Accelerated Adaptive Error Control and Refinement for SIE Scattering Problems

Abstract

We present an application of adjoint-based adaptive error control and refinement for scattering problems solved using the method of moments (MoM) in the electric field integral equation (EFIE) and the coupled EFIE and magnetic field integral equation (MFIE) formulations. Specifically, we examine the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) formulation of the EFIE-MFIE. We first construct the adjoint problems of the EFIE and the EFIE-MFIE for estimating the error of radar cross section (RCS) quantities of interest (QoIs) directly. We then introduce an effective adaptive refinement algorithm based on an error prediction heuristic and a posteriori error estimation, which enables rapid and consistent convergence regardless of a chosen tolerance and the coarseness of the starting discretization. The approach, moreover, inherently promotes equilibration of the QoI error contributions and produces, therefore, consistently balanced meshes. Numerical examples with canonical scattering targets and adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -refinement confirm the strength of the proposed refinement method, demonstrating the ability to generate high-quality discretizations, both in terms of accuracy and efficiency, without expert user intervention.