EFFICIENCY, SCALABILITY, AND ROBUSTNESS OF PARALLEL MULTILEVEL METHODS FOR NONLINEAR PARTIAL-DIFFERENTIAL EQUATIONS

In this paper we compare the performance, scalability, and robustness of different parallel algorithms for the numerical solution of nonline ar boundary value problems arising in magnetic field computation and s olid mechanics. These problems are discretized by using the finite ele ment method with triangular meshes and piecewise-linear functions. The nonlinearity is handled by a nested Newton solver, and the linear sys tems of algebraic equations within each Newton step are solved by mean s 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 implement ation of all solvers is a nonoverlapping domain decomposition data str ucture such that they are well suited for parallel machines with MIMD architecture.