Modelling High-Frequency Backscattering from a Mesh of Curved Surfaces Using Kirchhoff Approximation

TL;DR

This paper introduces a numerical model using curved surface meshes and iterative integration to improve high-frequency backscattering calculations with Kirchhoff approximation, validated against exact solutions.

Contribution

It presents a novel numerical approach employing curved triangles and iterative integration for high-frequency backscattering modeling, overcoming limitations of flat facet methods.

Findings

Achieved accurate high-frequency backscattering results

Validated model against exact solutions

Demonstrated effectiveness of curved surface meshes

Abstract

The Kirchhoff approximation (K-A) to calculate the acoustic backscattering of a complex structure can be evaluated using a discretized version of its surface (i.e. a $\textit{mesh}$). From the computational viewpoint, the most accesible approach is the one based on flat facets. However, in the high frequency range, where the K-A provides good agreement and is therefore applicable, it requires a mesh with such a large number of facets that it turns impractical. To avoid these difficulties a mesh of curved triangles can be used to model the scatterer's complex structure. Previous computational implementations reported in the literature did not accomplish satisfactory results for high frequency. In this work we propose a numerical model based upon an iterative integration using Gauss-Legendre rules. The model was validated against exact solutions and led us to achieve adequate results in the high-frequency range.