5 Point Stencil

Math 5620 Software Manual

Routine Name: void initMesh5(double start, double end, int meshSize)

Author: Tanner Wheeler

Language: C++. The code can be compiled using the cMake compiler.

Description/Purpose: This will define a mesh grid for your 5 point stencil. A matrix will be initialized from the Matrix class in Appendix B from the 5 point stencil constructor. This will then take the input from the function specified in code below and solve Ax = b using a LU factorization.

Input: Input includes: where is your starting point, where is your ending point, and the number of mxm grid size you want between them.

Output: This method will print the solution to the console when finished. It will not return any values.

Usage/Example: If I wanted to find all of the solution of the Laplace equation \Delta u = sin(xy) from starting point -1 and ending point 3 in the x and y directions with a mesh size of 3 I would enter:

initMesh5(-1, 3, 3);

This would then use the points (0, 0), (0, 1), (1, 0), (0, 2), (1, 1)… to initialize the right hand matrix and solve the equation.

Implementation/Code: The following is the code for ‘void initMesh5(double start, double end, int meshSize)’.

void initMesh5(double start, double end, int meshSize)
{
	double h = (end - start) / static_cast<double>(meshSize + 1);

	int size = meshSize * meshSize;

	Matrix f(size, 1, false);

	for (int i = 1; i <= meshSize; i++)
	{
		for (int j = 1; j <= meshSize; j++)
		{
			f.layout[((i-1) * meshSize) + (j-1)][0] = h * h * std::sin((start + (i * h))*(start + (j * h)));   
			// This is where you declare your function.
		}
	}

	Matrix mesh(meshSize);
	Matrix l(mesh.getM(), mesh.getN(), false);
	Matrix u(mesh.getM(), mesh.getN(), false);

	l_u_factorization(mesh, l, u);

	Matrix x = Gauss(u, Gauss(l, f));

	x.print();
}

Last Modified: February/2018