A. Yucel, Luis J. Gomez, W. Sheng, H. Bağcı, E. Michielssen
In this chapter, efficient collocation methods for EM analysis are reviewed. Traditional SC methods leveraging tensor-product, sparse grid, and Stroud cubature rules are described first. These methods are rather straightforward to implement and suitable for EM problems involving smoothly varying QoI. Then, the ME-PC method for efficiently constructing a surrogate model of a rapidly varying QoI is presented. Also detailed is the iterative HDMR technique for EM problems involving large numbers of random variables. Finally, an approximation technique based on the spectral quantic TT (QTT) (SQTT) for constructing a surrogate model in a high-dimensional random domain is briefly reviewed, before the chapter is concluded by numerical examples demonstrating applications of cutting-edge UQ methods to various EM problems.
{"title":"New trends in uncertainty quantification for large-scale electromagnetic analysis: from tensor product cubature rules to spectral quantic tensor-train approximation","authors":"A. Yucel, Luis J. Gomez, W. Sheng, H. Bağcı, E. Michielssen","doi":"10.1049/sbew533e_ch15","DOIUrl":"https://doi.org/10.1049/sbew533e_ch15","url":null,"abstract":"In this chapter, efficient collocation methods for EM analysis are reviewed. Traditional SC methods leveraging tensor-product, sparse grid, and Stroud cubature rules are described first. These methods are rather straightforward to implement and suitable for EM problems involving smoothly varying QoI. Then, the ME-PC method for efficiently constructing a surrogate model of a rapidly varying QoI is presented. Also detailed is the iterative HDMR technique for EM problems involving large numbers of random variables. Finally, an approximation technique based on the spectral quantic TT (QTT) (SQTT) for constructing a surrogate model in a high-dimensional random domain is briefly reviewed, before the chapter is concluded by numerical examples demonstrating applications of cutting-edge UQ methods to various EM problems.","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":"116922057","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 have focused on formulations of a TD-SIE solver and a TD -VIE solver for characterizing electromagnetic field interactions on plasmonic structures. The TD-SIE solver discretizes TD-PMCHWT-SIE using RWG basis and testing functions in space and polynomial basis functions and point testing in time. The resulting systems of equations are solved recursively using the MOT scheme. The TD -VIE solver discretizes TD-EFVIE using SWG basis and testing functions in space and polynomial basis functions and point testing in time. Similarly, the resulting systems of equations are solved recursively using the MOT scheme. Since the permittivity of a plasmonic structure is dispersive, both solvers call for discretization of temporal convolutions. This is carried out by projecting the result of the convolutions onto polynomial basis function space and testing the resulting equation at discrete times. The temporal samples of the time -domain Green function (for the TD-SIE solver) and the time -domain permittivity functions (for the TD-SIE and TD -VIE solvers), which are required by this discretization procedure (and also the MOT scheme), are obtained numerically from their frequency -domain samples. This is achieved by representing the frequency -domain Green function and permittivity in terms of summations of weighted rational functions. The weighting coefficients are found by applying the FRVF scheme to the frequency -domain samples. Time-domain functions are then obtained by analytically computing the inverse Fourier transform of the summation. Numerical results demonstrate the accuracy, stability, and applicability of both solvers.
{"title":"New trends in time-domain methods for plasmonic media","authors":"S. B. Sayed, I. Uysal, H. A. Ulku, H. Bağcı","doi":"10.1049/sbew533e_ch6","DOIUrl":"https://doi.org/10.1049/sbew533e_ch6","url":null,"abstract":"In this chapter, we have focused on formulations of a TD-SIE solver and a TD -VIE solver for characterizing electromagnetic field interactions on plasmonic structures. The TD-SIE solver discretizes TD-PMCHWT-SIE using RWG basis and testing functions in space and polynomial basis functions and point testing in time. The resulting systems of equations are solved recursively using the MOT scheme. The TD -VIE solver discretizes TD-EFVIE using SWG basis and testing functions in space and polynomial basis functions and point testing in time. Similarly, the resulting systems of equations are solved recursively using the MOT scheme. Since the permittivity of a plasmonic structure is dispersive, both solvers call for discretization of temporal convolutions. This is carried out by projecting the result of the convolutions onto polynomial basis function space and testing the resulting equation at discrete times. The temporal samples of the time -domain Green function (for the TD-SIE solver) and the time -domain permittivity functions (for the TD-SIE and TD -VIE solvers), which are required by this discretization procedure (and also the MOT scheme), are obtained numerically from their frequency -domain samples. This is achieved by representing the frequency -domain Green function and permittivity in terms of summations of weighted rational functions. The weighting coefficients are found by applying the FRVF scheme to the frequency -domain samples. Time-domain functions are then obtained by analytically computing the inverse Fourier transform of the summation. Numerical results demonstrate the accuracy, stability, and applicability of both solvers.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"111 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":"124048237","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}
