Georg, Niklas ; Römer, Ulrich (2020)
Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data.
In: International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 33 (6)
doi: 10.1002/jnm.2776
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for instance, further convergence acceleration may be important to tackle problems with high parametric sensitivities. In this work, we propose the use of conformal maps to construct a transformed gPC basis, in order to enhance the convergence order. The proposed basis still features orthogonality properties and hence, facilitates the computation of many statistical quantities such as sensitivities and moments. The corresponding surrogate models are computed by pseudo‐spectral projection using mapped quadrature rules, which leads to an improved cost accuracy ratio. We apply the methodology to Maxwell's source problem with random input data. In particular, numerical results for a parametric finite element model of an optical grating coupler are given.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2020 |
| Autor(en): | Georg, Niklas ; Römer, Ulrich |
| Art des Eintrags: | Bibliographie |
| Titel: | Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data |
| Sprache: | Englisch |
| Publikationsjahr: | 2020 |
| Ort: | Chichester |
| Verlag: | John Wiley & Sons |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | International Journal of Numerical Modelling: Electronic Networks, Devices and Fields |
| Jahrgang/Volume einer Zeitschrift: | 33 |
| (Heft-)Nummer: | 6 |
| Kollation: | 15 Seiten |
| DOI: | 10.1002/jnm.2776 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for instance, further convergence acceleration may be important to tackle problems with high parametric sensitivities. In this work, we propose the use of conformal maps to construct a transformed gPC basis, in order to enhance the convergence order. The proposed basis still features orthogonality properties and hence, facilitates the computation of many statistical quantities such as sensitivities and moments. The corresponding surrogate models are computed by pseudo‐spectral projection using mapped quadrature rules, which leads to an improved cost accuracy ratio. We apply the methodology to Maxwell's source problem with random input data. In particular, numerical results for a parametric finite element model of an optical grating coupler are given. |
| Freie Schlagworte: | conformal maps, nanoplasmonics, polynomial chaos, surrogate modeling, uncertainty quantification |
| ID-Nummer: | e2776 |
| Zusätzliche Informationen: | Special Issue: Advances in Forward and Inverse Surrogate Modeling for High‐Frequency Design |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau 600 Technik, Medizin, angewandte Wissenschaften > 621.3 Elektrotechnik, Elektronik |
| Fachbereich(e)/-gebiet(e): | 18 Fachbereich Elektrotechnik und Informationstechnik 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Teilchenbeschleunigung und Theorie Elektromagnetische Felder > Computational Electromagnetics 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Teilchenbeschleunigung und Theorie Elektromagnetische Felder Exzellenzinitiative Exzellenzinitiative > Graduiertenschulen Exzellenzinitiative > Graduiertenschulen > Graduate School of Computational Engineering (CE) |
| Hinterlegungsdatum: | 31 Jan 2024 10:12 |
| Letzte Änderung: | 31 Jan 2024 10:12 |
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Verfügbare Versionen dieses Eintrags
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Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data. (deposited 26 Jan 2024 13:57)
- Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data. (deposited 31 Jan 2024 10:12) [Gegenwärtig angezeigt]
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