In this chapter, we address the aforementioned issues one by one. We start by formulating periodic BVPs and, then, introduce a pFMNI and a contour -integral -based eigenvalue-solver called the Sakurai -Sugiura method (SSM). We discuss techniques related to the analytic continuation of tools for pFMNI to complex frequencies, as well as a simple method of making distinction between true and fictitious eigenvalues. We finally consider numerical examples, followed by conclusions. More information on the theoretical developments related to the content of this chapter can be found.
{"title":"New trends in periodic problems and determining related eigenvalues","authors":"K. Niino, Ryota Misawa, N. Nishimura","doi":"10.1049/sbew533e_ch12","DOIUrl":"https://doi.org/10.1049/sbew533e_ch12","url":null,"abstract":"In this chapter, we address the aforementioned issues one by one. We start by formulating periodic BVPs and, then, introduce a pFMNI and a contour -integral -based eigenvalue-solver called the Sakurai -Sugiura method (SSM). We discuss techniques related to the analytic continuation of tools for pFMNI to complex frequencies, as well as a simple method of making distinction between true and fictitious eigenvalues. We finally consider numerical examples, followed by conclusions. More information on the theoretical developments related to the content of this chapter can be found.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130343280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Aronsson, F. Ling, A. Menshov, Shucheng Zheng, V. Okhmatovski
In this chapter, we provide description of the trends and new advances in BEM formulations for analysis of scattering and radiation problems in layered media, with the emphasis on methods for efficient computation of the layered media Green's function, MoM formulations, as well as fast direct and iterative algorithms to accelerate MoM solutions.
{"title":"New trends in analysis of electromagnetic fields in multilayered media","authors":"J. Aronsson, F. Ling, A. Menshov, Shucheng Zheng, V. Okhmatovski","doi":"10.1049/sbew533e_ch10","DOIUrl":"https://doi.org/10.1049/sbew533e_ch10","url":null,"abstract":"In this chapter, we provide description of the trends and new advances in BEM formulations for analysis of scattering and radiation problems in layered media, with the emphasis on methods for efficient computation of the layered media Green's function, MoM formulations, as well as fast direct and iterative algorithms to accelerate MoM solutions.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125231137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This chapter addresses both the "old" body of knowledge and the "new" trends of research and practice in FEM as applied to electromagnetics. It presents the general mathematical background and numerical components of FEM and discusses FEM formulations, discretizations, and solution procedures, mostly in the context of the higher order FEM computation. This includes the generation of curvilinear elements for higher order modeling of geometry, implementation of polynomial vector basis functions for higher order modeling of fields within the elements, and Galerkin testing method for discretizing the wave equations. The chapter focuses on the higher order FEM as the most general and versatile approach, where the low -order modeling is naturally included in the higher order FEM paradigm.
{"title":"New trends in finite element methods","authors":"B. Notaroš, Su Yan","doi":"10.1049/sbew533e_ch7","DOIUrl":"https://doi.org/10.1049/sbew533e_ch7","url":null,"abstract":"This chapter addresses both the \"old\" body of knowledge and the \"new\" trends of research and practice in FEM as applied to electromagnetics. It presents the general mathematical background and numerical components of FEM and discusses FEM formulations, discretizations, and solution procedures, mostly in the context of the higher order FEM computation. This includes the generation of curvilinear elements for higher order modeling of geometry, implementation of polynomial vector basis functions for higher order modeling of fields within the elements, and Galerkin testing method for discretizing the wave equations. The chapter focuses on the higher order FEM as the most general and versatile approach, where the low -order modeling is naturally included in the higher order FEM paradigm.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129272283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this chapter, the author have presented ideas along these lines, focusing on two different numerical approaches, i.e., GMM and IGA, both of which rely on subdivision representation of geometries. Both methods take different approaches to solving integral equations. GMM is a highly flexible scheme that permits the use of different basis functions for each patch and, as a result, is highly customizable. The crux to this approach is local surface parameterization and transition maps between different local parameterizations in regions where patches overlap. Subdivision offers an effective approach to overcome this bottleneck. Its efficacy and related challenges have been demonstrated through examples. Indeed, it is possible to pair subdivision GMM with methods developed in [14] to efficiently evaluate integrals to solve problems that are electrically large and geometrically complex.
