TestCaseTransient Class Reference

The TestCaseTransient class provides definition of test cases. More...

#include <TestCaseTransient.hpp>

Public Member Functions
	TestCaseTransient (const std::vector< int > iTC, const double mPME)
	Initialise data.
std::function< double(const double &, const VectorRd &)>	solution ()
	Returns the exact solution at time t and point p.
std::function< VectorRd(const double &, const VectorRd &, const Cell *)>	grad_solution ()
std::function< Eigen::Matrix2d(const double &, const VectorRd &, const Cell *)>	hess_solution ()
	Note: the Hessian for the Barenblatt solution is NOT computed (left at 0) as it is not useful to compute the source term.
std::function< double(const double &, const VectorRd &)>	delt_solution ()
	Returns the time derivative of the exact solution at time t and point p.
Eigen::Matrix2d	diff (const double x, const double y, const Cell *cell)
	Returns the diffusion matrix at the point x, y (not depending on time for the moment)
Eigen::Vector2d	div_diff (const double x, const double y, const Cell *cell)
	Returns the divergence by row of the diffusion matrix at the point x, y.
double	minus_div_diff_grad (const double t, const double x, const double y, const Cell *cell)
	Returns -div(diff \nabla) of the exact solution at the point t, x, y.
double	get_lambda ()
	Returns the value of the parameter lambda.
void	validate ()
	Check if the provided test cases are valid (within range, and combination of solution/diffusion valid)
size_t	get_deg_diff ()
	Returns the degree of the diffusion tensor (useful to set up quadrature rules of proper degree)

Detailed Description

The TestCaseTransient class provides definition of test cases.

Constructor & Destructor Documentation

TestCaseTransient()

TestCaseTransient::TestCaseTransient	(	const std::vector< int >	iTC,
		const double	mPME
	)

Initialise data.

Parameters

iTC	The vector id of the test case: (id of solution, id of diffusion)
mPME	PME power, for the Barenblatt solution

Member Function Documentation

delt_solution()

std::function< double(const double &, const VectorRd &)> TestCaseTransient::delt_solution

(

)

Returns the time derivative of the exact solution at time t and point p.

diff()

Eigen::Matrix2d TestCaseTransient::diff	(	const double	x,
		const double	y,
		const Cell *	cell
	)

Returns the diffusion matrix at the point x, y (not depending on time for the moment)

iTC[1]=1: Diff = Id

iTC[1]=2: Diff = \(\left[\begin{array}{cc}y^2+1 & -xy\\ -xy & x^2+1\end{array}\right]\)

iTC[1]=3: Diff= \(\left[\begin{array}{cc}\lambda & 0\\ 0 & 1\end{array}\right]\) if \(y<1/2\), Diff=Id if \(y\ge 1/2\). Only valid with iTC[0]=2 ( \(\partial_x u\) must vanish along \(y=1/2\)).

iTC[1]=4: rotating diffusion. Diff= \(\left[\begin{array}{cc}\epsilon \bar{x}^2 + \bar{y}^2 & (\epsilon-1)\bar{x}\bar{y}\\ (\epsilon-1)\bar{x}\bar{y} & \bar{x}^2+\epsilon \bar{y}^2\end{array}\right]\), where \(\bar{x}=x+0.1\) and \(\bar{y}=y+0.1\).

iTC[1]=5: Diff= \(\left[\begin{array}{cc}\lambda & 0\\ 0 & 1\end{array}\right]\).

Parameters

cell	In case of discontinuity, we need to know the cell we're in to select the correct formula

div_diff()

Eigen::Vector2d TestCaseTransient::div_diff	(	const double	x,
		const double	y,
		const Cell *	cell
	)

Returns the divergence by row of the diffusion matrix at the point x, y.

Parameters

cell	In case of discontinuity, we need to know the cell we're in to select the correct formula

get_deg_diff()

size_t TestCaseTransient::get_deg_diff ( )

inline

Returns the degree of the diffusion tensor (useful to set up quadrature rules of proper degree)

get_lambda()

double TestCaseTransient::get_lambda ( )

inline

Returns the value of the parameter lambda.

grad_solution()

std::function< VectorRd(const double &, const VectorRd &, const Cell *)> TestCaseTransient::grad_solution

(

)

Returns the gradient of the exact solution at time t and point p In case of discontinuity, we need to know the cell we're in to select the correct formula Note: the gradient for the Barenblatt solution is NOT computed (left at 0) as it is not useful to compute the source term

hess_solution()

std::function< Eigen::Matrix2d(const double &, const VectorRd &, const Cell *)> TestCaseTransient::hess_solution

(

)

Note: the Hessian for the Barenblatt solution is NOT computed (left at 0) as it is not useful to compute the source term.

Returns the Hessian of the exact solution at time t and point p

minus_div_diff_grad()

double TestCaseTransient::minus_div_diff_grad	(	const double	t,
		const double	x,
		const double	y,
		const Cell *	cell
	)

Returns -div(diff \nabla) of the exact solution at the point t, x, y.

Parameters

cell	In case of discontinuity, we need to know the cell we're in to select the correct formula

solution()

std::function< double(const double &, const VectorRd &)> TestCaseTransient::solution

(

)

Returns the exact solution at time t and point p.

iTC[0]=1: \(u(x,y)=cos(t) sin(\pi x) sin(\pi y)\)

iTC[0]=2: \(u(x,y)=cos(t) cos(\pi x) cos(\pi y)\)

iTC[0]=3: \(u(x,y)= (1-t) x\)

iTC[0]=4: Barenblatt solution (with offset)

validate()

void TestCaseTransient::validate

(

)

Check if the provided test cases are valid (within range, and combination of solution/diffusion valid)

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The documentation for this class was generated from the following files:

• Schemes/TestCase/TestCaseTransient.hpp
• Schemes/TestCase/TestCaseTransient.cpp