A model for cardiac conduction. More...

#include <Bidomain.h>

Inheritance diagram for Nektar::Bidomain:

Collaboration diagram for Nektar::Bidomain:

Public Member Functions
virtual	~Bidomain ()
	Desctructor.
Public Member Functions inherited from Nektar::SolverUtils::UnsteadySystem
virtual SOLVER_UTILS_EXPORT	~UnsteadySystem ()
	Destructor.
SOLVER_UTILS_EXPORT NekDouble	GetTimeStep (const Array< OneD, const Array< OneD, NekDouble > > &inarray)
	Calculate the larger time-step mantaining the problem stable.
Public Member Functions inherited from Nektar::SolverUtils::EquationSystem
virtual SOLVER_UTILS_EXPORT	~EquationSystem ()
	Destructor.
SOLVER_UTILS_EXPORT void	SetUpTraceNormals (void)
SOLVER_UTILS_EXPORT void	InitObject ()
	Initialises the members of this object.
SOLVER_UTILS_EXPORT void	DoInitialise ()
	Perform any initialisation necessary before solving the problem.
SOLVER_UTILS_EXPORT void	DoSolve ()
	Solve the problem.
SOLVER_UTILS_EXPORT void	TransCoeffToPhys ()
	Transform from coefficient to physical space.
SOLVER_UTILS_EXPORT void	TransPhysToCoeff ()
	Transform from physical to coefficient space.
SOLVER_UTILS_EXPORT void	Output ()
	Perform output operations after solve.
SOLVER_UTILS_EXPORT NekDouble	LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Linf error computation.
SOLVER_UTILS_EXPORT std::string	GetSessionName ()
	Get Session name.
SOLVER_UTILS_EXPORT void	ResetSessionName (std::string newname)
	Reset Session name.
SOLVER_UTILS_EXPORT LibUtilities::SessionReaderSharedPtr	GetSession ()
	Get Session name.
SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	GetPressure ()
	Get pressure field if available.
SOLVER_UTILS_EXPORT void	PrintSummary (std::ostream &out)
	Print a summary of parameters and solver characteristics.
SOLVER_UTILS_EXPORT void	SetLambda (NekDouble lambda)
	Set parameter m_lambda.
SOLVER_UTILS_EXPORT void	EvaluateFunction (Array< OneD, Array< OneD, NekDouble > > &pArray, std::string pFunctionName, const NekDouble pTime=0.0, const int domain=0)
	Evaluates a function as specified in the session file.
SOLVER_UTILS_EXPORT void	EvaluateFunction (std::vector< std::string > pFieldNames, Array< OneD, Array< OneD, NekDouble > > &pFields, const std::string &pName, const int domain=0)
	Populate given fields with the function from session.
SOLVER_UTILS_EXPORT void	EvaluateFunction (std::vector< std::string > pFieldNames, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields, const std::string &pName, const int domain=0)
	Populate given fields with the function from session.
SOLVER_UTILS_EXPORT void	EvaluateFunction (std::string pFieldName, Array< OneD, NekDouble > &pArray, const std::string &pFunctionName, const NekDouble &pTime=0.0, const int domain=0)
SOLVER_UTILS_EXPORT std::string	DescribeFunction (std::string pFieldName, const std::string &pFunctionName, const int domain)
	Provide a description of a function for a given field name.
SOLVER_UTILS_EXPORT void	InitialiseBaseFlow (Array< OneD, Array< OneD, NekDouble > > &base)
	Perform initialisation of the base flow.
SOLVER_UTILS_EXPORT void	SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)
	Initialise the data in the dependent fields.
SOLVER_UTILS_EXPORT void	EvaluateExactSolution (int field, Array< OneD, NekDouble > &outfield, const NekDouble time)
	Evaluates an exact solution.
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.
SOLVER_UTILS_EXPORT NekDouble	L2Error (unsigned int field, bool Normalised=false)
	Compute the L2 error of the fields.
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].
SOLVER_UTILS_EXPORT void	WeakAdvectionGreensDivergenceForm (const Array< OneD, Array< OneD, NekDouble > > &F, Array< OneD, NekDouble > &outarray)
	Compute the inner product $(\nabla \phi \cdot F)$ .
SOLVER_UTILS_EXPORT void	WeakAdvectionDivergenceForm (const Array< OneD, Array< OneD, NekDouble > > &F, Array< OneD, NekDouble > &outarray)
	Compute the inner product $(\phi, \nabla \cdot F)$ .
SOLVER_UTILS_EXPORT void	WeakAdvectionNonConservativeForm (const Array< OneD, Array< OneD, NekDouble > > &V, const Array< OneD, const NekDouble > &u, Array< OneD, NekDouble > &outarray, bool UseContCoeffs=false)
