# Scattering in periodic waveguide: integral representation and spectrum decomposition

@article{Zhang2019ScatteringIP, title={Scattering in periodic waveguide: integral representation and spectrum decomposition}, author={Ruming Zhang}, journal={arXiv: Analysis of PDEs}, year={2019} }

Scattering problems in periodic waveguides are interesting but challenging topics in mathematics, both theoretically and numerically. Due to the existence of eigenvalue, the unique solvability of such problems is not always guaranteed. To obtain a unique solution that is physically meaningful, the limiting absorption principle (LAP) is a commenly used method. LAP assumes that the limit of a family of solutions of scattering problems with absorbing material converges, as the absorbing parameter…

## One Citation

### Numerical methods for scattering problems in periodic waveguides

- Mathematics, Computer ScienceNumerische Mathematik
- 2021

New numerical methods for scattering problems in periodic waveguides are proposed and based on the Limiting Absorption Principle, which does not need the LAP process during numerical approximations, thus a standard error estimation is easily carried out.

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