{"title":"New trends in geometric modeling and discretization for integral equations","authors":"Jie Li, D. Dault, B. Shanker","doi":"10.1049/sbew533e_ch8","DOIUrl":"https://doi.org/10.1049/sbew533e_ch8","url":null,"abstract":"In this chapter, the author have presented ideas along these lines, focusing on two different numerical approaches, i.e., GMM and IGA, both of which rely on subdivision representation of geometries. Both methods take different approaches to solving integral equations. GMM is a highly flexible scheme that permits the use of different basis functions for each patch and, as a result, is highly customizable. The crux to this approach is local surface parameterization and transition maps between different local parameterizations in regions where patches overlap. Subdivision offers an effective approach to overcome this bottleneck. Its efficacy and related challenges have been demonstrated through examples. Indeed, it is possible to pair subdivision GMM with methods developed in [14] to efficiently evaluate integrals to solve problems that are electrically large and geometrically complex.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116480598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Weile, Jielin Li, D. A. Hopkins, Christopher Kerwein
TDIE implementations have come a long way since their initial unstable first steps and are well on their way to becoming a fourth set of canonical methods in the computational electromagnetics toolbox. Five basic methods for temporal discretization have shown promise for the stable and accurate temporal discretization of TDIEs, and several fast methods have been concocted to improve their performances. While new applications of TDIEs are likely to continue pouring in, multiphysics and electromagnetic physics appear to be the short-term trajectory of these newest computational electromagnetics methods. Despite their unimpressive origins, TDIEs are finally poised to become a very new trend in computational electromagnetics.
{"title":"New trends in time-domain integral equations","authors":"D. Weile, Jielin Li, D. A. Hopkins, Christopher Kerwein","doi":"10.1049/sbew533e_ch5","DOIUrl":"https://doi.org/10.1049/sbew533e_ch5","url":null,"abstract":"TDIE implementations have come a long way since their initial unstable first steps and are well on their way to becoming a fourth set of canonical methods in the computational electromagnetics toolbox. Five basic methods for temporal discretization have shown promise for the stable and accurate temporal discretization of TDIEs, and several fast methods have been concocted to improve their performances. While new applications of TDIEs are likely to continue pouring in, multiphysics and electromagnetic physics appear to be the short-term trajectory of these newest computational electromagnetics methods. Despite their unimpressive origins, TDIEs are finally poised to become a very new trend in computational electromagnetics.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129642879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
W. Chew, Q. Dai, Qin S. Liu, T. Xia, T. Roth, H. Gan, A. Liu, Shu C. Chen, Mert Hidayetoglu, L. J. Jiang, Sheng Sun, Wen-mei W. Hwu
Electromagnetics is based on the study of Maxwell's equations, which are the result of the seminal work of James Clerk Maxwell completed in 1865, after his presentation to the British Royal Society in 1864. It has been over 150 years ago now, and this is a long time compared to the recent leaps and bounds progress made in technological advancements. Nevertheless, electromagnetics is still being continuously researched and studied despite its age. The reason is that electromagnetics is extremely useful and has impacted a large sector of modern technologies.
{"title":"New Trends in Computational Electromagnetics","authors":"W. Chew, Q. Dai, Qin S. Liu, T. Xia, T. Roth, H. Gan, A. Liu, Shu C. Chen, Mert Hidayetoglu, L. J. Jiang, Sheng Sun, Wen-mei W. Hwu","doi":"10.1049/sbew533e","DOIUrl":"https://doi.org/10.1049/sbew533e","url":null,"abstract":"Electromagnetics is based on the study of Maxwell's equations, which are the result of the seminal work of James Clerk Maxwell completed in 1865, after his presentation to the British Royal Society in 1864. It has been over 150 years ago now, and this is a long time compared to the recent leaps and bounds progress made in technological advancements. Nevertheless, electromagnetics is still being continuously researched and studied despite its age. The reason is that electromagnetics is extremely useful and has impacted a large sector of modern technologies.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130842098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Volume integral equations (VIEs) are powerful numerical techniques to analyze and simulate electromagnetic properties of structures involving inhomogeneous and anisotropic materials. A number of different VIE formulations exist, and generally speaking, finding the most optimal formulation for a given problem is not straightforward. This requires careful investigation of mapping and spectral properties of operators and selection of finite -element spaces used to convert continuous equations to discrete matrix equations. In this chapter, we review the most commonly used VIE formulations and discuss recent advances in theoretical considerations and numerical discretization techniques. We investigate accuracy, conditioning, and stability of formulations and introduce some recent applications of VIE -based methods
