Public Member Functions
	HeatEq1DNeumannBoundary (const double *thermalDiffusivity, unsigned nx, double spatialStep, double dt)

double	dt () const

double	time () const

unsigned	nCoords () const

double	intervalWidth () const

void	step ()

unsigned long	nSteps () const

double	gfWidth (unsigned index) const

Matrix< double >	GF () const

Matrix< double >	GFT () const

Matrix< double >	doublyStochasticGF (double tol, unsigned maxIter) const

Matrix< double >	doublyStochasticGFT (double tol, unsigned maxIter) const

Matrix< lapack_double >	diffScheme () const

double	maxAbsEigen () const

Constructor & Destructor Documentation

◆ HeatEq1DNeumannBoundary()

npstat::HeatEq1DNeumannBoundary::HeatEq1DNeumannBoundary	(	const double *	thermalDiffusivity,
		unsigned	nx,
		double	spatialStep,
		double	dt
	)

The number of spatial discretization points, nx, must be at least 3

Member Function Documentation

◆ diffScheme()

Matrix<lapack_double> npstat::HeatEq1DNeumannBoundary::diffScheme ( ) const

Matrix representing the differencing scheme. Note that this code is rather slow as it requires O(nx^3) operations.

◆ doublyStochasticGF()

Matrix<double> npstat::HeatEq1DNeumannBoundary::doublyStochasticGF	(	double	tol,
		unsigned	maxIter
	)		const

Doubly stochastic approximation to the Green's function. Arguments "tol" and "maxIter" will be passed to the "makeCopulaSteps" method of the ArrayND class used to build the approximation. If "maxIter" is 0, a less reliable non-iterative method will be used that can produce some negative entries in the matrix.

◆ doublyStochasticGFT()

Matrix<double> npstat::HeatEq1DNeumannBoundary::doublyStochasticGFT	(	double	tol,
		unsigned	maxIter
	)		const

Doubly stochastic approximation to the transposed Green's function. Arguments "tol" and "maxIter" will be passed to the "makeCopulaSteps" method of the ArrayND class used to build the approximation. If "maxIter" is 0, a less reliable non-iterative method will be used that can produce some negative entries in the matrix.

◆ dt()

double npstat::HeatEq1DNeumannBoundary::dt ( ) const

inline

A simple inspector of object properties

◆ GF()

Matrix<double> npstat::HeatEq1DNeumannBoundary::GF ( ) const

Note that the matrix representing the Green's Function changes after each step. To get the solution of the heat equation, multiply the GF matrix by the column of intitial conditions.

◆ GFT()

Matrix<double> npstat::HeatEq1DNeumannBoundary::GFT ( ) const

Transposed Green's function

◆ gfWidth()

double npstat::HeatEq1DNeumannBoundary::gfWidth ( unsigned index ) const

GF standard deviation for the given coordinate index. The index should be smaller than the "nx" argument provided in the constructor.

◆ maxAbsEigen()

double npstat::HeatEq1DNeumannBoundary::maxAbsEigen ( ) const

Maximum absolute eigenvalue of the differencing scheme matrix (for use in stability analysis). Note that this code is rather slow as it requires O(nx^3) operations.

◆ nSteps()

unsigned long npstat::HeatEq1DNeumannBoundary::nSteps ( ) const