FitzHugh-Nagumo model. More...

#include <FitzhughNagumo.h>

Inheritance diagram for Nektar::CellModelFitzHughNagumo:

Collaboration diagram for Nektar::CellModelFitzHughNagumo:

Public Member Functions
	CellModelFitzHughNagumo (const LibUtilities::SessionReaderSharedPtr &pSession, const MultiRegions::ExpListSharedPtr &pField)
virtual	~CellModelFitzHughNagumo ()
Public Member Functions inherited from Nektar::CellModel
	CellModel (const LibUtilities::SessionReaderSharedPtr &pSession, const MultiRegions::ExpListSharedPtr &pField)
virtual	~CellModel ()
void	Initialise ()
	Initialise the cell model storage and set initial conditions.
void	TimeIntegrate (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, const NekDouble time)
	Time integrate the cell model by one PDE timestep.
void	Update (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, const NekDouble time)
	Compute the derivatives of cell model variables.
void	GenerateSummary (SummaryList &s)
	Print a summary of the cell model.
unsigned int	GetNumCellVariables ()
std::string	GetCellVarName (unsigned int idx)
Array< OneD, NekDouble >	GetCellSolutionCoeffs (unsigned int idx)
Array< OneD, NekDouble >	GetCellSolution (unsigned int idx)

Static Public Member Functions
static CellModelSharedPtr	create (const LibUtilities::SessionReaderSharedPtr &pSession, const MultiRegions::ExpListSharedPtr &pField)
	Creates an instance of this class.

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

Protected Member Functions
virtual void	v_Update (const Array< OneD, const Array< OneD, NekDouble > > &inarray, Array< OneD, Array< OneD, NekDouble > > &outarray, const NekDouble time)
virtual void	v_GenerateSummary (SummaryList &s)
virtual void	v_SetInitialConditions ()
Protected Member Functions inherited from Nektar::CellModel
virtual std::string	v_GetCellVarName (unsigned int idx)
void	LoadCellModel ()

Private Attributes
NekDouble	m_beta
NekDouble	m_epsilon
Array< OneD, NekDouble >	m_uuu
	Temporary space for storing when computing reaction term.

Additional Inherited Members
Protected Attributes inherited from Nektar::CellModel
LibUtilities::SessionReaderSharedPtr	m_session
	Session.
MultiRegions::ExpListSharedPtr	m_field
	Transmembrane potential field from PDE system.
int	m_nq
	Number of physical points.
int	m_nvar
	Number of variables in cell model (inc. transmembrane voltage)
NekDouble	m_lastTime
	Timestep for pde model.
int	m_substeps
	Number of substeps to take.
Array< OneD, Array< OneD, NekDouble > >	m_cellSol
	Cell model solution variables.
Array< OneD, Array< OneD, NekDouble > >	m_wsp
	Cell model integration workspace.
bool	m_useNodal
	Flag indicating whether nodal projection in use.
StdRegions::StdNodalTriExpSharedPtr	m_nodalTri
	StdNodalTri for cell model calculations.
StdRegions::StdNodalTetExpSharedPtr	m_nodalTet
Array< OneD, Array< OneD, NekDouble > >	m_nodalTmp
	Temporary array for nodal projection.
std::vector< int >	m_concentrations
	Indices of cell model variables which are concentrations.
std::vector< int >	m_gates
	Indices of cell model variables which are gates.
Array< OneD, Array< OneD, NekDouble > >	m_gates_tau
	Storage for gate tau values.

Detailed Description

FitzHugh-Nagumo model.

Definition at line 44 of file FitzhughNagumo.h.

Constructor & Destructor Documentation

Nektar::CellModelFitzHughNagumo::CellModelFitzHughNagumo	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const MultiRegions::ExpListSharedPtr &	pField
	)

Definition at line 53 of file FitzhughNagumo.cpp.

References m_beta, Nektar::CellModel::m_concentrations, m_epsilon, Nektar::CellModel::m_nq, Nektar::CellModel::m_nvar, and m_uuu.

            : CellModel(pSession, pField)
    {
        pSession->LoadParameter("beta",          m_beta,         0.0);
        pSession->LoadParameter("epsilon",       m_epsilon,      1.0);
        m_uuu  = Array<OneD, NekDouble>(m_nq, 0.0);
        m_nvar = 2;
        m_concentrations.push_back(1);
    }

virtual Nektar::CellModelFitzHughNagumo::~CellModelFitzHughNagumo ( )

inlinevirtual

Definition at line 62 of file FitzhughNagumo.h.