	Compute the inner product $(\phi, V\cdot \nabla u)$ .
f SOLVER_UTILS_EXPORT void	AdvectionNonConservativeForm (const Array< OneD, Array< OneD, NekDouble > > &V, const Array< OneD, const NekDouble > &u, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wk=NullNekDouble1DArray)
	Compute the non-conservative advection.
SOLVER_UTILS_EXPORT void	WeakDGAdvection (const Array< OneD, Array< OneD, NekDouble > > &InField, Array< OneD, Array< OneD, NekDouble > > &OutField, bool NumericalFluxIncludesNormal=true, bool InFieldIsInPhysSpace=false, int nvariables=0)
	Calculate the weak discontinuous Galerkin advection.
SOLVER_UTILS_EXPORT void	WeakDGDiffusion (const Array< OneD, Array< OneD, NekDouble > > &InField, Array< OneD, Array< OneD, NekDouble > > &OutField, bool NumericalFluxIncludesNormal=true, bool InFieldIsInPhysSpace=false)
	Calculate weak DG Diffusion in the LDG form.
SOLVER_UTILS_EXPORT void	Checkpoint_Output (const int n)
	Write checkpoint file of m_fields.
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.
SOLVER_UTILS_EXPORT void	WriteFld (const std::string &outname)
	Write field data to the given filename.
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.
SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields)
	Input field data from the given file.
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.
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.
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.
SOLVER_UTILS_EXPORT void	ScanForHistoryPoints ()
	Builds map of which element holds each history point.
SOLVER_UTILS_EXPORT void	WriteHistoryData (std::ostream &out)
	Probe each history point and write to file.
SOLVER_UTILS_EXPORT void	SessionSummary (SummaryList &vSummary)
	Write out a session summary.
SOLVER_UTILS_EXPORT Array < OneD, MultiRegions::ExpListSharedPtr > &	UpdateFields ()
SOLVER_UTILS_EXPORT LibUtilities::FieldMetaDataMap &	UpdateFieldMetaDataMap ()
	Get hold of FieldInfoMap so it can be updated.
SOLVER_UTILS_EXPORT NekDouble	GetFinalTime ()
	Return final time.
SOLVER_UTILS_EXPORT int	GetNcoeffs ()
SOLVER_UTILS_EXPORT int	GetNcoeffs (const int eid)
SOLVER_UTILS_EXPORT int	GetNumExpModes ()
SOLVER_UTILS_EXPORT const Array< OneD, int >	GetNumExpModesPerExp ()
SOLVER_UTILS_EXPORT int	GetNvariables ()
SOLVER_UTILS_EXPORT const std::string	GetVariable (unsigned int i)
SOLVER_UTILS_EXPORT int	GetTraceTotPoints ()
SOLVER_UTILS_EXPORT int	GetTraceNpoints ()
SOLVER_UTILS_EXPORT int	GetExpSize ()
SOLVER_UTILS_EXPORT int	GetPhys_Offset (int n)
SOLVER_UTILS_EXPORT int	GetCoeff_Offset (int n)
SOLVER_UTILS_EXPORT int	GetTotPoints ()
SOLVER_UTILS_EXPORT int	GetTotPoints (int n)
SOLVER_UTILS_EXPORT int	GetNpoints ()
SOLVER_UTILS_EXPORT int	GetNumElmVelocity ()
SOLVER_UTILS_EXPORT int	GetSteps ()
SOLVER_UTILS_EXPORT NekDouble	GetTimeStep ()
SOLVER_UTILS_EXPORT void	CopyFromPhysField (const int i, Array< OneD, NekDouble > &output)
SOLVER_UTILS_EXPORT void	CopyToPhysField (const int i, Array< OneD, NekDouble > &output)
SOLVER_UTILS_EXPORT void	SetStepsToOne ()
SOLVER_UTILS_EXPORT void	ZeroPhysFields ()
SOLVER_UTILS_EXPORT void	FwdTransFields ()
SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)
SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &fluxX, Array< OneD, Array< OneD, NekDouble > > &fluxY)
SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, const int j, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)
SOLVER_UTILS_EXPORT void	NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numflux)
SOLVER_UTILS_EXPORT void	NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxX, Array< OneD, Array< OneD, NekDouble > > &numfluxY)
SOLVER_UTILS_EXPORT void	NumFluxforScalar (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &uflux)
SOLVER_UTILS_EXPORT void	NumFluxforVector (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &qfield, Array< OneD, Array< OneD, NekDouble > > &qflux)
SOLVER_UTILS_EXPORT void	SetModifiedBasis (const bool modbasis)
SOLVER_UTILS_EXPORT int	NoCaseStringCompare (const string &s1, const string &s2)
	Perform a case-insensitive string comparison.

