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A nonuniform mesh method in the Floquet parameter domain for wave scattered by periodic surfaces
  • Ruming Zhang,
  • Tilo Arens
Ruming Zhang
Karlsruhe Institute of Technology

Corresponding Author:[email protected]

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Tilo Arens
Karlsruhe Institute of Technology
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Abstract

In this paper, we propose a new nonuniform mesh method to simulate acoustic scattering problems in two dimensional periodic structures with non-periodic incident fields numerically. As existing methods are difficult to extend to higher dimensions, we have designed the new method with such extensions in mind. With the help of the Floquet-Bloch transform, the solution to the original scattering problem is written as an integral of a family of quasi-periodic problems. These are defined in bounded domains for each value of the Floquet parameter which varies in a bounded interval. The key step in our method is the numerical approximation of the integral by a quadrature rule adapted to the regularity of the family of quasi-periodic solutions. We design a nonuniform mesh with a Gaussian quadrature rule applied on each subinterval. We prove that the numerical method converges exponentially with respect to both the number of subintervals and the number of Gaussian quadrature points. Some numerical experiments are provided to illustrate the results.
01 Sep 2022Submitted to Mathematical Methods in the Applied Sciences
02 Sep 2022Assigned to Editor
02 Sep 2022Submission Checks Completed
20 Sep 2022Reviewer(s) Assigned