{"title":"手性介质中电磁波散射问题的分析与计算","authors":"Gang Bao, Lei Zhang","doi":"10.4310/cms.2024.v22.n3.a5","DOIUrl":null,"url":null,"abstract":"This paper considers an obstacle scattering problem in a chiral medium under circularly polarized oblique plane wave incidence, which can be represented as a combination of a left-circularly polarized plane wave and a right-circularly polarized one. We apply a reduced model problem with coupled oblique derivative boundary conditions, describing the cross-coupling effect of electric and magnetic fields. A novel boundary integral equation is constructed by introducing single-layer potential operators and the corresponding normal and tangential derivative operators. The corresponding properties are obtained by splitting techniques to overcome the singularity of integral operators. A numerical method for solving the boundary integral equation is developed, whose convergence is proved. Numerical results are presented to show the performance of the proposed method.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"6 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis and computation for the scattering problem of electromagnetic waves in chiral media\",\"authors\":\"Gang Bao, Lei Zhang\",\"doi\":\"10.4310/cms.2024.v22.n3.a5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper considers an obstacle scattering problem in a chiral medium under circularly polarized oblique plane wave incidence, which can be represented as a combination of a left-circularly polarized plane wave and a right-circularly polarized one. We apply a reduced model problem with coupled oblique derivative boundary conditions, describing the cross-coupling effect of electric and magnetic fields. A novel boundary integral equation is constructed by introducing single-layer potential operators and the corresponding normal and tangential derivative operators. The corresponding properties are obtained by splitting techniques to overcome the singularity of integral operators. A numerical method for solving the boundary integral equation is developed, whose convergence is proved. Numerical results are presented to show the performance of the proposed method.\",\"PeriodicalId\":50659,\"journal\":{\"name\":\"Communications in Mathematical Sciences\",\"volume\":\"6 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/cms.2024.v22.n3.a5\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cms.2024.v22.n3.a5","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Analysis and computation for the scattering problem of electromagnetic waves in chiral media
This paper considers an obstacle scattering problem in a chiral medium under circularly polarized oblique plane wave incidence, which can be represented as a combination of a left-circularly polarized plane wave and a right-circularly polarized one. We apply a reduced model problem with coupled oblique derivative boundary conditions, describing the cross-coupling effect of electric and magnetic fields. A novel boundary integral equation is constructed by introducing single-layer potential operators and the corresponding normal and tangential derivative operators. The corresponding properties are obtained by splitting techniques to overcome the singularity of integral operators. A numerical method for solving the boundary integral equation is developed, whose convergence is proved. Numerical results are presented to show the performance of the proposed method.
期刊介绍:
Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.