{"title":"对比度和时间扩展对按时间行进的对比度电流密度体积积分方程的影响","authors":"Petrus W.N. van Diepen, M. C. Beurden, R. Dilz","doi":"10.2528/PIERB23091305","DOIUrl":null,"url":null,"abstract":"The contrast current density volume integral equation, discretized with piecewise constant spatial basis and test functions and Dirac-delta temporal test functions and the piecewise polynomial temporal basis functions, results in a causal implicit marching-on-in-time scheme that we refer to as the marching-on-in-time contrast current density volume integral equation (MOT-JVIE). The companion matrix stability analysis of the MOT-JVIE solver shows that for a fixed spatial and temporal step size, the stability is independent of the scatterer's dielectric contrast for quadratic spline temporal basis functions. Whereas, Lagrange and cubic spline exhibit instabilities at higher contrast. We relate this stability performance to the expansion and testing procedure in time. We further illustrate the capabilities of the MOT-JVIE based on quadratic spline temporal basis functions by: comparing the MOT-JVIE solution to time-domain results from literature and frequency-domain results from a commercial combined field integral equation solver. Finally, we present a long time sequence for a high-constrast scatterer discretized with 24,000 spatial unknowns.","PeriodicalId":20829,"journal":{"name":"Progress In Electromagnetics Research B","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Influence of Contrast and Temporal Expansion on the Marching-on-in-Time Contrast Current Density Volume Integral Equation\",\"authors\":\"Petrus W.N. van Diepen, M. C. Beurden, R. Dilz\",\"doi\":\"10.2528/PIERB23091305\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The contrast current density volume integral equation, discretized with piecewise constant spatial basis and test functions and Dirac-delta temporal test functions and the piecewise polynomial temporal basis functions, results in a causal implicit marching-on-in-time scheme that we refer to as the marching-on-in-time contrast current density volume integral equation (MOT-JVIE). The companion matrix stability analysis of the MOT-JVIE solver shows that for a fixed spatial and temporal step size, the stability is independent of the scatterer's dielectric contrast for quadratic spline temporal basis functions. Whereas, Lagrange and cubic spline exhibit instabilities at higher contrast. We relate this stability performance to the expansion and testing procedure in time. We further illustrate the capabilities of the MOT-JVIE based on quadratic spline temporal basis functions by: comparing the MOT-JVIE solution to time-domain results from literature and frequency-domain results from a commercial combined field integral equation solver. Finally, we present a long time sequence for a high-constrast scatterer discretized with 24,000 spatial unknowns.\",\"PeriodicalId\":20829,\"journal\":{\"name\":\"Progress In Electromagnetics Research B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Progress In Electromagnetics Research B\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2528/PIERB23091305\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Progress In Electromagnetics Research B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2528/PIERB23091305","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
The Influence of Contrast and Temporal Expansion on the Marching-on-in-Time Contrast Current Density Volume Integral Equation
The contrast current density volume integral equation, discretized with piecewise constant spatial basis and test functions and Dirac-delta temporal test functions and the piecewise polynomial temporal basis functions, results in a causal implicit marching-on-in-time scheme that we refer to as the marching-on-in-time contrast current density volume integral equation (MOT-JVIE). The companion matrix stability analysis of the MOT-JVIE solver shows that for a fixed spatial and temporal step size, the stability is independent of the scatterer's dielectric contrast for quadratic spline temporal basis functions. Whereas, Lagrange and cubic spline exhibit instabilities at higher contrast. We relate this stability performance to the expansion and testing procedure in time. We further illustrate the capabilities of the MOT-JVIE based on quadratic spline temporal basis functions by: comparing the MOT-JVIE solution to time-domain results from literature and frequency-domain results from a commercial combined field integral equation solver. Finally, we present a long time sequence for a high-constrast scatterer discretized with 24,000 spatial unknowns.
期刊介绍:
Progress In Electromagnetics Research (PIER) B publishes peer-reviewed original, comprehensive and tutorial review articles on all aspects of electromagnetic theory and applications. It is a new journal in 2008, and freely available to all readers via the Internet. Manuscripts submitted to PIER B must not have been submitted simultaneously to other journals. Authors are solely responsible for the factual accuracy of their articles, and all articles are understood to have received clearance(s) for publication.