A model for cardiac conduction. More...

#include <Bidomain.h>

Inheritance diagram for Nektar::Bidomain:

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

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 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
	Bidomain (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
	Constructor. More...

virtual void	v_InitObject ()

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...

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

virtual void	v_GenerateSummary (SummaryList &s)
	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...

virtual SOLVER_UTILS_EXPORT void	v_InitObject (bool DeclareField=true)
	Init object for UnsteadySystem class. 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_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 void	v_ExtraFldOutput (std::vector< Array< OneD, NekDouble >> &fieldcoeffs, std::vector< std::string > &variables)

Private Attributes
CellModelSharedPtr	m_cell
	Cell model. More...

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. More...

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). More...

NekDouble	m_cflNonAcoustic

NekDouble	m_CFLGrowth
	CFL growth rate. More...

NekDouble	m_CFLEnd
	maximun cfl in cfl growth More...

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. 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...

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

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 47 of file Bidomain.h.

Constructor & Destructor Documentation

◆ ~Bidomain()

Nektar::Bidomain::~Bidomain ( )

virtual

Desctructor.

Definition at line 165 of file Bidomain.cpp.

166 {

167 }

◆ Bidomain()

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

protected

Constructor.

Definition at line 68 of file Bidomain.cpp.

     : UnsteadySystem(pSession, pGraph)
 {
 }

Member Function Documentation

◆ create()

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

inlinestatic

Creates an instance of this class.

Definition at line 53 of file Bidomain.h.

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

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

◆ DoImplicitSolve()

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 175 of file Bidomain.cpp.

 {
     int nvariables = inarray.size();
     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(), 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(), 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(), 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(), 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(), 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(), 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();
             }
         }
     }
 }

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, Vmath::Smul(), Vmath::Vadd(), and Vmath::Vcopy().

Referenced by v_InitObject().

◆ DoOdeRhs()

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 417 of file Bidomain.cpp.

 {
     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);
 }

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().

◆ v_GenerateSummary()

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

protectedvirtual

Prints a summary of the model parameters.

@TODO Update summary

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 454 of file Bidomain.cpp.

 {
     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);
 }

References ASSERTL0, m_cell, and Nektar::SolverUtils::UnsteadySystem::v_GenerateSummary().

◆ v_InitObject()

void Nektar::Bidomain::v_InitObject ( )

protectedvirtual

Definition at line 74 of file Bidomain.cpp.

 {
     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.
     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 (!m_explicitDiffusion)
     {
         m_ode.DefineImplicitSolve(&Bidomain::DoImplicitSolve, this);
     }
     m_ode.DefineOdeRhs(&Bidomain::DoOdeRhs, this);
 }

◆ v_SetInitialConditions()

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 442 of file Bidomain.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< Bidomain >

friend class MemoryManager< Bidomain >

friend

Definition at line 1 of file Bidomain.h.

Member Data Documentation

◆ className

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.

◆ m_capMembrane

NekDouble Nektar::Bidomain::m_capMembrane

private

Definition at line 99 of file Bidomain.h.

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

◆ m_cell

CellModelSharedPtr Nektar::Bidomain::m_cell

private

Cell model.

Definition at line 97 of file Bidomain.h.

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

◆ m_chi

NekDouble Nektar::Bidomain::m_chi

private

Definition at line 99 of file Bidomain.h.

Referenced by DoImplicitSolve(), and v_InitObject().

◆ m_sigmaex

NekDouble Nektar::Bidomain::m_sigmaex

private

Definition at line 99 of file Bidomain.h.

◆ m_sigmaey

NekDouble Nektar::Bidomain::m_sigmaey

private

Definition at line 100 of file Bidomain.h.

◆ m_sigmaez

NekDouble Nektar::Bidomain::m_sigmaez

private

Definition at line 100 of file Bidomain.h.

◆ m_sigmaix

NekDouble Nektar::Bidomain::m_sigmaix

private

Definition at line 99 of file Bidomain.h.

◆ m_sigmaiy

NekDouble Nektar::Bidomain::m_sigmaiy

private

Definition at line 99 of file Bidomain.h.

◆ m_sigmaiz

NekDouble Nektar::Bidomain::m_sigmaiz

private

Definition at line 99 of file Bidomain.h.

◆ m_stimDuration

NekDouble Nektar::Bidomain::m_stimDuration

private

Stimulus current.

Definition at line 110 of file Bidomain.h.

Referenced by DoOdeRhs(), and v_InitObject().

◆ m_vardiffi

StdRegions::VarCoeffMap Nektar::Bidomain::m_vardiffi

private

Definition at line 102 of file Bidomain.h.

Referenced by DoImplicitSolve(), and v_InitObject().

◆ m_vardiffie

StdRegions::VarCoeffMap Nektar::Bidomain::m_vardiffie

private

Definition at line 103 of file Bidomain.h.

Referenced by DoImplicitSolve(), and v_InitObject().

◆ tmp1

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

private

Definition at line 105 of file Bidomain.h.

Referenced by v_InitObject().

◆ tmp2

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

private

Definition at line 106 of file Bidomain.h.

Referenced by v_InitObject().

◆ tmp3

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

private

Definition at line 107 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

◆ ~Bidomain()

◆ Bidomain()

Member Function Documentation

◆ create()

◆ DoImplicitSolve()

◆ DoOdeRhs()

◆ v_GenerateSummary()

◆ v_InitObject()

◆ v_SetInitialConditions()

Friends And Related Function Documentation

◆ MemoryManager< Bidomain >

Member Data Documentation

◆ className

◆ m_capMembrane

◆ m_cell

◆ m_chi

◆ m_sigmaex

◆ m_sigmaey

◆ m_sigmaez

◆ m_sigmaix

◆ m_sigmaiy

◆ m_sigmaiz

◆ m_stimDuration

◆ m_vardiffi

◆ m_vardiffie

◆ tmp1

◆ tmp2

◆ tmp3