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

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

Protected Member Functions
	Bidomain (const LibUtilities::SessionReaderSharedPtr &pSession)
	Constructor.
virtual void	v_InitObject ()
	Init object for UnsteadySystem class.
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.
void	DoOdeRhs (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, const NekDouble time)
	Computes the reaction terms and .
virtual void	v_SetInitialConditions (NekDouble initialtime, bool dumpInitialConditions, const int domain)
	Sets a custom initial condition.
virtual void	v_GenerateSummary (SummaryList &s)
	Prints a summary of the model parameters.
Protected Member Functions inherited from Nektar::SolverUtils::UnsteadySystem
SOLVER_UTILS_EXPORT	UnsteadySystem (const LibUtilities::SessionReaderSharedPtr &pSession)
	Initialises UnsteadySystem class members.
SOLVER_UTILS_EXPORT NekDouble	MaxTimeStepEstimator ()
	Get the maximum timestep estimator for cfl control.
virtual SOLVER_UTILS_EXPORT void	v_DoSolve ()
	Solves an unsteady problem.
virtual SOLVER_UTILS_EXPORT void	v_DoInitialise ()
	Sets up initial conditions.
virtual SOLVER_UTILS_EXPORT void	v_AppendOutput1D (Array< OneD, Array< OneD, NekDouble > > &solution1D)
	Print the solution at each solution point in a txt file.
virtual SOLVER_UTILS_EXPORT void	v_NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numflux)
virtual SOLVER_UTILS_EXPORT void	v_NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxX, Array< OneD, Array< OneD, NekDouble > > &numfluxY)
virtual SOLVER_UTILS_EXPORT void	v_NumFluxforScalar (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &uflux)
virtual SOLVER_UTILS_EXPORT void	v_NumFluxforVector (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &qfield, Array< OneD, Array< OneD, NekDouble > > &qflux)
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.
virtual SOLVER_UTILS_EXPORT bool	v_PreIntegrate (int step)
virtual SOLVER_UTILS_EXPORT bool	v_PostIntegrate (int step)
SOLVER_UTILS_EXPORT void	CheckForRestartTime (NekDouble &time)
Protected Member Functions inherited from Nektar::SolverUtils::EquationSystem
SOLVER_UTILS_EXPORT	EquationSystem (const LibUtilities::SessionReaderSharedPtr &pSession)
	Initialises EquationSystem class members.
int	nocase_cmp (const string &s1, const string &s2)
SOLVER_UTILS_EXPORT void	SetBoundaryConditions (NekDouble time)
	Evaluates the boundary conditions at the given time.
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.
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.
virtual SOLVER_UTILS_EXPORT void	v_TransCoeffToPhys ()
	Virtual function for transformation to physical space.
virtual SOLVER_UTILS_EXPORT void	v_TransPhysToCoeff ()
	Virtual function for transformation to coefficient space.
virtual SOLVER_UTILS_EXPORT void	v_EvaluateExactSolution (unsigned int field, Array< OneD, NekDouble > &outfield, const NekDouble time)
SOLVER_UTILS_EXPORT void	SetUpBaseFields (SpatialDomains::MeshGraphSharedPtr &mesh)
SOLVER_UTILS_EXPORT void	ImportFldBase (std::string pInfile, SpatialDomains::MeshGraphSharedPtr pGraph)
virtual SOLVER_UTILS_EXPORT void	v_Output (void)
virtual SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	v_GetPressure (void)
virtual SOLVER_UTILS_EXPORT void	v_ExtraFldOutput (std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)

Private Attributes
CellModelSharedPtr	m_cell
	Cell model.
NekDouble	m_chi
NekDouble	m_capMembrane
NekDouble	m_sigmaix
NekDouble	m_sigmaiy
NekDouble	m_sigmaiz
NekDouble	m_sigmaex
NekDouble	m_sigmaey
NekDouble	m_sigmaez
StdRegions::VarCoeffMap	m_vardiffi
StdRegions::VarCoeffMap	m_vardiffie
Array< OneD, Array< OneD, NekDouble > >	tmp1
Array< OneD, Array< OneD, NekDouble > >	tmp2
Array< OneD, Array< OneD, NekDouble > >	tmp3
NekDouble	m_stimDuration
	Stimulus current.

