,
        StdRegions::eVarCoeffD11, StdRegions::eVarCoeffD02,
        StdRegions::eVarCoeffD12, StdRegions::eVarCoeffD22};
    std::string varCoeffString[6] = {"xx", "xy", "yy", "xz", "yz", "zz"};
    std::string aniso_var[3]      = {"fx", "fy", "fz"};
 
    const int nq            = m_fields[0]->GetNpoints();
    const int nVarDiffCmpts = m_spacedim * (m_spacedim + 1) / 2;
 
    // Allocate storage for variable coeffs and initialize to 1.
    for (int i = 0, k = 0; i < m_spacedim; ++i)
    {
        for (int j = 0; j < i + 1; ++j)
        {
            if (i == j)
            {
                m_vardiff[varCoeffEnum[k]] = Array<OneD, NekDouble>(nq, 1.0);
            }
            else
            {
                m_vardiff[varCoeffEnum[k]] = Array<OneD, NekDouble>(nq, 0.0);
            }
            ++k;
        }
    }
 
    // Apply fibre map f \in [0,1], scale to conductivity range
    // [o_min,o_max], specified by the session parameters o_min and o_max
    if (m_session->DefinesFunction("AnisotropicConductivity"))
    {
        if (m_session->DefinesCmdLineArgument("verbose"))
        {
            cout << "Loading Anisotropic Fibre map." << endl;
        }
 
        NekDouble o_min = m_session->GetParameter("o_min");
        NekDouble o_max = m_session->GetParameter("o_max");
        int k           = 0;
 
        Array<OneD, NekDouble> vTemp_i;
        Array<OneD, NekDouble> vTemp_j;
 
        /*
         * Diffusivity matrix D is upper triangular and defined as
         *    d_00   d_01  d_02
         *           d_11  d_12
         *                 d_22
         *
         * Given a principle fibre direction _f_ the diffusivity is given
         * by
         *    d_ij = { D_2 + (D_1 - D_2) f_i f_j   if i==j
         *           {       (D_1 - D_2) f_i f_j   if i!=j
         *
         * The vector _f_ is given in terms of the variables fx,fy,fz in the
         * function AnisotropicConductivity. The values of D_1 and D_2 are
         * the parameters o_max and o_min, respectively.
         */
 
        // Loop through columns of D
        for (int j = 0; j < m_spacedim; ++j)
        {
            ASSERTL0(m_session->DefinesFunction("AnisotropicConductivity",
                                                aniso_var[j]),
                     "Function 'AnisotropicConductivity' not correctly "
                     "defined.");
            GetFunction("AnisotropicConductivity")
                ->Evaluate(aniso_var[j], vTemp_j);
 
            // Loop through rows of D
            for (int i = 0; i < j + 1; ++i)
            {
                ASSERTL0(m_session->DefinesFunction("AnisotropicConductivity",
                                                    aniso_var[i]),
                         "Function 'AnisotropicConductivity' not correctly "
                         "defined.");
                GetFunction("AnisotropicConductivity")
                    ->Evaluate(aniso_var[i], vTemp_i);
 
                Array<OneD, NekDouble> tmp(vTemp_i.size());
 
                Vmath::Vmul(nq, vTemp_i, 1, vTemp_j, 1, tmp, 1);
                Vmath::Smul(nq, o_max - o_min, tmp, 1, tmp, 1);
 
                if (i == j)
                {
                    Vmath::Sadd(nq, o_min, tmp, 1, tmp, 1);
                }
 
                m_vardiff[varCoeffEnum[k]] = tmp;
                ++k;
            }
        }
    }
    else
    {
        // Otherwise apply isotropic conductivity value (o_max) to
        // diagonal components of tensor
        NekDouble o_max = m_session->GetParameter("o_max");
        for (int i = 0; i < nVarDiffCmpts; ++i)
        {
            Array<OneD, NekDouble> tmp(m_vardiff[varCoeffEnum[i]].GetValue());
            Vmath::Smul(nq, o_max, tmp, 1, tmp, 1);
            m_vardiff[varCoeffEnum[i]] = tmp;
        }
    }
 
    // Scale by scar map (range 0->1) derived from intensity map
    // (range d_min -> d_max)
    if (m_session->DefinesFunction("IsotropicConductivity"))
    {
        if (m_session->DefinesCmdLineArgument("verbose"))
        {
            cout << "Loading Isotropic Conductivity map." << endl;
        }
 
        const std::string varName = "intensity";
        Array<OneD, NekDouble> vTemp;
        GetFunction("IsotropicConductivity")->Evaluate(varName, vTemp);
 
        // If the d_min and d_max parameters are defined, then we need to
        // rescale the isotropic conductivity to convert from the source
        // domain (e.g. late-gad intensity) to conductivity
        if (m_session->DefinesParameter("d_min") ||
            m_session->DefinesParameter("d_max"))
        {
            const NekDouble f_min    = m_session->GetParameter("d_min");
            const NekDouble f_max    = m_session->GetParameter("d_max");
            const NekDouble scar_min = 0.0;
            const NekDouble scar_max = 1.0;
 
            // Threshold based on d_min, d_max
            for (int j = 0; j < nq; ++j)
            {
                vTemp[j] = (vTemp[j] < f_min ? f_min : vTemp[j]);
                vTemp[j] = (vTemp[j] > f_max ? f_max : vTemp[j]);
            }
 
