WKB Across Caustics: The Screened-WKB Method

TL;DR

This paper introduces a novel WKB-based method combined with FFTs for accurately simulating wave propagation through inhomogeneous media with caustics, achieving high precision and computational efficiency for large-scale problems.

Contribution

The paper presents a new WKB and FFT-based approach that accurately handles caustics and high-frequency wave propagation with significantly reduced computation times.

Findings

Accurately simulates radar wave propagation over large distances

Achieves errors as low as 0.1% to 0.001% in tests

Runs in a few minutes on a single CPU core

Abstract

We present a new methodology, based on the WKB approximation and Fast Fourier Transforms, for the evaluation of wave propagation through inhomogeneous media. This method can accurately resolve fields containing caustics, while still enjoying the computational advantages of the WKB approximation, namely, the ability to resolve arbitrarily high-frequency problems in computing times which are orders-of-magnitude shorter than those required by other algorithms presently available. For example, the proposed approach can simulate with high accuracy (with errors such as e.g. 0.1\%--0.001\%) the propagation of 5 cm radar signals across two-dimensional configurations resembling atmospheric ducting conditions, spanning hundreds of kilometers and millions of wavelengths in electrical size, in computing times of a few minutes in a single CPU core. [Preliminary version]