Friends
class	MemoryManager< Bidomain >

Additional Inherited Members
Public Attributes inherited from Nektar::SolverUtils::UnsteadySystem
NekDouble	m_cflSafetyFactor
	CFL safety factor (comprise between 0 to 1).
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
int	m_infosteps
	Number of time steps between outputting status information.
LibUtilities::TimeIntegrationWrapperSharedPtr	m_intScheme
	Wrapper to the time integration scheme.
LibUtilities::TimeIntegrationSchemeOperators	m_ode
	The time integration scheme operators to use.
LibUtilities::TimeIntegrationSolutionSharedPtr	m_intSoln
NekDouble	m_epsilon
bool	m_explicitDiffusion
	Indicates if explicit or implicit treatment of diffusion is used.
bool	m_explicitAdvection
	Indicates if explicit or implicit treatment of advection is used.
bool	m_explicitReaction
	Indicates if explicit or implicit treatment of reaction is used.
bool	m_homoInitialFwd
	Flag to determine if simulation should start in homogeneous forward transformed state.
std::vector< int >	m_intVariables
std::vector< FilterSharedPtr >	m_filters

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 49 of file Bidomain.h.

Constructor & Destructor Documentation

Nektar::Bidomain::~Bidomain ( )

virtual

Desctructor.

Definition at line 177 of file Bidomain.cpp.

    {
    }

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

protected

Constructor.

Definition at line 70 of file Bidomain.cpp.

    : UnsteadySystem(pSession)
    {
    }

Member Function Documentation

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

inlinestatic

Creates an instance of this class.

Definition at line 55 of file Bidomain.h.

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

void Nektar::Bidomain::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 189 of file Bidomain.cpp.

References Nektar::StdRegions::eFactorLambda, m_capMembrane, m_chi, Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::EquationSystem::m_session, Nektar::SolverUtils::EquationSystem::m_spacedim, m_vardiffi, m_vardiffie, Nektar::NullFlagList, Vmath::Smul(), Vmath::Vadd(), and Vmath::Vcopy().

Referenced by v_InitObject().

    {
        int nvariables  = inarray.num_elements();
        int nq          = m_fields[0]->GetNpoints();
        Array<OneD, NekDouble> grad0(nq), grad1(nq), grad2(nq), grad(nq);
        Array<OneD, NekDouble> ggrad0(nq), ggrad1(nq), ggrad2(nq), ggrad(nq), temp(nq);
        // We solve ( \sigma\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)
        {
            // Only apply diffusion to first variable.
            if (i > 1) {
                Vmath::Vcopy(nq, &inarray[i][0], 1, &outarray[i][0], 1);
                continue;
            }
            if (i == 0) {
                StdRegions::ConstFactorMap factors;
                factors[StdRegions::eFactorLambda] = (1.0/lambda)*(m_capMembrane*m_chi);
                if (m_spacedim==1) {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(inarray[1],ggrad0);
                // Take second partial derivative
                m_fields[i]->PhysDeriv(0,ggrad0,ggrad0);
                // Multiply by Intracellular-Conductivity
        if (m_session->DefinesFunction("IntracellularConductivity") && m_session->DefinesFunction("ExtracellularConductivity"))
        {
                Vmath::Smul(nq, m_session->GetParameter("sigmaix"), ggrad0, 1, ggrad0, 1);
                }
                // Add partial derivatives together
                Vmath::Vcopy(nq, ggrad0, 1, ggrad, 1);
                Vmath::Smul(nq, -1.0, ggrad, 1, ggrad, 1);
                // Multiply 1.0/timestep/lambda
                Vmath::Smul(nq, -factors[StdRegions::eFactorLambda], inarray[i], 1, temp, 1);
                Vmath::Vadd(nq, ggrad, 1, temp, 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(),NullFlagList,factors);
                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();
                }
                
                if (m_spacedim==2) {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(inarray[1],ggrad0,ggrad1);
                // Take second partial derivative
                m_fields[i]->PhysDeriv(0,ggrad0,ggrad0);
                m_fields[i]->PhysDeriv(1,ggrad1,ggrad1);
                // Multiply by Intracellular-Conductivity 
        if (m_session->DefinesFunction("IntracellularConductivity") && m_session->DefinesFunction("ExtracellularConductivity"))
        {                 
                Vmath::Smul(nq, m_session->GetParameter("sigmaix"), ggrad0, 1, ggrad0, 1);   
                Vmath::Smul(nq, m_session->GetParameter("sigmaiy"), ggrad1, 1, ggrad1, 1); 
                }
                // Add partial derivatives together
                Vmath::Vadd(nq, ggrad0, 1, ggrad1, 1, ggrad, 1);
                Vmath::Smul(nq, -1.0, ggrad, 1, ggrad, 1); 
                // Multiply 1.0/timestep/lambda
                Vmath::Smul(nq, -factors[StdRegions::eFactorLambda], inarray[i], 1, temp, 1);
                Vmath::Vadd(nq, ggrad, 1, temp, 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(),NullFlagList,factors,m_vardiffi);
                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();                                                                          
                }
                
