Manufactured Solutions for the Method-of-Moments Implementation of the Electric-Field Integral Equation

TL;DR

This paper introduces a manufactured solutions approach for verifying the method-of-moments implementation of the electric-field integral equation, helping to isolate and verify discretization errors in computational electromagnetics.

Contribution

It presents a novel method to verify solution-discretization errors by manufacturing surface currents and Green's functions, reformulating the problem as an optimization with constraints.

Findings

Effective in isolating discretization errors

Works with and without coding errors

Reformulates poorly conditioned equations as optimization constraints

Abstract

Though the method-of-moments implementation of the electric-field integral equation plays an important role in computational electromagnetics, it provides many code-verification challenges due to the different sources of numerical error. In this paper, we provide an approach through which we can apply the method of manufactured solutions to isolate and verify the solution-discretization error. We accomplish this by manufacturing both the surface current and the Green's function. Because the arising equations are poorly conditioned, we reformulate them as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. We demonstrate the effectiveness of this approach for cases with and without coding errors.