| Records |
| Author |
Aylwin, R.; Jerez-Hanckes, C.; Schwab, C.; Zech, J. |
| Title |
Domain Uncertainty Quantification in Computational Electromagnetics |
Type |
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| Year |
2020 |
Publication |
Siam-Asa Journal On Uncertainty Quantification |
Abbreviated Journal |
SIAM-ASA J. Uncertain. Quantif. |
| Volume |
8 |
Issue |
1 |
Pages |
301-341 |
| Keywords |
computational electromagnetics; uncertainty quantification; finite elements; shape holomorphy; sparse grid quadrature; Bayesian inverse problems |
| Abstract |
We study the numerical approximation of time-harmonic, electromagnetic fields inside a lossy cavity of uncertain geometry. Key assumptions are a possibly high-dimensional parametrization of the uncertain geometry along with a suitable transformation to a fixed, nominal domain. This uncertainty parametrization results in families of countably parametric, Maxwell-like cavity problems that are posed in a single domain, with inhomogeneous coefficients that possess finite, possibly low spatial regularity, but exhibit holomorphic parametric dependence in the differential operator. Our computational scheme is composed of a sparse grid interpolation in the high-dimensional parameter domain and an Hcurl -conforming edge element discretization of the parametric problem in the nominal domain. As a stepping-stone in the analysis, we derive a novel Strang-type lemma for Maxwell-like problems in the nominal domain, which is of independent interest. Moreover, we accommodate arbitrary small Sobolev regularity of the electric field and also cover uncertain isotropic constitutive or material laws. The shape holomorphy and edge-element consistency error analysis for the nominal problem are shown to imply convergence rates for multilevel Monte Carlo and for quasi-Monte Carlo integration, as well as sparse grid approximations, in uncertainty quantification for computational electromagnetics. They also imply expression rate estimates for deep ReLU networks of shape-to-solution maps in this setting. Finally, our computational experiments confirm the presented theoretical results. |
| Address |
[Aylwin, Ruben] Pontificia Univ Catolica Chile, Sch Engn, Santiago 7820436, Chile, Email: rdaylwin@uc.cl; |
| Corporate Author |
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Thesis |
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| Publisher |
Siam Publications |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
2166-2525 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000551383300011 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
1207 |
| Permanent link to this record |
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| Author |
Pinto, J.; Henríquez, F.; Jerez-Hanckes, C. |
| Title |
Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs |
Type |
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| Year |
2024 |
Publication |
Journal of Fourier Analysis and Applications |
Abbreviated Journal |
J. Fourier Anal. Appl. |
| Volume |
30 |
Issue |
2 |
Pages |
14 |
| Keywords |
Integral operators; Open arcs; Shape regularity; Shape holomorphy |
| Abstract |
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting the corresponding boundary value problems as boundary integral equations, we prove that their solutions depend holomorphically upon perturbations of the arcs� parametrizations. These results are key to prove the shape (domain) holomorphy of domain-to-solution maps associated to boundary integral equations appearing in uncertainty quantification, inverse problems and deep learning, to name a few applications. |
| Address |
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| Corporate Author |
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Thesis |
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| Publisher |
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Place of Publication |
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Editor |
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| Language |
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Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
1069-5869 |
ISBN |
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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:001171237400001 |
Approved |
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| Call Number |
UAI @ alexi.delcanto @ |
Serial |
1934 |
| Permanent link to this record |
