正交各向同性介质散射问题的自适应 DtN-FEM

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-11-20 DOI:10.1016/j.apnum.2024.11.013

Lei Lin , Junliang Lv , Tian Niu

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引用次数: 0

摘要

本文研究正交无限圆柱体对电磁波的散射。这种散射问题被模拟为正交介质散射问题。通过构造 Dirichlet-to-Neumann (DtN) 算子并引入透明边界条件，正交介质问题被重新表述为有界边界值问题。利用截断的 DtN 边界算子，得出了有限元方法的后验误差估计值。后验误差估计包含有限元近似误差和 DtN 边界算子的截断误差，后者与截断参数成指数衰减。根据后验误差估计，提出了一种自适应有限元算法，用于求解各向同性介质问题。通过数值示例证明了所提方法的有效性和稳健性。

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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An adaptive DtN-FEM for the scattering problem from orthotropic media

This paper is concerned with scattering of electromagnetic waves by an orthotropic infinite cylinder. Such a scattering problem is modeled by a orthotropic media scattering problem. By constructing the Dirichlet-to-Neumann (DtN) operator and introducing a transparent boundary condition, the orthotropic media problem is reformulated as a bounded boundary value problem. An a posteriori error estimate is derived for the finite element method with the truncated DtN boundary operator. The a posteriori error estimate contains the finite element approximation error and the truncation error of the DtN boundary operator, where the latter decays exponentially with respect to the truncation parameter. Based on the a posteriori error estimate, an adaptive finite element algorithm is proposed for solving the orthotropic media problem. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed method.

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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.