Integral equations for flexural-gravity waves: analysis and numerical methods
Numerical Analysis
2025-01-03 v1 Numerical Analysis
Geophysics
Abstract
In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This problem commonly arises in the study of sea ice and ice shelves, which can have complicated heterogeneities that include ridges and rolls. With certain natural assumptions on the thickness, we present an integral equation formulation for solving this class of problems and analyze its mathematical properties. The integral equation is then discretized and solved using a high-order-accurate, FFT-accelerated algorithm. The speed, accuracy, and scalability of this approach are demonstrated through a variety of illustrative examples.
Cite
@article{arxiv.2501.00887,
title = {Integral equations for flexural-gravity waves: analysis and numerical methods},
author = {Travis Askham and Jeremy G. Hoskins and Peter Nekrasov and Manas Rachh},
journal= {arXiv preprint arXiv:2501.00887},
year = {2025}
}