Error analysis of the Moment Method

Because of the widespread use of the Method of Moments for simulation of radiation and scattering problems, analysis and control of solution error is a significant concern in computational electromagnetics. The physical problem to be solved, its mesh representation, and the numerical method all impact accuracy. Although empirical approaches such as benchmarking are used almost exclusively in practice for code validation and accuracy assessment, a number of significant theoretical results have been obtained in recent years, including proofs of convergence and solution-error estimates. This paper reviews fundamental concepts such as types of error measures, properties of the problem and numerical method that affect error, the optimality principle, and basic approximation error estimates. Analyses are given for surface-current and scattering-amplitude errors for several scatterers, including the effects of edge and corner singularities and quadrature error. We also review results on ill-conditioning due to resonance effects and the convergence rates of iterative linear-system solutions.