克莱因-戈登奇异波导的积分公式

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2024-10-06 DOI:10.1002/cpa.22227

Guillaume Bal, Jeremy Hoskins, Solomon Quinn, Manas Rachh

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引用次数: 0

摘要

我们考虑分析在二维空间中分隔绝缘相的奇异波导。绝缘域由大质量薛定谔方程建模，奇异波导由沿分隔绝缘体的一维界面的适当跃迁条件建模。我们提出了问题的积分公式，并分析了其数学特性。我们还实现了一种求解积分方程的快速多极和扫频加速迭代算法，并在数值上证明了这种方法的快速收敛性。几个求解和散射效应的数值示例说明了我们的理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Integral formulation of Klein–Gordon singular waveguides

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Integral formulation of Klein–Gordon singular waveguides

We consider the analysis of singular waveguides separating insulating phases in two-space dimensions. The insulating domains are modeled by a massive Schrödinger equation and the singular waveguide by appropriate jump conditions along the one-dimensional interface separating the insulators. We present an integral formulation of the problem and analyze its mathematical properties. We also implement a fast multipole and sweeping-accelerated iterative algorithm for solving the integral equations, and demonstrate numerically the fast convergence of this method. Several numerical examples of solutions and scattering effects illustrate our theory.

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.