Preconditioned GMRES on a 3D MOM code

We present the convergence history of preconditioned GMRES (generalized minimum residual) applied to a 3D moment method (MOM) code. GMRES is an iterative method for general unsymmetric systems of linear equations. It can be considered as a generalization of the conjugate gradient (CG) method which only applies to symmetric positive definite linear systems. If GMRES is applied to the impedance matrix equation ZJ=V/sub 1/, the method will converge in one iteration if Z were an identity matrix. Unfortunately, the matrix Z is never an identity matrix and is often not well-conditioned. Our goal is to have GMRES solve a linear system of equations with the coefficient matrix ´close´ to an identity matrix.