                if (m_spacedim==3) {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(inarray[1],ggrad0,ggrad1,ggrad2);
                // Take second partial derivative
                m_fields[i]->PhysDeriv(0,ggrad0,ggrad0);
                m_fields[i]->PhysDeriv(1,ggrad1,ggrad1);                
                m_fields[i]->PhysDeriv(2,ggrad2,ggrad2); 
                // Multiply by Intracellular-Conductivity 
        if (m_session->DefinesFunction("IntracellularConductivity") && m_session->DefinesFunction("ExtracellularConductivity"))
        {                 
                Vmath::Smul(nq, m_session->GetParameter("sigmaix"), ggrad0, 1, ggrad0, 1);  
                Vmath::Smul(nq, m_session->GetParameter("sigmaiy"), ggrad1, 1, ggrad1, 1);
                Vmath::Smul(nq, m_session->GetParameter("sigmaiz"), ggrad2, 1, ggrad2, 1);
                }
                // Add partial derivatives together
                Vmath::Vadd(nq, ggrad0, 1, ggrad1, 1, ggrad, 1);
                Vmath::Vadd(nq, ggrad2, 1, ggrad, 1, ggrad, 1);
                Vmath::Smul(nq, -1.0, ggrad, 1, ggrad, 1);
                // Multiply 1.0/timestep/lambda
                Vmath::Smul(nq, -factors[StdRegions::eFactorLambda], inarray[i], 1, temp, 1);
                Vmath::Vadd(nq, ggrad, 1, temp, 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(),NullFlagList,factors,m_vardiffi);
                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();                                         
                }                                
            }
            if (i == 1) {
                StdRegions::ConstFactorMap factors;
                factors[StdRegions::eFactorLambda] = 0.0;
                if (m_spacedim==1) {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(m_fields[0]->UpdatePhys(),grad0);
                // Take second derivative
                m_fields[i]->PhysDeriv(0,grad0,grad0);  
                // Multiply by Intracellular-Conductivity
        if (m_session->DefinesFunction("IntracellularConductivity") && m_session->DefinesFunction("ExtracellularConductivity"))
        {                
                Vmath::Smul(nq, m_session->GetParameter("sigmaix"), grad0, 1, grad0, 1);   
                }
                // and sum terms
                Vmath::Vcopy(nq, grad0, 1, grad, 1);
                Vmath::Smul(nq, (-1.0*m_session->GetParameter("sigmaix"))/(m_session->GetParameter("sigmaix")+m_session->GetParameter("sigmaix")), grad, 1, grad, 1);  
                // Now solve Poisson problem for \phi_e
                m_fields[i]->SetPhys(grad);
                m_fields[i]->HelmSolve(m_fields[i]->GetPhys(), m_fields[i]->UpdateCoeffs(), NullFlagList, factors);
                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();                                                         
                }
                
                if (m_spacedim==2) {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(m_fields[0]->UpdatePhys(),grad0,grad1);
                // Take second derivative
                m_fields[i]->PhysDeriv(0,grad0,grad0);
                m_fields[i]->PhysDeriv(1,grad1,grad1);  
                // Multiply by Intracellular-Conductivity
        if (m_session->DefinesFunction("IntracellularConductivity") && m_session->DefinesFunction("ExtracellularConductivity"))
        {                
                Vmath::Smul(nq, m_session->GetParameter("sigmaix"), grad0, 1, grad0, 1);
                Vmath::Smul(nq, m_session->GetParameter("sigmaiy"), grad1, 1, grad1, 1); 
                }
                // and sum terms
                Vmath::Vadd(nq, grad0, 1, grad1, 1, grad, 1);
                Vmath::Smul(nq, -1.0, grad, 1, grad, 1);   
                // Now solve Poisson problem for \phi_e
                m_fields[i]->SetPhys(grad);
                m_fields[i]->HelmSolve(m_fields[i]->GetPhys(), m_fields[i]->UpdateCoeffs(), NullFlagList, factors, m_vardiffie);
                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();                                                        
                }
                
