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Shape deformations in rough-surface scattering: improved algorithms.

David P Nicholls1, Fernando Reitich

  • 1Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, USA. Nicholls.2@nd.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|April 14, 2004
PubMed
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New stabilized shape-perturbation methods improve calculations of scattering from rough surfaces. These algorithms address instabilities, enabling more accurate and wider-ranging surface scattering analyses.

Area of Science:

  • Computational physics
  • Electromagnetics
  • Surface science

Background:

  • Shape-perturbation methods are used for scattering calculations.
  • Instabilities in these methods arise from cancellations in recursive calculations.
  • Previous work identified the mechanism behind these instabilities.

Purpose of the Study:

  • To present new, stabilized shape-perturbation methods for scattering from rough surfaces.
  • To develop algorithms for both low- and high-order implementations.
  • To address and resolve instabilities in existing methods.

Main Methods:

  • Development of stabilized shape-perturbation algorithms.
  • Low-order implementations consider recurrence explicitly.
  • High-order implementations use implicit methods like variable change and Dirichlet-to-interior-derivative operators.

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Main Results:

  • New low-order algorithms show improved performance.
  • High-order calculations are enabled by resolving cancellations.
  • The domain of applicability for shape-perturbation methods is significantly expanded.

Conclusions:

  • Stabilized shape-perturbation methods offer enhanced accuracy for scattering calculations.
  • The developed algorithms successfully mitigate instabilities.
  • These advancements allow for more complex and accurate surface scattering analyses.