A novel, parallel PDE solver for unstructured grids

Abstract

We propose a new parallel domain decomposition algorithm to solve symmetric linear systems of equations derived from the discretization of PDEs on general unstructured grids of triangles or tetrahedra. The algorithm is based on a single-level Schwarz alternating procedure and a modified conjugate gradient solver. A single layer of overlap has been adopted in order to simplify the data-structure and minimize the overhead. This approach makes the global convergence rate to vary slightly with the number of domains and the algorithm becomes highly scalable. The algorithm has been implemented in FORTRAN 90 using MPI and hence portable to different architectures. Numerical experiments have been carried out on a SUNFIRE 15K parallel computer and there have been shown superlinear performance in some cases. © Springer-Verlag Berlin Heidelberg 2006.