Comparative Analysis of Different Preconditioning Methods in Electromagnetic Scattering Problems using MoM-FMM

The numerical solution of the electric field integral equation in electromagnetic scattering problems involving metallic bodies, using the method of moments in conjunction with the fast multipole method, gives rise a full matrix with highly spread complex eigenvalues and consequently with a low condition number. Thus, iterative methods may not converge or it will require an extremely large number of iterations, which make this strategy unfeasible due to the high solution time and the expensive computational resources required. To overcome this drawback, the system matrix must be preconditioned to ensure the convergence in a reasonable number of iterations and with appropriate accuracy. In this work, some preconditioning techniques are revised and applied to a linear equation system derived from such type of problems, and the performance of these preconditioners is estimated and analyzed comparatively using the generalized minimal residual iterative method.