Name
Title | ||
|---|---|---|
Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map. |
Abstract | ||
|---|---|---|
We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains. We consider a variational formulation and show that the spectrum consists of isolated eigenvalues of finite multiplicity that only can accumulate at infinity. The proposed method is based on a high order finite element discretization combined with a specialization of the Tensor Infinite Arnoldi method (TIAR). Using Toeplitz matrices, we show how to specialize this method to our specific structure. In particular we introduce a pole cancellation technique in order to increase the radius of convergence for computation of eigenvalues that lie close to the poles of the matrix-valued function. The solution scheme can be applied to multiple resonators with a varying refractive index that is not necessarily piecewise constant. We present two test cases to show stability, performance and numerical accuracy of the method. In particular the use of a high order finite element discretization together with TIAR results in an efficient and reliable method to compute resonances. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.cam.2017.08.012 | Journal of Computational and Applied Mathematics |
Keywords | Field | DocType |
Nonlinear eigenvalue problems,Helmholtz problem,Scattering resonances,Dirichlet-to-Neumann map,Arnoldi’s method,Matrix functions | Discretization,Mathematical optimization,Radius of convergence,Matrix (mathematics),Mathematical analysis,Helmholtz free energy,Finite element method,Toeplitz matrix,Piecewise,Mathematics,Eigenvalues and eigenvectors | Journal |
Volume | ISSN | Citations |
330 | 0377-0427 | 0 |
PageRank | References | Authors |
0.34 | 15 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Juan Carlos Araujo-Cabarcas | 1 | 0 | 0.34 |
| Christian Engström | 2 | 13 | 4.97 |
| Jarlebring Elias | 3 | 84 | 11.48 |