Iterative techniques for 3-D boundary element method systems of equations

A key issue in the boundary element method (BEM) is the solution of the associated system of algebraic equations whose matrices are dense, nonsymmetric and sometimes ill conditioned. For large scale tridimensional problems, direct methods like Gauss elimination become too expensive and iterative methods may be preferable. This paper presents a comparison of the performances of some iterative techniques based on conjugate gradient solvers as conjugate gradient squared (CGS) and bi-conjugate gradient (Bi-CG) that seem to have the potential to be efficient and competitive for BEM algebraic systems of equations, specially when used with an appropriate preconditioner. A comparison with the direct application of the conjugate gradient method to the normalized systems of equations (CGNE and CGNR) is also presented.