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Parallel solvers for linear and nonlinear exterior magnetic field problems based upon coupled FE/BE Formulations

Parallele Lösungsstrategien für lineare und nichtlineare Außenraum-Magnetfeldprobleme auf der Grundlage gekoppelter Finite Elemente/Randelemente-Formulierungen

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Abstract

An efficient parallel algorithm for solving linear and nonlinear exterior boundary value problems arising, e.g., in magnetostatics is presented. It is based upon the domaindecomposition-(DD)-coupling of Finite Element and Galerkin Boundary Element Methods which results in a unified variational formulation. In this way, e.g., magnetic field problems in an unbounded 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 being applied. Test computations on a multiprocessor system were performed for two problems of practical interest including a nonlinear example.

Zusammenfassung

In der vorliegenden Arbeit wird ein effizienter paralleler Algorithmus zur Lösung linearer und nichtlinearer Außenraumprobleme, wie sie z.B. in der Magnetostatik auftreten, beschrieben. Er basiert auf der Kopplung der Finite Elemente Methode mit der Galerkin-Randelementmethode mit Hilfe von Gebietszerlegungstechniken über eine einheitliche Variationsformulierung. Auf diese Weise können z.B. Magnetfeldprobleme mit der Sommerfeldschen Abstrahlbedingung vollständig modelliert werden. Die durch die Galerkin-Randelementmethode entstehende nichtsymmetrische Matrix wird in eine symmetrische indefinite Matrix transformiert, um Bramble/Pasciak's CG-Verfahren für indefinite Systeme anzuwenden. Zur Vorkonditionierung werden die neuesten Resultate auf dem Gebiet der Gebietszerlegungsmethoden genutzt. Numerische Resultate, die für zwei praktisch interessante Probleme, darunter ein nichtlineares, auf einem Mehrprozessorsystem erhalten wurden, werden diskutiert.

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Authors and Affiliations

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

    B. Heise & M. Kuhn

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  1. B. Heise
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  2. M. Kuhn
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This research has been supported by the German Research Foundation DFG within the Priority Research Programme “Boundary Element Methods” under Grant La 767/1-3.

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Heise, B., Kuhn, M. Parallel solvers for linear and nonlinear exterior magnetic field problems based upon coupled FE/BE Formulations. Computing 56, 237–258 (1996). https://doi.org/10.1007/BF02238514

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  • DOI: https://doi.org/10.1007/BF02238514

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