FAST PARALLEL SOLVERS FOR SYMMETRICAL BOUNDARY-ELEMENT DOMAIN DECOMPOSITION EQUATIONS

The boundary element method (BEM) is of advantage in many applications including far-field computations in magnetostatics and solid mechanic s as well as accurate computations of singularities. Since the numeric al 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 thi s paper, we discuss fast solution techniques for the linear systems of equations obtained by the BEM (BE-equations) utilizing the non-overla pping domain decomposition (DD), We study parallel algorithms for solv ing large scale Galerkin BE-equations approximating linear potential p roblems in plane,bounded domains with piecewise homogeneous material p roperties. We give an elementary spectral equivalence analysis of the BEM Schur complement that provides the tool for constructing and analy sing appropriate preconditioners. Finally, we present numerical result s 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 experime nts, the methods are of O(h(-2)) algebraic complexity and of high para llel efficiency, where h denotes the usual discretization parameter.