Integral equations for flexural-gravity waves: analysis and numerical methods

TL;DR

This paper introduces a fast, accurate integral equation method with FFT acceleration for modeling flexural-gravity wave scattering by heterogeneous thin plates, relevant to sea ice and ice shelf studies.

Contribution

It develops a novel integral equation formulation and high-order numerical algorithm for efficient simulation of complex flexural-gravity wave interactions.

Findings

Method achieves high accuracy and speed.

Algorithm scales well with problem size.

Demonstrated effectiveness on realistic sea ice models.

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.