Example 9
This code solves a system corresponding to a discretization of the biharmonic problem treated as a system of equations on the unit square. Specifically, instead of solving Delta^2(u) = f with zero boundary conditions for u and Delta(u), we solve the system A x = b, where
A = [ Delta -I ; 0 Delta], x = [ u ; v] and b = [ 0 ; f] The corresponding boundary conditions are u = 0 and v = 0.
The domain is split into an N x N processor grid. Thus, the given number of processors should be a perfect square. Each processor's piece of the grid has n x n cells with n x n nodes. We use cell-centered variables, and, therefore, the nodes are not shared. Note that we have two variables, u and v, and need only one part to describe the domain. We use the standard 5-point stencil to discretize the Laplace operators. The boundary conditions are incorporated as in Example 3.
We recommend viewing Examples 3, 6 and 7 before this example.
Example 10
This code solves a system corresponding to a discretization of the Laplace equation with zero boundary conditions on the unit square. The domain is split into a n x n grid of quadrilateral elements and each processors owns a horizontal strip of size m x n, where m = n/nprocs. We use bilinear finite element discretization, so there are nodes (vertices) that are shared between neighboring processors. The Finite Element Interface is used to assemble the matrix and solve the problem. Nine different solvers are available.