Summary.
The boundary element method (BEM) is of advantage in many applications including far-field computations in magnetostatics and solid mechanics as well as accurate computations of singularities. Since the numerical approximation is essentially reduced to the boundary of the domain under consideration, the mesh generation and handling is simpler than, for example, in a finite element discretization of the domain. In this paper, we discuss fast solution techniques for the linear systems of equations obtained by the BEM (BE-equations) utilizing the non-overlapping domain decomposition (DD). We study parallel algorithms for solving large scale Galerkin BE–equations approximating linear potential problems in plane, bounded domains with piecewise homogeneous material properties. We give an elementary spectral equivalence analysis of the BEM Schur complement that provides the tool for constructing and analysing appropriate preconditioners. Finally, we present numerical results obtained on a massively parallel machine using up to 128 processors, and we sketch further applications to elasticity problems and to the coupling of the finite element method (FEM) with the boundary element method. As shown theoretically and confirmed by the numerical experiments, the methods are of \(O(h^{-2})\) algebraic complexity and of high parallel efficiency, where \(h\) denotes the usual discretization parameter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received August 28, 1996 / Revised version received March 10, 1997
Rights and permissions
About this article
Cite this article
Carstensen, C., Kuhn, M. & Langer, U. Fast parallel solvers for symmetric boundary element domain decomposition equations. Numer. Math. 79, 321–347 (1998). https://doi.org/10.1007/s002110050342
Issue Date:
DOI: https://doi.org/10.1007/s002110050342