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Boundary Element Tearing and Interconnecting Domain Decomposition Methods

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Multifield Problems in Solid and Fluid Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 28))

Summary

The combination of non-overlapping domain decomposition methods with fast boundary element methods provides an efficient simulation tool to handle coupled boundary value problems with piecewise constant coefficients. Based on a standard boundary element domain decomposition formulation using the symmetric boundary integral representation of the Dirichlet to Neumann map, i.e., the Steklov—Poincaré operator, we have to solve a system of linear equations in parallel, where the assembled stiffness matrix is symmetric and positive definite. Instead, by using a boundary element tearing and interconnecting approach we have to solve a saddle point problem or the dual problem for finding the Lagrange multipliers. For this method, we describe different preconditioned solution strategies using both, local and global preconditioning techniques. All local boundary integral operators are realized via a fast multipole method leading to an almost optimal algorithm. Besides a rigorous mathematical analysis we give numerical examples and applications for the potential equation as well as for the system of linear elastostatics with jumping coefficients.

Research Project C10 “Domain Decomposition Methods”

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Authors and Affiliations

  1. Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Wolfgang L. Wendland

  2. Institute for Computational Mathematics, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria

    Günther Of & Olaf Steinbach

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  1. Günther Of
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  2. Olaf Steinbach
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Editors and Affiliations

  1. Institut für Wasserbau, Hydromechanik und Hydrosystemmodellierung, Universität Stuttgart, Pfaffenwaldring 61, 70569, Stuttgart, Germany

    Rainer Helmig

  2. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117, Berlin, Germany

    Alexander Mielke

  3. Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Barbara I. Wohlmuth

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Of, G., Steinbach, O., Wendland, W.L. (2006). Boundary Element Tearing and Interconnecting Domain Decomposition Methods. In: Helmig, R., Mielke, A., Wohlmuth, B.I. (eds) Multifield Problems in Solid and Fluid Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 28. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-34961-7_14

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