Surface integral equations (SIEs) are widely used to simulate and analyze electromagnetic scattering and radiation from arbitrary -shaped conducting and piecewise homogeneous penetrable structures. These methods are based on the surface equivalence principle, where the original boundary value problem for (time -harmonic) Maxwell's equations is reformulated and expressed in terms of surface -integral operators and equivalent sources. The attractive feature of this procedure is that it essentially decreases the dimensionality of the problem by one. Another great advantage of SIEbased methods is that, in unbounded regions, radiation conditions are automatically satisfied, and thus, absorbing boundary conditions or mesh truncation techniques is not needed. These nice features, however, do not come without a cost. The linear system obtained after a discretization process involves a fully populated matrix that is expensive to solve and requiring advanced fast solution strategies as the problem size increases. Special integration routines are needed to evaluate singular integrals efficiently and accurately. The underlying integral operators, equations, and the corresponding discretized linear systems may suffer from low -frequency and dense-discretization breakdowns, low -frequency cancellation, or other types of inaccuracies, as well as instabilities and ill conditioning due to resonances and extreme material parameter
{"title":"New trends in frequency-domain surface integral equations","authors":"P. Ylä‐Oijala, S. Jarvenpaa","doi":"10.1049/sbew533e_ch3","DOIUrl":"https://doi.org/10.1049/sbew533e_ch3","url":null,"abstract":"Surface integral equations (SIEs) are widely used to simulate and analyze electromagnetic scattering and radiation from arbitrary -shaped conducting and piecewise homogeneous penetrable structures. These methods are based on the surface equivalence principle, where the original boundary value problem for (time -harmonic) Maxwell's equations is reformulated and expressed in terms of surface -integral operators and equivalent sources. The attractive feature of this procedure is that it essentially decreases the dimensionality of the problem by one. Another great advantage of SIEbased methods is that, in unbounded regions, radiation conditions are automatically satisfied, and thus, absorbing boundary conditions or mesh truncation techniques is not needed. These nice features, however, do not come without a cost. The linear system obtained after a discretization process involves a fully populated matrix that is expensive to solve and requiring advanced fast solution strategies as the problem size increases. Special integration routines are needed to evaluate singular integrals efficiently and accurately. The underlying integral operators, equations, and the corresponding discretized linear systems may suffer from low -frequency and dense-discretization breakdowns, low -frequency cancellation, or other types of inaccuracies, as well as instabilities and ill conditioning due to resonances and extreme material parameter","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128771045","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 reviews recent advances in computational electromagnetics regarding simple techniques for the systematic construction of higher order vector bases used by advanced numerical codes. Higher order functions are used in numerical solutions of differential and integrodifferential equations by the application of the finite element method (FEM) and the method of moments (MoM). First, we consider divergence-conforming and curl-conforming polynomial vector bases and then introduce substitutive and additive vector bases that are able to model field singularities in the vicinity of edges or vertices. The advantages offered by the use of these higher order models are illustrated by numerical results. Mathematical aspects and numerical techniques presented in this chapter are dealt with in detail in [1], except for the most recent developments concerning singular vector basis functions and their numerical implementation. For background information and further details, the interested reader may refer to [1] and references therein.
{"title":"New trends in hierarchical vector basis functions","authors":"R. Graglia, A. Peterson","doi":"10.1049/sbew533e_ch9","DOIUrl":"https://doi.org/10.1049/sbew533e_ch9","url":null,"abstract":"This chapter reviews recent advances in computational electromagnetics regarding simple techniques for the systematic construction of higher order vector bases used by advanced numerical codes. Higher order functions are used in numerical solutions of differential and integrodifferential equations by the application of the finite element method (FEM) and the method of moments (MoM). First, we consider divergence-conforming and curl-conforming polynomial vector bases and then introduce substitutive and additive vector bases that are able to model field singularities in the vicinity of edges or vertices. The advantages offered by the use of these higher order models are illustrated by numerical results. Mathematical aspects and numerical techniques presented in this chapter are dealt with in detail in [1], except for the most recent developments concerning singular vector basis functions and their numerical implementation. For background information and further details, the interested reader may refer to [1] and references therein.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125194576","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, a fast MoM-PO hybrid framework, including EI-MoM-PO, AIM acceleration, and half-space solutions, is presented as an exemplar of recent trends in high-frequency techniques and hybridizations. The beauty of the presented fast MoM-P0 framework is that its solution process clearly follows the underlying physics of the MoM-PO hybridization, where source-platform interactions are physically described. Besides, considering fl exibility and extendibility of the framework, one can easily replace AIM by any other suitable fast algorithms, in accordance with the properties of the complex structures under investigation.
{"title":"New trends in high-frequency techniques and hybridizations","authors":"Zi-Liang Liu, Chao‐Fu Wang","doi":"10.1049/sbew533e_ch14","DOIUrl":"https://doi.org/10.1049/sbew533e_ch14","url":null,"abstract":"In this chapter, a fast MoM-PO hybrid framework, including EI-MoM-PO, AIM acceleration, and half-space solutions, is presented as an exemplar of recent trends in high-frequency techniques and hybridizations. The beauty of the presented fast MoM-P0 framework is that its solution process clearly follows the underlying physics of the MoM-PO hybridization, where source-platform interactions are physically described. Besides, considering fl exibility and extendibility of the framework, one can easily replace AIM by any other suitable fast algorithms, in accordance with the properties of the complex structures under investigation.","PeriodicalId":287175,"journal":{"name":"New Trends in Computational Electromagnetics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116105640","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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