A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media

TL;DR

This paper introduces a modified Born series method for efficiently and accurately solving the inhomogeneous Helmholtz equation in large media, outperforming traditional pseudospectral time-domain simulations in speed and precision.

Contribution

A novel convergent Born series approach that enables fast and accurate solutions for large-scale scattering problems in arbitrary media.

Findings

Two orders of magnitude faster than pseudospectral methods

Nine orders of magnitude more accurate in benchmark tests

Effective for arbitrarily large and strong scattering media

Abstract

We present a fast method for numerically solving the inhomogeneous Helmholtz equation. Our iterative method is based on the Born series, which we modified to achieve convergence for scattering media of arbitrary size and scattering strength. Compared to pseudospectral time-domain simulations, our modified Born approach is two orders of magnitude faster and nine orders of magnitude more accurate in benchmark tests in 1-dimensional and 2-dimensional systems.