{"title":"New trends in frequency-domain volume integral equations","authors":"J. Markkanen, P. Ylä‐Oijala","doi":"10.1049/sbew533e_ch4","DOIUrl":"https://doi.org/10.1049/sbew533e_ch4","url":null,"abstract":"Volume integral equations (VIEs) are powerful numerical techniques to analyze and simulate electromagnetic properties of structures involving inhomogeneous and anisotropic materials. A number of different VIE formulations exist, and generally speaking, finding the most optimal formulation for a given problem is not straightforward. This requires careful investigation of mapping and spectral properties of operators and selection of finite -element spaces used to convert continuous equations to discrete matrix equations. In this chapter, we review the most commonly used VIE formulations and discuss recent advances in theoretical considerations and numerical discretization techniques. We investigate accuracy, conditioning, and stability of formulations and introduce some recent applications of VIE -based methods","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122673180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Araújo, D. M. Solís, J. Rodríguez, Luis Landesa Porras, F. O. Basteiro, José Manuel Taboada Varela
Rigorous solutions of large-scale radiation and scattering problems are permanently present among the goals of the scientific community dedicated to computational electromagnetics. Research aimed at solving complex electromagnetic problems that can involve large numbers of unknowns plays a relevant role in the development of many real-life applications. In this context, the fast multipole method (FMM) and the multilevel fast multipole algorithm (MLFMA) have been extensively used for accelerating iterative solutions of dense matrix systems resulting from the application of the method of moments (MoM) to problems formulated with surface integral equations (SIEs). The purpose of using these acceleration techniques is to extend the applicability of MoM, whose matrix storage requirement is O(N2 ), while the number of operations is O(N3 ) for direct solutions or O(N2 ) for iterative solutions, to larger problems. FMM and MLFMA reduce computational costs to O(N1.5 ) and 0(N log N), respectively.
{"title":"New trends in acceleration and parallelization techniques","authors":"M. Araújo, D. M. Solís, J. Rodríguez, Luis Landesa Porras, F. O. Basteiro, José Manuel Taboada Varela","doi":"10.1049/sbew533e_ch11","DOIUrl":"https://doi.org/10.1049/sbew533e_ch11","url":null,"abstract":"Rigorous solutions of large-scale radiation and scattering problems are permanently present among the goals of the scientific community dedicated to computational electromagnetics. Research aimed at solving complex electromagnetic problems that can involve large numbers of unknowns plays a relevant role in the development of many real-life applications. In this context, the fast multipole method (FMM) and the multilevel fast multipole algorithm (MLFMA) have been extensively used for accelerating iterative solutions of dense matrix systems resulting from the application of the method of moments (MoM) to problems formulated with surface integral equations (SIEs). The purpose of using these acceleration techniques is to extend the applicability of MoM, whose matrix storage requirement is O(N2 ), while the number of operations is O(N3 ) for direct solutions or O(N2 ) for iterative solutions, to larger problems. FMM and MLFMA reduce computational costs to O(N1.5 ) and 0(N log N), respectively.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125251852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this chapter, we discuss trends and problems in the design of preconditioned Krylov methods for large-scale problems, particularly when they are formulated with surface integral equations such that dense and large matrices arise. We cover various numerical linear algebra aspects, such as the choice of iterative methods, characteristics and performances of fast integral-equation solvers for the required matrix-vector products, and the design of algebraic preconditioners based on multilevel incomplete LU factorization, sparse approximate inverses, inner-outer methods, and spectral approaches, particularly when they are combined with fast solvers. As shown via examples, the developed numerical linear algebra tools can enable efficient solutions of large electromagnetic problems on moderate number of cores and processors.
{"title":"New trends in algebraic preconditioning","authors":"B. Carpentieri","doi":"10.1049/sbew533e_ch13","DOIUrl":"https://doi.org/10.1049/sbew533e_ch13","url":null,"abstract":"In this chapter, we discuss trends and problems in the design of preconditioned Krylov methods for large-scale problems, particularly when they are formulated with surface integral equations such that dense and large matrices arise. We cover various numerical linear algebra aspects, such as the choice of iterative methods, characteristics and performances of fast integral-equation solvers for the required matrix-vector products, and the design of algebraic preconditioners based on multilevel incomplete LU factorization, sparse approximate inverses, inner-outer methods, and spectral approaches, particularly when they are combined with fast solvers. As shown via examples, the developed numerical linear algebra tools can enable efficient solutions of large electromagnetic problems on moderate number of cores and processors.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116820775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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