Electromagnetic wave scattering by random surfaces: Shape holomorphy

Carlos Jerez-Hanckes, Christoph Schwab, Jakob Zech

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


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.

Original languageEnglish
Pages (from-to)2229-2259
Number of pages31
JournalMathematical Models and Methods in Applied Sciences
Issue number12
StatePublished - 1 Nov 2017
Externally publishedYes


  • Electromagnetic scattering
  • Smolyak quadrature
  • shape calculus
  • uncertainty quantification


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