The Galerkin method for a regularised combined field integral equation without a dual basis function

TL;DR

This paper introduces a Galerkin discretisation method for a regularised combined field integral equation that avoids the need for dual basis functions, simplifying computations and potentially improving efficiency.

Contribution

It presents a novel Galerkin discretisation of the regularised CFIE using only Rao-Wilton-Glisson basis functions, eliminating the need for dual basis functions.

Findings

Discretisation with Rao-Wilton-Glisson basis functions is feasible for regularised CFIE.

The proposed method simplifies implementation by avoiding dual basis functions.

Potential reduction in computational time compared to Calderon preconditioning.

Abstract

We propose discretisation of a regularised combined field integral equation (regularised CFIE) only with the Rao-Wilton-Glisson (RWG) basis function. The CFIE is a formulation of integral equations, which avoids the so-called ficticious frequencies of integral equations. The most typical CFIE, which is a linear combination of the electric field integral equation (EFIE) and magnetic field integral equation (MFIE), is known to be ill-conditioned and requires many iterations when solved with iteration methods such as the generalised minimum residual (GMRES) method. The regularised CFIE is another formulation of the CFIE to solve this problem by applying a regularising operator to the part of the EFIE. In several previous studies the regularising operator is determined based on the Calderon preconditioning. This regularising operator however takes much more computatonal time than the standard CFIE since discretising the EFIE with the Calderon preconditioner requires the dual basis function. In this article we propose a formulation of the regularised CFIE, which can be discretised with the Galerkin method without the dual basis function.