标题： 弯曲重力波的积分方程：分析与数值方法 显示英文标题

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

摘要： 在这项工作中，我们开发了一种快速且精确的方法，用于求解无限深度流体上方变厚度薄板对弯曲重力波的散射问题。 该问题通常出现在海冰和冰架的研究中，这些对象可能具有包括脊和卷的复杂异质性。 在对厚度作某些自然假设的基础上，我们提出了求解此类问题的积分方程公式，并分析了其数学性质。 然后使用高阶精度、FFT加速的算法对积分方程进行离散化和求解。 通过多种说明性例子展示了这种方法的速度、准确性和可扩展性。 显示英文摘要

摘要： 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.