                if (m_spacedim==3) {
                // Take first partial derivative
                m_fields[i]->PhysDeriv(m_fields[0]->UpdatePhys(),grad0,grad1,grad2);
                // Take second derivative
                m_fields[i]->PhysDeriv(0,grad0,grad0);
                m_fields[i]->PhysDeriv(1,grad1,grad1);
                m_fields[i]->PhysDeriv(2,grad2,grad2); 
                // Multiply by Intracellular-Conductivity
        if (m_session->DefinesFunction("IntracellularConductivity") && m_session->DefinesFunction("ExtracellularConductivity"))
        {                
                Vmath::Smul(nq, m_session->GetParameter("sigmaix"), grad0, 1, grad0, 1);
                Vmath::Smul(nq, m_session->GetParameter("sigmaiy"), grad1, 1, grad1, 1);
                Vmath::Smul(nq, m_session->GetParameter("sigmaiz"), grad2, 1, grad2, 1);       
                }
                // and sum terms
                Vmath::Vadd(nq, grad0, 1, grad1, 1, grad, 1);
                Vmath::Vadd(nq, grad2, 1, grad, 1, grad, 1);
                Vmath::Smul(nq, -1.0, grad, 1, grad, 1);  
                // Now solve Poisson problem for \phi_e
                m_fields[i]->SetPhys(grad);
                m_fields[i]->HelmSolve(m_fields[i]->GetPhys(), m_fields[i]->UpdateCoeffs(), NullFlagList, factors, m_vardiffie);
                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();                                                      
                }
                                                
            }
        }
    }

void Nektar::Bidomain::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 379 of file Bidomain.cpp.

References m_capMembrane, m_cell, Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::EquationSystem::m_session, m_stimDuration, Vmath::Smul(), and Vmath::Vadd().

Referenced by v_InitObject().

    {
        int nq = m_fields[0]->GetNpoints();
        m_cell->TimeIntegrate(inarray, outarray, time);
        if (m_stimDuration > 0 && time < m_stimDuration)
        {
            Array<OneD,NekDouble> x0(nq);
            Array<OneD,NekDouble> x1(nq);
            Array<OneD,NekDouble> x2(nq);
            Array<OneD,NekDouble> result(nq);
            // get the coordinates
            m_fields[0]->GetCoords(x0,x1,x2);
            LibUtilities::EquationSharedPtr ifunc
                    = m_session->GetFunction("Stimulus", "u");
            ifunc->Evaluate(x0,x1,x2,time, result);
            Vmath::Vadd(nq, outarray[0], 1, result, 1, outarray[0], 1);
        }        
        Vmath::Smul(nq, 1.0/m_capMembrane, outarray[0], 1, outarray[0], 1);
    }

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

protectedvirtual

Prints a summary of the model parameters.

Update summary

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 417 of file Bidomain.cpp.

References ASSERTL0, and m_cell.

    {
        UnsteadySystem::v_GenerateSummary(s);
        /// @TODO Update summary
        ASSERTL0(false, "Update the generate summary");
//
//        out << "\tChi         : " << m_chi << endl;
//        out << "\tCm          : " << m_capMembrane << endl;
//        if (m_session->DefinesFunction("IntracellularConductivity", "AnisotropicConductivityX") &&
//            m_session->GetFunctionType("IntracellularConductivity", "AnisotropicConductivityX") == LibUtilities::eFunctionTypeExpression)
//        {
//            out << "\tIntra-Diffusivity-x   : "
//                << m_session->GetFunction("IntracellularConductivity", "AnisotropicConductivityX")->GetExpression()
//                << endl;
//        }
//        if (m_session->DefinesFunction("IntracellularConductivity", "AnisotropicConductivityY") &&
//            m_session->GetFunctionType("IntracellularConductivity", "AnisotropicConductivityY") == LibUtilities::eFunctionTypeExpression)
//        {
//            out << "\tIntra-Diffusivity-y   : "
//                << m_session->GetFunction("IntracellularConductivity", "AnisotropicConductivityY")->GetExpression()
//                << endl;
//        }
//        if (m_session->DefinesFunction("IntracellularConductivity", "AnisotropicConductivityZ") &&
//            m_session->GetFunctionType("IntracellularConductivity", "AnisotropicConductivityZ") == LibUtilities::eFunctionTypeExpression)
//        {
//            out << "\tIntra-Diffusivity-z   : "
//                << m_session->GetFunction("IntracellularConductivity", "AnisotropicConductivityZ")->GetExpression()
//                << endl;
//        }
//        if (m_session->DefinesFunction("ExtracellularConductivity", "AnisotropicConductivityX") &&
//            m_session->GetFunctionType("ExtracellularConductivity", "AnisotropicConductivityX") == LibUtilities::eFunctionTypeExpression)
//        {
//            out << "\tExtra-Diffusivity-x   : "
//                << m_session->GetFunction("ExtracellularConductivity", "AnisotropicConductivityX")->GetExpression()
//                << endl;
//        }
//        if (m_session->DefinesFunction("ExtracellularConductivity", "AnisotropicConductivityY") &&
//            m_session->GetFunctionType("ExtracellularConductivity", "AnisotropicConductivityY") == LibUtilities::eFunctionTypeExpression)
//        {
//            out << "\tExtra-Diffusivity-y   : "
//                << m_session->GetFunction("ExtracellularConductivity", "AnisotropicConductivityY")->GetExpression()
//                << endl;
//        }
//        if (m_session->DefinesFunction("ExtracellularConductivity", "AnisotropicConductivityZ") &&
//            m_session->GetFunctionType("ExtracellularConductivity", "AnisotropicConductivityZ") == LibUtilities::eFunctionTypeExpression)
//        {
//            out << "\tExtra-Diffusivity-z   : "
//                << m_session->GetFunction("ExtracellularConductivity", "AnisotropicConductivityZ")->GetExpression()
//                << endl;
//        }
        m_cell->GenerateSummary(s);
    }

