#include <AveragedSourceParabolicPde.hpp>

Inheritance diagram for AveragedSourceParabolicPde< DIM >:

Collaboration diagram for AveragedSourceParabolicPde< DIM >:

Public Member Functions
	AveragedSourceParabolicPde (AbstractCellPopulation< DIM, DIM > &rCellPopulation, double duDtCoefficient=1.0, double diffusionCoefficient=1.0, double sourceCoefficient=0.0)

const AbstractCellPopulation< DIM > &	rGetCellPopulation () const

virtual void	SetupSourceTerms (TetrahedralMesh< DIM, DIM > &rCoarseMesh, std::map< CellPtr, unsigned > *pCellPdeElementMap=nullptr)

virtual double	ComputeDuDtCoefficientFunction (const ChastePoint< DIM > &rX)

virtual double	ComputeSourceTerm (const ChastePoint< DIM > &rX, double u, Element< DIM, DIM > *pElement=NULL)

virtual double	ComputeSourceTermAtNode (const Node< DIM > &rNode, double u)

virtual c_matrix< double, DIM, DIM >	ComputeDiffusionTerm (const ChastePoint< DIM > &rX, Element< DIM, DIM > *pElement=NULL)

double	GetUptakeRateForElement (unsigned elementIndex)

Public Member Functions inherited from AbstractLinearParabolicPde< DIM, DIM >
	AbstractLinearParabolicPde ()

virtual	~AbstractLinearParabolicPde ()

virtual double	ComputeDuDtCoefficientFunction (const ChastePoint< SPACE_DIM > &rX)=0

virtual double	ComputeSourceTerm (const ChastePoint< SPACE_DIM > &rX, double u, Element< ELEMENT_DIM, SPACE_DIM > *pElement=nullptr)=0

virtual double	ComputeSourceTermAtNode (const Node< SPACE_DIM > &rNode, double u)

virtual c_matrix< double, SPACE_DIM, SPACE_DIM >	ComputeDiffusionTerm (const ChastePoint< SPACE_DIM > &rX, Element< ELEMENT_DIM, SPACE_DIM > *pElement=NULL)=0

Public Member Functions inherited from AbstractLinearPde< ELEMENT_DIM, SPACE_DIM >
	AbstractLinearPde ()

virtual	~AbstractLinearPde ()

Protected Attributes
AbstractCellPopulation< DIM, DIM > &	mrCellPopulation

double	mDuDtCoefficient

double	mDiffusionCoefficient

double	mSourceCoefficient

std::vector< double >	mCellDensityOnCoarseElements

Private Member Functions
template<class Archive >
void	serialize (Archive &archive, const unsigned int version)

Friends
class	TestCellBasedParabolicPdes

class	boost::serialization::access

Detailed Description

template<unsigned DIM>
class AveragedSourceParabolicPde< DIM >

A parabolic PDE to be solved numerically using the finite element method, for coupling to a cell-based simulation.

The PDE takes the form

c*du/dt = Grad.(D*Grad(u)) + k*u*rho(x),

where the scalars c, D and k are specified by the members mDuDtCoefficient, mDiffusionCoefficient and mSourceCoefficient, respectively. Their values must be set in the constructor.

The function rho(x) denotes the local density of non-apoptotic cells. This quantity is computed for each element of a 'coarse' finite element mesh that is passed to the method SetupSourceTerms() and stored in the member mCellDensityOnCoarseElements. For a point x, rho(x) is defined to be the number of non-apoptotic cells whose centres lie in each finite element containing that point, scaled by the area of that element.

Definition at line 66 of file AveragedSourceParabolicPde.hpp.

Constructor & Destructor Documentation

template<unsigned DIM>

AveragedSourceParabolicPde< DIM >::AveragedSourceParabolicPde	(	AbstractCellPopulation< DIM, DIM > &	rCellPopulation,
		double	duDtCoefficient = `1.0`,
		double	diffusionCoefficient = `1.0`,
		double	sourceCoefficient = `0.0`
	)

Constructor.

Parameters

rCellPopulation	reference to the cell population
duDtCoefficient	rate of reaction (defaults to 1.0)
diffusionCoefficient	rate of diffusion (defaults to 1.0)
sourceCoefficient	the source term coefficient (defaults to 0.0)

Definition at line 40 of file AveragedSourceParabolicPde.cpp.

