Returns a sparse matrix for 2D Poisson PDE.
A = scibench_poissonA ( N )
a 1-by-1 matrix of doubles, integer values. The number of cells.
a m-by-m matrix of doubles, the sparse matrix where m = N^2.
We compute the numerical solution with finite differences for the Poisson problem with homogeneous Dirichlet boundary conditions.
We consider the 2 dimensional problem Partial Differential Equation:
where the Laplace operator is
We consider the domain 0 <= x1 <= 1, 0 <= x2 <= 1. The function f is defined by f(x, y) = -2pi^2 cos(2pix) sin^2(piy) - 2pi^2 sin^2(pix) cos(2piy). The solution is u(x, y) = sin^2(pix) sin^2(piy). We use a grid of N-by-N points. We use a second order finite difference approximation of the Laplace operator.
The Kronecker operator is used, so that the computation is vectorized.
stacksize("max"); A = scibench_poissonA(50); PlotSparse(A) | ![]() | ![]() |
"A Comparative Evaluation Of Matlab, Octave, Freemat, And Scilab For Research And Teaching", 2010, Neeraj Sharma and Matthias K. Gobbert