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A high‐order numerical method for solving non‐periodic scattering problems in three‐dimensional bi‐periodic structures.

Authors :
Arens, Tilo
Shafieeabyaneh, Nasim
Zhang, Ruming
Source :
ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik; Sep2024, Vol. 104 Issue 9, p1-21, 21p
Publication Year :
2024

Abstract

In this paper, we focus on scattering of non‐periodic incident fields in three‐dimensional bi‐periodic structures, as they can not be solved by the classical methods used for the quasi‐periodic scattering problems. To solve such non‐periodic scattering problems, the Floquet–Bloch transform, which decomposes the unbounded problem into a family of periodic problems in a bounded unit cell, has been applied together with a numerical method by Lechleiter and Zhang (2017). However, its theoretical result indicates that the computational order is too low. Hence, our aim is to propose a high‐order numerical approach by using the Floquet–Bloch transform. To this end, the first crucial part is to analyze the regularity of the transformed solution with respect to the Floquet parameter. The second challenging part is to propose a high‐order tailor‐made quadrature method adapted to singularities of the transformed solution formed by a finite number of circular arcs. Afterwards, we obtain the error estimation of the proposed numerical approach. Eventually, the accuracy and efficiency of the mentioned approach are revealed by several numerical examples. [ABSTRACT FROM AUTHOR]

Subjects

Subjects :
UNIT cell

Details

Language :
English
ISSN :
00442267
Volume :
104
Issue :
9
Database :
Complementary Index
Journal :
ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Publication Type :
Academic Journal
Accession number :
180172622
Full Text :
https://doi.org/10.1002/zamm.202300650