void Nektar::Bidomain::v_InitObject ( )

protectedvirtual

Init object for UnsteadySystem class.

Initialization object for UnsteadySystem class.

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 76 of file Bidomain.cpp.

References ASSERTL0, Nektar::LibUtilities::NekFactory< tKey, tBase, >::CreateInstance(), Nektar::LibUtilities::TimeIntegrationSchemeOperators::DefineImplicitSolve(), Nektar::LibUtilities::TimeIntegrationSchemeOperators::DefineOdeRhs(), DoImplicitSolve(), DoOdeRhs(), Nektar::StdRegions::eVarCoeffD00, Nektar::StdRegions::eVarCoeffD11, Nektar::StdRegions::eVarCoeffD22, Nektar::GetCellModelFactory(), m_capMembrane, m_cell, m_chi, Nektar::SolverUtils::UnsteadySystem::m_explicitDiffusion, Nektar::SolverUtils::EquationSystem::m_fields, Nektar::SolverUtils::UnsteadySystem::m_filters, Nektar::SolverUtils::UnsteadySystem::m_intVariables, Nektar::SolverUtils::UnsteadySystem::m_ode, Nektar::SolverUtils::EquationSystem::m_session, Nektar::SolverUtils::EquationSystem::m_spacedim, m_stimDuration, m_vardiffi, m_vardiffie, Nektar::FilterCheckpointCellModel::SetCellModel(), tmp1, tmp2, tmp3, and Vmath::Vadd().

    {
        UnsteadySystem::v_InitObject();
        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);
        m_intVariables.push_back(1);       
        // Load variable coefficients
        StdRegions::VarCoeffType varCoeffEnum[3] = {
                StdRegions::eVarCoeffD00,
                StdRegions::eVarCoeffD11,
                StdRegions::eVarCoeffD22
        };
        std::string varName[3] = {
                "AnisotropicConductivityX", 
                "AnisotropicConductivityY", 
                "AnisotropicConductivityZ"
        };
    if (m_session->DefinesFunction("IntracellularConductivity") && m_session->DefinesFunction("ExtracellularConductivity"))
    {
            for (int i = 0; i < m_spacedim; ++i)
                {
                    int nq = m_fields[0]->GetNpoints();
                    Array<OneD,NekDouble> x0(nq);
                    Array<OneD,NekDouble> x1(nq);
                    Array<OneD,NekDouble> x2(nq);
                    // get the coordinates
                    m_fields[0]->GetCoords(x0,x1,x2);
            tmp1 = Array<OneD, const Array<OneD, NekDouble> >(nq);
            tmp2 = Array<OneD, const Array<OneD, NekDouble> >(nq);
            tmp3 = Array<OneD, const Array<OneD, NekDouble> >(nq);
            tmp1[i] = Array<OneD, NekDouble>(nq);
            tmp2[i] = Array<OneD, NekDouble>(nq);
            tmp3[i] = Array<OneD, NekDouble>(nq);
                    LibUtilities::EquationSharedPtr ifunc1
                            = m_session->GetFunction("IntracellularConductivity", varName[i]);
                    LibUtilities::EquationSharedPtr ifunc2
                            = m_session->GetFunction("ExtracellularConductivity", varName[i]);
                    for(int j = 0; j < nq; j++)
                    {
                        tmp1[i][j] = ifunc1->Evaluate(x0[j],x1[j],x2[j],0.0);
                        tmp2[i][j] = ifunc2->Evaluate(x0[j],x1[j],x2[j],0.0);
                    }
            Vmath::Vadd(nq, tmp1[i], 1, tmp2[i], 1, tmp3[i], 1);
                    m_vardiffi[varCoeffEnum[i]] = tmp1[i];
                    m_vardiffie[varCoeffEnum[i]] = tmp3[i];
            }
        } 
        
