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Numerical methods for scattering problems in periodic waveguides
- Source :
- Numerische Mathematik, 148, 959–996
- Publication Year :
- 2021
- Publisher :
- Springer, 2021.
-
Abstract
- In this paper, we propose new numerical methods for scattering problems in periodic waveguides. Based on [20], the “physically meaningful” solution, which is obtained via the Limiting Absorption Principle (LAP) and is called an LAP solution, is written as an integral of quasi-periodic solutions on a contour. The definition of the contour depends both on the wavenumber and the periodic structure. The contour integral is then written as the combination of finite propagation modes and a contour integral on a small circle. Numerical methods are developed and based on the two representations. Compared with other numerical methods, we do not need the LAP process during numerical approximations, thus a standard error estimation is easily carried out. Based on this method, we also develop a numerical solver for halfguide problems. The method is based on the result that any LAP solution of a halfguide problem can be extended to the LAP solution of a fullguide problem. At the end of this paper, we also give some numerical results to show the efficiency of our numerical methods.
Details
- Language :
- English
- ISSN :
- 0029599X and 09453245
- Database :
- OpenAIRE
- Journal :
- Numerische Mathematik, 148, 959–996
- Accession number :
- edsair.doi.dedup.....be7d5d570a3bacee9e399d8cc7861999