            // Rescale to s \in [0,1] (0 maps to d_max, 1 maps to d_min)
            Vmath::Sadd(nq, -f_min, vTemp, 1, vTemp, 1);
            Vmath::Smul(nq, -1.0 / (f_max - f_min), vTemp, 1, vTemp, 1);
            Vmath::Sadd(nq, 1.0, vTemp, 1, vTemp, 1);
            Vmath::Smul(nq, scar_max - scar_min, vTemp, 1, vTemp, 1);
            Vmath::Sadd(nq, scar_min, vTemp, 1, vTemp, 1);
        }
 
        // Scale anisotropic conductivity values
        for (int i = 0; i < nVarDiffCmpts; ++i)
        {
            Array<OneD, NekDouble> tmp = m_vardiff[varCoeffEnum[i]].GetValue();
            Vmath::Vmul(nq, vTemp, 1, tmp, 1, tmp, 1);
            m_vardiff[varCoeffEnum[i]] = tmp;
        }
    }
 
    // Write out conductivity values
    for (int j = 0, k = 0; j < m_spacedim; ++j)
    {
        // Loop through rows of D
        for (int i = 0; i < j + 1; ++i)
        {
            // Transform variable coefficient and write out to file.
            m_fields[0]->FwdTransLocalElmt(
                m_vardiff[varCoeffEnum[k]].GetValue(),
                m_fields[0]->UpdateCoeffs());
            std::stringstream filename;
            filename << "Conductivity_" << varCoeffString[k] << ".fld";
            WriteFld(filename.str());
 
            ++k;
        }
    }
 
    // Search through the loaded filters and pass the cell model to any
    // CheckpointCellModel filters loaded.
    for (auto &x : m_filters)
    {
        if (x.first == "CheckpointCellModel")
        {
            std::shared_ptr<FilterCheckpointCellModel> c =
                std::dynamic_pointer_cast<FilterCheckpointCellModel>(x.second);
            c->SetCellModel(m_cell);
        }
        if (x.first == "CellHistoryPoints")
        {
            std::shared_ptr<FilterCellHistoryPoints> c =
                std::dynamic_pointer_cast<FilterCellHistoryPoints>(x.second);
            c->SetCellModel(m_cell);
        }
    }
 
    // Load stimuli
    m_stimulus = Stimulus::LoadStimuli(m_session, m_fields[0]);
 
    if (!m_explicitDiffusion)
    {
        m_ode.DefineImplicitSolve(&Monodomain::DoImplicitSolve, this);
    }
    m_ode.DefineOdeRhs(&Monodomain::DoOdeRhs, this);
    m_ode.DefineProjection(&Monodomain::DoDummyProjection, this);
}

◆ v_SetInitialConditions()

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

overrideprotectedvirtual

Sets a custom initial condition.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 367 of file Monodomain.cpp.

{
    EquationSystem::v_SetInitialConditions(initialtime, dumpInitialConditions,
                                           domain);
    m_cell->Initialise();
}

References m_cell, and Nektar::SolverUtils::EquationSystem::v_SetInitialConditions().

Friends And Related Function Documentation

◆ MemoryManager< Monodomain >

friend class MemoryManager< Monodomain >

friend

Definition at line 1 of file Monodomain.h.

Member Data Documentation

◆ className

string Nektar::Monodomain::className

static

Initial value:

=
    GetEquationSystemFactory().RegisterCreatorFunction(
        "Monodomain", Monodomain::create,
        "Monodomain model of cardiac electrophysiology.")

Name of class.

Registers the class with the Factory.

Definition at line 65 of file Monodomain.h.

◆ m_capMembrane

NekDouble Nektar::Monodomain::m_capMembrane

private

Definition at line 106 of file Monodomain.h.

Referenced by DoImplicitSolve(), and v_InitObject().

◆ m_cell

CellModelSharedPtr Nektar::Monodomain::m_cell

private

Cell model.

Definition at line 98 of file Monodomain.h.

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

◆ m_chi

NekDouble Nektar::Monodomain::m_chi

private

Definition at line 105 of file Monodomain.h.

Referenced by DoImplicitSolve(), and v_InitObject().

◆ m_stimDuration

NekDouble Nektar::Monodomain::m_stimDuration

private

Stimulus current.

Definition at line 109 of file Monodomain.h.

◆ m_stimulus

std::vector<StimulusSharedPtr> Nektar::Monodomain::m_stimulus

private

Definition at line 100 of file Monodomain.h.

Referenced by DoOdeRhs(), and v_InitObject().

◆ m_vardiff

StdRegions::VarCoeffMap Nektar::Monodomain::m_vardiff

private

Variable diffusivity.

Definition at line 103 of file Monodomain.h.

Referenced by DoImplicitSolve(), and v_InitObject().

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Member Functions

Private Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ~Monodomain()

◆ Monodomain()

Member Function Documentation

◆ create()

◆ DoImplicitSolve()

◆ DoOdeRhs()

◆ LoadStimuli()

◆ v_GenerateSummary()

◆ v_InitObject()

◆ v_SetInitialConditions()

Friends And Related Function Documentation

◆ MemoryManager< Monodomain >

Member Data Documentation

◆ className

◆ m_capMembrane

◆ m_cell

◆ m_chi

◆ m_stimDuration

◆ m_stimulus

◆ m_vardiff