论文标题
基于Neumann和Dirichlet正常模式扩展的二维外部Helmholtz问题的耦合模式理论
A coupled-mode theory for two-dimensional exterior Helmholtz problems based on the Neumann and Dirichlet normal mode expansion
论文作者
论文摘要
这项研究提出了一种新型的耦合模式理论，用于二维外部Helmholtz问题。提出的方法基于将整个空间R2分离为虚拟磁盘及其外部。分配磁盘的方式包括所有不均匀性。因此，外部支持连续光谱的圆柱波。对于内部，我们使用正常模式扩展一个未知的波场，该模式满足磁盘表面上的某些辅助边界条件。对于内部膨胀，我们提出结合Neumann和Dirichlet正常模式。我们表明，拟议的扩展牺牲了L2正交性，但显着改善了收敛性。最后，我们介绍了提出的耦合模式理论的一些数值验证。
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 R2 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 L2 orthogonality but significantly improve the convergence. Finally, we present some numerical verifications of the proposed coupled-mode theory.
