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Electromagnetic wave scattering by random surfaces: Shape holomorphy

School of Engineering, Pontificia Universidad Católica de Chile (PUC Chile), Av. Vicuña Mackenna 4860, 7820436, Santiago, Chile

E-mail Address: [email protected]

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Christoph Schwab

Seminar for Applied Mathematics (SAM), Eidgenössische Technische Hochschule Zürich (ETHZ), Rämistrasse 101, 8092 Zürich, Switzerland

E-mail Address: [email protected]

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Jakob Zech

Seminar for Applied Mathematics (SAM), Eidgenössische Technische Hochschule Zürich (ETHZ), Rämistrasse 101, 8092 Zürich, Switzerland

E-mail Address: [email protected]

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https://doi.org/10.1142/S0218202517500439Cited by:33 (Source: Crossref)

Abstract

For time-harmonic electromagnetic waves scattered by either perfectly conducting or dielectric bounded obstacles, we show that the fields depend holomorphically on the shape of the scatterer. In the presence of random geometrical perturbations, our results imply strong measurability of the fields, in weighted spaces in the exterior of the scatterer. These findings are key to prove dimension-independent convergence rates of sparse approximation techniques of polynomial chaos type for forward and inverse computational uncertainty quantification. Also, our shape-holomorphy results imply parsimonious approximate representations of the corresponding parametric solution families, which are produced, for example, by greedy strategies such as model order reduction or reduced basis approximations. Finally, the presently proved shape holomorphy results imply convergence of shape Taylor expansions of far-field patterns for fixed amplitude domain perturbations in a vicinity of the nominal domain, thereby extending the widely used asymptotic linearizations employed in first-order, second moment domain uncertainty quantification.

Communicated by F. Brezzi

Keywords:

AMSC: 35A20, 35B30, 32D05, 35Q61

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