An investigation of near-zone preconditioning techniques for integral equation solutions by method of moments

The iterative solution of linear equation systems resulting from Method of Moments (MoM) discretizations of integral equations is of particular attractiveness because of the possibility to employ fast integral methods such as the Multilevel Fast Multipole Method (MLFMM). However, the robustness of the iterative solvers is often still not satisfying and the search for improved preconditioners is an ongoing process. In this paper, we concentrate on two classical near-zone preconditioning techniques: Gauss-Seidel smoothing and a special form of incomplete LU factorization. It is found that Gauss-Seidel smoothing is a relatively cheap preconditioner working well for fine meshes. Our special form of incomplete LU factorization gives reliable convergence for complex problems with very bad convergence behavior, regardless of mesh density but for the cost of increased memory requirements.