Planewave density interpolation methods for the EFIE on simple and composite surfaces

TL;DR

This paper extends the planewave density interpolation (PWDI) method to the EFIE for scattering problems involving PEC objects, enabling regularized, easily computable surface integrals on simple and composite surfaces with complex geometries.

Contribution

The paper introduces an extension of PWDI to the EFIE, allowing regularized integral operators on complex, composite surfaces with non-conformal meshes, simplifying numerical evaluation.

Findings

Effective regularization of EFIE operators on complex surfaces.

Applicability to multi-scale and intricate structures.

Simplified numerical integration using elementary quadrature.

Abstract

This paper presents an extension of the recently introduced planewave density interpolation (PWDI) method to the electric field integral equation (EFIE) formulation of problems of scattering and radiation by perfect electric conducting (PEC) objects. Relying on Kirchhoff integral formula and local interpolation of surface current densities that regularize the kernel singularities, the PWDI method enables off- and on-surface EFIE operators to be re-expressed in terms of integrands that are globally bounded (or even more regular) over the whole domain of integration, regardless of the magnitude of the distance between target and source points. Surface integrals resulting from the application of the method-of-moments (MoM) using Rao-Wilton-Glisson (RWG) basis functions, can then be directly and easily evaluated by means of elementary quadrature rules irrespective of the singularity location. The proposed technique can be applied to simple and composite surfaces comprising two or more simply-connected overlapping components. The use of composite surfaces can significantly simplify the geometric treatment of complex structures, as the PWDI method enables the use of separate non-conformal meshes for the discretization of each of the surface components that make up the composite surface. A variety of examples, including multi-scale and intricate structures, demonstrate the effectiveness of the proposed methodology.