Abstract
In this paper we compare the performance, scalability, and robustness of different parallel algorithms for the numerical solution of nonlinear boundary value problems arising in magnetic field computation and solid mechanics. These problems are discretized by using the finite element method with triangular meshes and piecewise-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 nonoverlapping domain decomposition data structure such that they are well suited for parallel machines with MIMD architecture.
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