{}

Member Function Documentation

static CellModelSharedPtr Nektar::CellModelFitzHughNagumo::create	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const MultiRegions::ExpListSharedPtr &	pField
	)

inlinestatic

Creates an instance of this class.

Definition at line 48 of file FitzhughNagumo.h.

        {
            return MemoryManager<CellModelFitzHughNagumo>::AllocateSharedPtr(pSession, pField);
        }

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

protectedvirtual

Implements Nektar::CellModel.

Definition at line 97 of file FitzhughNagumo.cpp.

References Nektar::SolverUtils::AddSummaryItem(), and m_beta.

    {
        SolverUtils::AddSummaryItem(s, "Cell model","FitzHugh-Nagumo");
        SolverUtils::AddSummaryItem(s, "Cell model beta", m_beta);
    }

void Nektar::CellModelFitzHughNagumo::v_SetInitialConditions ( )

protectedvirtual

Implements Nektar::CellModel.

Definition at line 107 of file FitzhughNagumo.cpp.

References Vmath::Fill(), Nektar::CellModel::m_cellSol, and Nektar::CellModel::m_nq.

    {
        Vmath::Fill(m_nq, 0.0,        m_cellSol[0],  1);
        Vmath::Fill(m_nq, 0.0,        m_cellSol[1],  1);
    }

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

protectedvirtual

Implements Nektar::CellModel.

Definition at line 68 of file FitzhughNagumo.cpp.

References m_beta, m_epsilon, Nektar::CellModel::m_nq, m_uuu, Vmath::Sadd(), Vmath::Smul(), Vmath::Svtvp(), Vmath::Vmul(), and Vmath::Vsub().

    {
        NekDouble m_gamma = 0.5;
        // compute u^2: m_u = u*u
        Vmath::Vmul(m_nq, &inarray[0][0], 1, &inarray[0][0], 1, &m_uuu[0], 1);
        // compute u^3: m_u = u*u*u
        Vmath::Vmul(m_nq, &inarray[0][0], 1, &m_uuu[0], 1, &m_uuu[0], 1);
        // For u: (1/m_epsilon)*( u*-u*u*u/3 - v )
        // physfield = u - (1.0/3.0)*u*u*u
        Vmath::Svtvp(m_nq, (-1.0/3.0), &m_uuu[0], 1, &inarray[0][0], 1, &outarray[0][0], 1);
        Vmath::Vsub(m_nq, &inarray[1][0], 1, &outarray[0][0], 1, &outarray[0][0], 1);
        Vmath::Smul(m_nq, -1.0/m_epsilon, &outarray[0][0], 1, &outarray[0][0], 1);
        // For v: m_epsilon*( u + m_beta - m_gamma*v )
        Vmath::Svtvp(m_nq, -1.0*m_gamma, &inarray[1][0], 1, &inarray[0][0], 1, &outarray[1][0], 1);
        Vmath::Sadd(m_nq, m_beta, &outarray[1][0], 1, &outarray[1][0], 1);
        Vmath::Smul(m_nq, m_epsilon, &outarray[1][0], 1, &outarray[1][0], 1);
    }

Member Data Documentation

std::string Nektar::CellModelFitzHughNagumo::className

static

Initial value:

 GetCellModelFactory().RegisterCreatorFunction(
                "FitzHughNagumo",
                CellModelFitzHughNagumo::create,
                "Phenomological model of squid nerve cell.")

Name of class.

Registers the class with the Factory.

Definition at line 56 of file FitzhughNagumo.h.

NekDouble Nektar::CellModelFitzHughNagumo::m_beta

private

Definition at line 75 of file FitzhughNagumo.h.

Referenced by CellModelFitzHughNagumo(), v_GenerateSummary(), and v_Update().

NekDouble Nektar::CellModelFitzHughNagumo::m_epsilon

private

Definition at line 76 of file FitzhughNagumo.h.

Referenced by CellModelFitzHughNagumo(), and v_Update().

Array<OneD, NekDouble> Nektar::CellModelFitzHughNagumo::m_uuu

private

Temporary space for storing $u^3$ when computing reaction term.

Definition at line 79 of file FitzhughNagumo.h.

Referenced by CellModelFitzHughNagumo(), and v_Update().

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation