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Numerical Treatment of Coupled Systems pp 73–85Cite as

Parallel Solvers for coupled FEM-BEM equations with applications to non-linear magnetic field problems

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Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NONUFM,volume 51))

Summary

An efficient parallel algorithm for solving nonlinear boundary value problems arising, e.g., in the magnetic field computation, is presented. It is based on both the idea of ”nested iteration” (also called Full Multilevel Method) and parallel domain decomposition (DD) solvers for the linear systems suited for computations on MIMD computers with local memory and message-passing principle. It makes use of the parallel data structure of these solvers, the linearization is done by Newton’s method, the linear system is solved by CG with DD preconditioning.

The DD approach allows us to couple Finite Element and Galerkin Boundary Element Methods in a unified variational problem. In this way, e.g., magnetic field problems in an infinite domain with Sommerfeld’s radiation condition can be modelled correctly. The problem of a nonsymmetric system matrix due to Galerkin-BEM is overcome by transforming it into a symmetric but indefinite matrix and applying Bramble/Pasciak’s CG for indefinite systems. For preconditioning, the main ideas of recent DD research are applied.

Test computations on a Power Xplorer parallel system were performed for model problems.

This research has been supported by the German Research Foundation DFG within the Priority Research Programme “Boundary Element Methods” under the grant La 767/1–3.

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Authors and Affiliations

  1. Institute of Mathematics, Johannes Kepler University Linz, Altenbergerstr. 69, A-4040, Linz, Austria

    Bodo Heise

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  1. Kiel, Germany

    Wolfgang Hackbusch  & Gabriel Wittum  & 

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© 1995 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

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Heise, B. (1995). Parallel Solvers for coupled FEM-BEM equations with applications to non-linear magnetic field problems. In: Hackbusch, W., Wittum, G. (eds) Numerical Treatment of Coupled Systems. Notes on Numerical Fluid Mechanics (NNFM), vol 51. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86859-6_7

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  • DOI: https://doi.org/10.1007/978-3-322-86859-6_7

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-322-86861-9

  • Online ISBN: 978-3-322-86859-6

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