        if (m_session->DefinesParameter("StimulusDuration"))
        {
            ASSERTL0(m_session->DefinesFunction("Stimulus", "u"),
                    "Stimulus function not defined.");
            m_session->LoadParameter("StimulusDuration", m_stimDuration);
        }
        else
        {
            m_stimDuration = 0;
        }
        // Search through the loaded filters and pass the cell model to any
        // CheckpointCellModel filters loaded.
        int k = 0;
        const LibUtilities::FilterMap& f = m_session->GetFilters();
        LibUtilities::FilterMap::const_iterator x;
        for (x = f.begin(); x != f.end(); ++x, ++k)
        {
            if (x->first == "CheckpointCellModel")
            {
                boost::shared_ptr<FilterCheckpointCellModel> c
                    = boost::dynamic_pointer_cast<FilterCheckpointCellModel>(
                                                                m_filters[k]);
                c->SetCellModel(m_cell);
            }
        }
        if (!m_explicitDiffusion)
        {
            m_ode.DefineImplicitSolve (&Bidomain::DoImplicitSolve, this);
        }
        m_ode.DefineOdeRhs(&Bidomain::DoOdeRhs, this);
    }

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

protectedvirtual

Sets a custom initial condition.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 406 of file Bidomain.cpp.

References m_cell.

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

Friends And Related Function Documentation

friend class MemoryManager< Bidomain >

friend

Definition at line 52 of file Bidomain.h.

Member Data Documentation

string Nektar::Bidomain::className

static

Initial value:

 GetEquationSystemFactory().RegisterCreatorFunction(
            "Bidomain",
            Bidomain::create,
            "Bidomain model of cardiac electrophysiology with 3D diffusion.")

Name of class.

Registers the class with the Factory.

Definition at line 64 of file Bidomain.h.

NekDouble Nektar::Bidomain::m_capMembrane

private

Definition at line 101 of file Bidomain.h.

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

CellModelSharedPtr Nektar::Bidomain::m_cell

private

Cell model.

Definition at line 99 of file Bidomain.h.

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

NekDouble Nektar::Bidomain::m_chi

private

Definition at line 101 of file Bidomain.h.

Referenced by DoImplicitSolve(), and v_InitObject().

NekDouble Nektar::Bidomain::m_sigmaex

private

Definition at line 101 of file Bidomain.h.

NekDouble Nektar::Bidomain::m_sigmaey

private

Definition at line 101 of file Bidomain.h.

NekDouble Nektar::Bidomain::m_sigmaez

private

Definition at line 101 of file Bidomain.h.

NekDouble Nektar::Bidomain::m_sigmaix

private

Definition at line 101 of file Bidomain.h.

NekDouble Nektar::Bidomain::m_sigmaiy

private

Definition at line 101 of file Bidomain.h.

NekDouble Nektar::Bidomain::m_sigmaiz

private

Definition at line 101 of file Bidomain.h.

NekDouble Nektar::Bidomain::m_stimDuration

private

Stimulus current.

Definition at line 111 of file Bidomain.h.

Referenced by DoOdeRhs(), and v_InitObject().

StdRegions::VarCoeffMap Nektar::Bidomain::m_vardiffi

private

Definition at line 103 of file Bidomain.h.

Referenced by DoImplicitSolve(), and v_InitObject().

StdRegions::VarCoeffMap Nektar::Bidomain::m_vardiffie

private

Definition at line 104 of file Bidomain.h.

Referenced by DoImplicitSolve(), and v_InitObject().

Array<OneD, Array<OneD, NekDouble> > Nektar::Bidomain::tmp1

private

Definition at line 106 of file Bidomain.h.

Referenced by v_InitObject().

Array<OneD, Array<OneD, NekDouble> > Nektar::Bidomain::tmp2

private

Definition at line 107 of file Bidomain.h.

Referenced by v_InitObject().

Array<OneD, Array<OneD, NekDouble> > Nektar::Bidomain::tmp3

private

Definition at line 108 of file Bidomain.h.

Referenced by v_InitObject().

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation