Preconditioning for boundary element methods in domain decomposition

This paper is concerned with asymptotically almost optimal preconditioning techniques for the solution of coupled elliptic problems with piecewise continuous coefficients: by domain decomposition methods. Spectrally equivalent, two- and multilevel interface preconditioners are proposed and analyzed. They are applied to two basic formulations: strongly elliptic skew symmetric problems and symmetric, positive definite variational problems: the former involves the classical boundary potentials from the Calderon projections and the latter is based on the Steklov-Poincare operators associated with subdomains of the decomposition. The preconditioners considered are shown to be robust with respect to both mesh-parameters and jumps in the coefficients. (C) 2001 Elsevier Science Ltd. All rights reserved.