Acceleration of an iterative method for the evaluation of high-frequency multiple scattering effects

TL;DR

This paper introduces a new Krylov subspace method combined with Kirchhoff-based preconditioning to significantly speed up the evaluation of multiple scattering effects in high-frequency integral equation problems, reducing computational costs.

Contribution

The paper presents a novel Krylov subspace approach with Kirchhoff preconditioning that accelerates the convergence of Neumann series in high-frequency multiple scattering computations.

Findings

Accelerates convergence of multiple scattering evaluations.

Reduces overall computational cost.

Effective in geometrically challenging configurations.

Abstract

High frequency integral equation methodologies display the capability of reproducing single-scattering returns in frequency-independent computational times and employ a Neumann series formulation to handle multiple-scattering effects. This requires the solution of an enormously large number of single-scattering problems to attain a reasonable numerical accuracy in geometrically challenging configurations. Here we propose a novel and effective Krylov subspace method suitable for the use of high frequency integral equation techniques and significantly accelerates the convergence of Neumann series. We additionally complement this strategy utilizing a preconditioner based upon Kirchhoff approximations that provides a further reduction in the overall computational cost.