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Welcome to the openmp-laplace wiki!

This code provides a tutorial on how to accelerate a Laplace solver using OpenMP 4.X to offload to GPUs.

Sorry that github does not nicely support latex (gitlab does…​.). This section will later be replaced by a pdf.

Mathematical Description:

Using finite differences to discretize the following differential equation -u_{xx}(x,y) - u_{yy}(x,y) = f(x,y), a<x,y<b,

over $N+2$ grid points leads to the following equations for the interior grid points

\frac{1}{h^2} (- u_{i-1} + 2 u_{i} - u_{i+1}) = f_i. \quad 1\leq i\leq N.

Rather than finding u, i.e. a direct solution of this linear algebra equation, we consider finding an approximate solution, $v$, via iterative solvers. The goal is to understand OpenMP offloading so we consider the weighted Jacobi method because of it’s simplicity (Colored Gauss-Sidel and SOR and even multigrid would be interesting tutorials that may come later).