Elsevier

Parallel Computing

Volume 22, Issue 11, January 1997, Pages 1527-1544
Parallel Computing

Practical aspect and experience
Parallel solvers for nonlinear elliptic problems based on domain decomposition ideas

https://doi.org/10.1016/S0167-8191(96)00055-5Get rights and content

Abstract

In the present paper, the solution of nonlinear elliptic boundary value problems (b.v.p.) on parallel machines with Multiple Instruction Multiple Data (MIMD) architecture is discussed. Especially, we consider electro-magnetic field problems the numerical solution of which is based on finite element (FE) discretizations and a nested Newton solver. For solving the linear systems of algebraic FE equations in each Newton step, parallel conjugate gradient methods with a Domain Decomposition preconditioner (DD-PCG) as well as parallelized global multigrid (GMG) methods are applied. The implementation of the whole algorithm, i.e. the mesh generation, the generation of the FE equations, the nested Newton algorithm, the DD-PCG method and the GMG method, is based on a non-overlapping DD data structure.

The efficiency of the parallel DD-PCG methods and the parallelized GMG methods, which are embedded in the nested Newton solver, are compared. Furthermore, the performance on different machines (GC Power Plus, Multicluster with transputers T805, and workstation cluster) is demonstrated by numerical results.

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    This work is supported by the Austrian Science Fund — “Fonds zur Förderung der wissenschaftlichen Forschung” — under project P 11215-TEC.

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