{"title":"跨越式复散隐式时域有限差分法的入射平面波源公式","authors":"Shuo Liu;Eng Leong Tan;Bin Zou","doi":"10.1109/JMMCT.2022.3164679","DOIUrl":null,"url":null,"abstract":"The commonly used unconditionally stable finite-difference time-domain (FDTD) methods such as alternating direction implicit (ADI)-FDTD, and its one-step formulation, leapfrog ADI-FDTD, have been found to violate the divergence condition of Gauss's law. The recently proposed leapfrog complying-divergence implicit (CDI)-FDTD not only addresses this problem, but also features many advantages, including unconditional stability, minimal floating-point operations and one-step leapfrog update. To further expand its application, this paper presents the incident plane-wave source formulations for leapfrog CDI-FDTD. Two stable and efficient formulations with different advantages are presented for introducing the far-zone plane-wave source into the FDTD problem space, namely, the scattered-field (SF) formulation and total-field / scattered field (TF/SF) formulation. To deal with the discontinuity and inconsistency across TF/SF boundaries, the fields on the boundaries need special treatments with careful modifications to ensure stability and proper plane-wave injection. Numerical results show that the incident fields can be effectively injected into the problem space with the stability of leapfrog CDI-FDTD maintained in both formulations. In addition, comparisons of radar cross sections computed using leapfrog CDI-FDTD, leapfrog ADI-FDTD and explicit FDTD with both SF and TF/SF formulations are presented. These demonstrate the advantages of leapfrog CDI-FDTD method in solving far-zone plane-wave source problems, including high efficiency, unconditional stability and complying divergence.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Incident Plane-Wave Source Formulations for Leapfrog Complying-Divergence Implicit FDTD Method\",\"authors\":\"Shuo Liu;Eng Leong Tan;Bin Zou\",\"doi\":\"10.1109/JMMCT.2022.3164679\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The commonly used unconditionally stable finite-difference time-domain (FDTD) methods such as alternating direction implicit (ADI)-FDTD, and its one-step formulation, leapfrog ADI-FDTD, have been found to violate the divergence condition of Gauss's law. The recently proposed leapfrog complying-divergence implicit (CDI)-FDTD not only addresses this problem, but also features many advantages, including unconditional stability, minimal floating-point operations and one-step leapfrog update. To further expand its application, this paper presents the incident plane-wave source formulations for leapfrog CDI-FDTD. Two stable and efficient formulations with different advantages are presented for introducing the far-zone plane-wave source into the FDTD problem space, namely, the scattered-field (SF) formulation and total-field / scattered field (TF/SF) formulation. To deal with the discontinuity and inconsistency across TF/SF boundaries, the fields on the boundaries need special treatments with careful modifications to ensure stability and proper plane-wave injection. Numerical results show that the incident fields can be effectively injected into the problem space with the stability of leapfrog CDI-FDTD maintained in both formulations. In addition, comparisons of radar cross sections computed using leapfrog CDI-FDTD, leapfrog ADI-FDTD and explicit FDTD with both SF and TF/SF formulations are presented. These demonstrate the advantages of leapfrog CDI-FDTD method in solving far-zone plane-wave source problems, including high efficiency, unconditional stability and complying divergence.\",\"PeriodicalId\":52176,\"journal\":{\"name\":\"IEEE Journal on Multiscale and Multiphysics Computational Techniques\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2022-04-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Journal on Multiscale and Multiphysics Computational Techniques\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/9749856/\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/9749856/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Incident Plane-Wave Source Formulations for Leapfrog Complying-Divergence Implicit FDTD Method
The commonly used unconditionally stable finite-difference time-domain (FDTD) methods such as alternating direction implicit (ADI)-FDTD, and its one-step formulation, leapfrog ADI-FDTD, have been found to violate the divergence condition of Gauss's law. The recently proposed leapfrog complying-divergence implicit (CDI)-FDTD not only addresses this problem, but also features many advantages, including unconditional stability, minimal floating-point operations and one-step leapfrog update. To further expand its application, this paper presents the incident plane-wave source formulations for leapfrog CDI-FDTD. Two stable and efficient formulations with different advantages are presented for introducing the far-zone plane-wave source into the FDTD problem space, namely, the scattered-field (SF) formulation and total-field / scattered field (TF/SF) formulation. To deal with the discontinuity and inconsistency across TF/SF boundaries, the fields on the boundaries need special treatments with careful modifications to ensure stability and proper plane-wave injection. Numerical results show that the incident fields can be effectively injected into the problem space with the stability of leapfrog CDI-FDTD maintained in both formulations. In addition, comparisons of radar cross sections computed using leapfrog CDI-FDTD, leapfrog ADI-FDTD and explicit FDTD with both SF and TF/SF formulations are presented. These demonstrate the advantages of leapfrog CDI-FDTD method in solving far-zone plane-wave source problems, including high efficiency, unconditional stability and complying divergence.