Member Function Documentation

template<unsigned DIM>

c_matrix< double, DIM, DIM > AveragedSourceParabolicPde< DIM >::ComputeDiffusionTerm	(	const ChastePoint< DIM > &	rX,
		Element< DIM, DIM > *	pElement = `NULL`
	)

virtual

Overridden ComputeDiffusionTerm() method.

Parameters

rX	the point in space at which the diffusion term is computed
pElement	the mesh element that x is contained in (optional; defaults to NULL).

Returns: a matrix.

Definition at line 129 of file AveragedSourceParabolicPde.cpp.

References AveragedSourceParabolicPde< DIM >::mDiffusionCoefficient.

template<unsigned DIM>

double AveragedSourceParabolicPde< DIM >::ComputeDuDtCoefficientFunction ( const ChastePoint< DIM > & rX )

virtual

Overridden ComputeDuDtCoefficientFunction() method.

Returns: the function c(x) in "c(x) du/dt = Grad.(DiffusionTerm(x)*Grad(u))+LinearSourceTerm(x)+NonlinearSourceTerm(x, u)"

Parameters

rX	the point in space at which the function c is computed

Definition at line 104 of file AveragedSourceParabolicPde.cpp.

References AveragedSourceParabolicPde< DIM >::mDuDtCoefficient.

template<unsigned DIM>

double AveragedSourceParabolicPde< DIM >::ComputeSourceTerm	(	const ChastePoint< DIM > &	rX,
		double	u,
		Element< DIM, DIM > *	pElement = `NULL`
	)

virtual

Overridden ComputeSourceTerm() method.

Returns: computed source term.

Parameters

rX	the point in space at which the nonlinear source term is computed
u	the value of the dependent variable at the point
pElement	the mesh element that x is contained in (optional; defaults to NULL).

Definition at line 110 of file AveragedSourceParabolicPde.cpp.

References AbstractElement< ELEMENT_DIM, SPACE_DIM >::GetIndex(), AveragedSourceParabolicPde< DIM >::mCellDensityOnCoarseElements, and AveragedSourceParabolicPde< DIM >::mSourceCoefficient.

template<unsigned DIM>

double AveragedSourceParabolicPde< DIM >::ComputeSourceTermAtNode	(	const Node< DIM > &	rNode,
		double	u
	)

virtual

Overridden ComputeSourceTermAtNode() method. That is never called.

Returns: computed source term at a node.

Parameters

rNode	the node at which the nonlinear source term is computed
u	the value of the dependent variable at the node

Definition at line 121 of file AveragedSourceParabolicPde.cpp.

References NEVER_REACHED.

template<unsigned DIM>

double AveragedSourceParabolicPde< DIM >::GetUptakeRateForElement ( unsigned elementIndex )

Returns: the uptake rate.

Parameters

elementIndex the element we wish to return the uptake rate for

Definition at line 135 of file AveragedSourceParabolicPde.cpp.

References EXPORT_TEMPLATE_CLASS_SAME_DIMS, and AveragedSourceParabolicPde< DIM >::mCellDensityOnCoarseElements.

template<unsigned DIM>

const AbstractCellPopulation< DIM, DIM > & AveragedSourceParabolicPde< DIM >::rGetCellPopulation ( ) const

Returns: const reference to the cell population (used in archiving).

Definition at line 52 of file AveragedSourceParabolicPde.cpp.

References AveragedSourceParabolicPde< DIM >::mrCellPopulation.

template<unsigned DIM>

template<class Archive >

void AveragedSourceParabolicPde< DIM >::serialize	(	Archive &	archive,
		const unsigned int	version
	)

inlineprivate

Serialize the PDE and its member variables.

Parameters

archive	the archive
version	the current version of this class

Definition at line 81 of file AveragedSourceParabolicPde.hpp.

References AveragedSourceParabolicPde< DIM >::mCellDensityOnCoarseElements, AveragedSourceParabolicPde< DIM >::mDiffusionCoefficient, AveragedSourceParabolicPde< DIM >::mDuDtCoefficient, and AveragedSourceParabolicPde< DIM >::mSourceCoefficient.

template<unsigned DIM>

void AveragedSourceParabolicPde< DIM >::SetupSourceTerms	(	TetrahedralMesh< DIM, DIM > &	rCoarseMesh,
		std::map< CellPtr, unsigned > *	pCellPdeElementMap = `nullptr`
	)