{"title":"多连通域间稳定FDTD相互作用的离散格林函数对光","authors":"B. P. de Hon, J. Arnold","doi":"10.1109/ICEAA.2007.4387393","DOIUrl":null,"url":null,"abstract":"We have developed FDTD boundary conditions based on discrete Green's function diakoptics for arbitrary multiply-connected 2D domains. The associated Z-domain boundary operator is symmetric, with an imaginary part that can be proved to be positive semi-definite on the upper half of the unit circle in the complex Z-plane. Through Schwarz' exterior formula an integral representation of this operator is obtained that is analytic outside that unit circle. A quadrature-rule based rational approximation of the operator corresponds to a self-consistent finite-lookback scheme in the discretised time domain. This scheme is demonstrably stable, in that only secular, non-growing, source-free solutions remain, which may be suppressed.","PeriodicalId":273595,"journal":{"name":"2007 International Conference on Electromagnetics in Advanced Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Discrete Green's function diakoptics for stable FDTD interaction between multiply-connected domains\",\"authors\":\"B. P. de Hon, J. Arnold\",\"doi\":\"10.1109/ICEAA.2007.4387393\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We have developed FDTD boundary conditions based on discrete Green's function diakoptics for arbitrary multiply-connected 2D domains. The associated Z-domain boundary operator is symmetric, with an imaginary part that can be proved to be positive semi-definite on the upper half of the unit circle in the complex Z-plane. Through Schwarz' exterior formula an integral representation of this operator is obtained that is analytic outside that unit circle. A quadrature-rule based rational approximation of the operator corresponds to a self-consistent finite-lookback scheme in the discretised time domain. This scheme is demonstrably stable, in that only secular, non-growing, source-free solutions remain, which may be suppressed.\",\"PeriodicalId\":273595,\"journal\":{\"name\":\"2007 International Conference on Electromagnetics in Advanced Applications\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-11-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2007 International Conference on Electromagnetics in Advanced Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICEAA.2007.4387393\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2007 International Conference on Electromagnetics in Advanced Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICEAA.2007.4387393","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Discrete Green's function diakoptics for stable FDTD interaction between multiply-connected domains
We have developed FDTD boundary conditions based on discrete Green's function diakoptics for arbitrary multiply-connected 2D domains. The associated Z-domain boundary operator is symmetric, with an imaginary part that can be proved to be positive semi-definite on the upper half of the unit circle in the complex Z-plane. Through Schwarz' exterior formula an integral representation of this operator is obtained that is analytic outside that unit circle. A quadrature-rule based rational approximation of the operator corresponds to a self-consistent finite-lookback scheme in the discretised time domain. This scheme is demonstrably stable, in that only secular, non-growing, source-free solutions remain, which may be suppressed.