{"title":"An adaptive DtN-FEM for the scattering problem from orthotropic media","authors":"Lei Lin , Junliang Lv , Tian Niu","doi":"10.1016/j.apnum.2024.11.013","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 140-154"},"PeriodicalIF":2.2000,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927424003210","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
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.
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.
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