Hierarchical bases preconditioner to enhance convergence of the CFIE with multiscale meshes

TL;DR

This paper introduces a hierarchical preconditioning technique that significantly improves the convergence of the Combined Field Integral Equation (CFIE) when dealing with multiscale meshes, especially in complex real-world electromagnetic problems.

Contribution

The paper applies a hierarchical quasi-Helmholtz decomposition combined with an algebraic preconditioner to enhance CFIE convergence for multiscale meshes, addressing challenges in electromagnetic simulations.

Findings

Effective in simple test cases

Performs well on real-life large-scale problems

Improves convergence speed and robustness

Abstract

A hierarchical quasi-Helmholtz decomposition, originally developed to address the low-frequency and dense-discretization breakdowns for the EFIE, is applied together with an algebraic preconditioner to improve the convergence of the CFIE in multiscale problems. The effectiveness of the proposed method is studied first on some simple examples; next, test on real-life cases up to several hundreds wavelengths show its good performance.