Returns the A*u sparse product for 2D Poisson PDE.
v = scibench_poissonAu ( u )
a m-by-1 matrix of doubles, the vector.
a m-by-m matrix of doubles, the matrix-vector product v=A*u
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 matrix A is not stored: only the matrix-vector product v=A*u is performed.
"A Comparative Evaluation Of Matlab, Octave, Freemat, And Scilab For Research And Teaching", 2010, Neeraj Sharma and Matthias K. Gobbert