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

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.

Characterization and integration of the singular test integrals in the method‐of‐moments implementation of the electric‐field integral equation

“…This work continues the efforts of Reference [38] by assessing the numerical errors from the basis functions and numerical integration together and separately for a manufactured Green's function, as well as the actual Green's function. We accomplish this by first measuring the error norms of the MoM implementation of the EFIE using the actual Green's function and considering the contributions from the magnetic vector potential and electric scalar potential separately and together.…”

“…Therefore, the usefulness of this approach alone in the context of code verification is limited. The solution-discretization error can be verified without contamination from numerical-integration error using the approach of Reference [38], whereas this assessment can confirm the singularities are integrated suitably.…”

“…However, as described in the introduction, not only is it impossible to analytically evaluate the integrals in V MSi (17), but the singular nature of the Green's function (4) when R → 0 complicates their accurate approximation, potentially contaminating convergence studies. In Reference [38], this problem is overcome by manufacturing a Green's function, such that ( 17) can be computed exactly. Alternatively, in this paper, we integrate (17) approximately but sufficiently accurately using the deterministic globally adaptive subdivision quadrature approach [41,42] in the Cuhre subroutine of the CUBA library [43].…”

“…where V MS (J h MS ) is computed using the definition in (17). For a manufactured Green's function G MS [38], V MS (J h MS ) in ( 21) can be computed exactly. For the actual Green's function G k (4), V MS (J h MS ) can be computed with sufficient accuracy using the CUBA library.…”

“…Code verification has been performed on computational physics codes associated with several physics disciplines, including fluid dynamics [20][21][22][23][24][25], solid mechanics [26], fluid-structure interaction [27], heat transfer in fluid-solid interaction [28], multiphase flows [29], radiation hydrodynamics [30], electrodynamics [31], and ablation [32][33][34][35]. For integral equations in computational electromagnetics, code-verification activities that employ manufactured solutions have been limited to the works of Marchand et al [36,37], through which the MMS source term is computed using additional quadrature points, and Freno et al [38], through which the Green's function is additionally manufactured, permitting the numerical-integration error to be eliminated and the solution-discretization error isolated.…”