An unconditionally stable second-order scheme for Maxwell's equations in the Cole–Cole dispersive medium

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-01-22 DOI:10.1016/j.apnum.2025.01.009

Jingjing Xiao , Desong Kong

引用次数: 0

Abstract

Coupling the averaged L1 scheme and the Crank–Nicolson scheme for temporal derivatives, we study Maxwell's equations in the Cole–Cole dispersive medium. A rigorous analysis is carried out to show that the proposed scheme is unconditionally stable and has a second-order convergence in time for sufficiently smooth solutions. We avoid using the mathematical induction method, which simplifies the analysis than the existing schemes. A fully discrete scheme with a finite difference method at Yee's grid is proposed. Numerical experiments are carefully designed to illustrate our theoretical analysis.

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Cole-Cole色散介质中麦克斯韦方程组的无条件稳定二阶格式

结合时间导数的平均L1格式和Crank-Nicolson格式，研究了Cole-Cole色散介质中的麦克斯韦方程组。严格的分析表明，该格式是无条件稳定的，并且对于足够光滑的解具有二阶收敛性。我们避免了使用数学归纳法，与现有方案相比简化了分析。提出了一种基于Yee网格的有限差分全离散格式。为了说明我们的理论分析，我们精心设计了数值实验。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.