MathTL::CornerTimeSingularity Class Reference

#include <corner_singularity.h>

Inheritance diagram for MathTL::CornerTimeSingularity:

List of all members.

Public Member Functions
	CornerTimeSingularity (const Point< 2 > &x0, const double theta0, const double omega)
virtual	~CornerTimeSingularity ()
	destructor
double	value (const Point< 2 > &x, const unsigned int component=0) const
	point value at x
void	vector_value (const Point< 2 > &p, Vector< double > &values) const
	vector-valued value at x (for compatibility with Function)
Protected Attributes
Point< 2 >	x0
	corner
double	theta0
	starting angle
double	omega
	inner angle

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Detailed Description

A time--dependent corner singularity function w.r.t. to the reentrant corner at x0 in a polygonal domain in R^2. In polar coordinates w.r.t. the corner, the function looks like

s(r,theta) = t^{3/4}*r^{pi/omega}*sin((pi/omega)*theta)*(1-x^2)*(1-y^2)

with x=r*cos(theta0+theta), y=r*sin(theta0+theta).

This function was used in [GSS+] as a test function for the heat equation on the L--shaped domain in R^2.

References: [GSS+]

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Constructor & Destructor Documentation

MathTL::CornerTimeSingularity::CornerTimeSingularity	(	const Point< 2 > &	x0,
		const double	theta0,
		const double	omega
	)

constructor from a corner x0, a starting angle theta0 (times pi, against positive x-axis) and an inner angle omega (times pi);

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

• numerics/corner_singularity.h
• numerics/corner_singularity.cpp