Iterative solvers for BEM algebraic systems of equations

A key issue in the boundary element method (BEM) is the solution of the associated system of algebraic equations with matrices that are dense and sometimes ill-conditioned. For tridimensional problems, with large scale systems (several thousands of equations) direct methods like Gauss elimination become too expensive and iterative methods may be preferable. For these problems there are already many algorithms, namely for general non-symmetric systems. Most of them can be viewed as Lanczos or conjugate gradient-like methods. Here we present some iterative techniques based on conjugate gradient solvers as descent methods (DM), bi-conjugate gradient (Bi-CG), conjugate gradient squared (CGS) and bi-conjugate gradient stab (Bi-CGstab), that seem to have the potential to be competitive for BEM algebraic systems of equations, especially when used with an appropriate preconditioner. (C) 1998 Elsevier Science Ltd. All rights reserved.