• Corpus ID: 246240845

A coupled-mode theory for two-dimensional exterior Helmholtz problems based on the Neumann and Dirichlet normal mode expansion

@article{Matsushima2022ACT,
  title={A coupled-mode theory for two-dimensional exterior Helmholtz problems based on the Neumann and Dirichlet normal mode expansion},
  author={Kei Matsushima and Yuki Noguchi and Takayuki Yamada},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.09502}
}

• K. Matsushima, Y. Noguchi, Takayuki Yamada
• Published 24 January 2022
• Mathematics
• ArXiv

This study proposes a novel coupled-mode theory for two-dimensional exterior Helmholtz problems. The proposed approach is based on the separation of the entire space R into a fictitious disk and its exterior. The disk is allocated in such a way that it comprises all the inhomogeneity; therefore, the exterior supports cylindrical waves with a continuous spectrum. For the interior, we expand an unknown wave field using normal modes that satisfy some auxiliary boundary conditions on the surface of the disk. For the interior expansion, we propose combining the Neumann and Dirichlet normal modes. We show that the proposed expansion sacrifices L orthogonality but significantly improve the convergence. Finally, we present some numerical verifications of the proposed coupled-mode theory.