Numerische Simulation Auf Massiv Parallelen Rechnern Preprint-reihe Des Chemnitzer Sfb 393

In this paper we compare the performance, scalability, and robustness of diierent parallel algorithms for the numerical solution of nonlinear boundary value problems arising in the magnetic eld computation and in solid mechanics. These problems are discretized by using the nite element method with triangular meshes and piece-wise linear functions. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely multigrid methods and conjugate gradient methods with preconditioners based on domain decomposition, multigrid, or BPX techniques, respectively. The basis of the implementation of all solvers is a non-overlapping domain decomposition data structure such that they are well-suited for parallel machines with MIMD architecture.