Name
Abstract | ||
|---|---|---|
We present a new computational approach for a class of large-scale nonlinear eigen-value problems (NEPs) that are nonlinear in the eigenvalue. The contribution of this paper is twofold. We derive a new iterative algorithm for NEPs, the tensor infinite Arnoldi method (TIAR), which is applicable to a general class of NEPs, and we show how to specialize the algorithm to a specific NEP: the waveguide eigenvalue problem. The waveguide eigenvalue problem arises from a finite-element discretization of a partial differential equation used in the study waves propagating in a periodic medium. The algorithm is successfully applied to accurately solve benchmark problems as well as complicated waveguides. We study the complexity of the specialized algorithm with respect to the number of iterations m and the size of the problem n, both from a theoretical perspective and in practice. For the waveguide eigenvalue problem, we establish that the computationally dominating part of the algorithm has complexity O(nm(2) + root nm(3)). Hence, the asymptotic complexity of TIAR applied to the waveguide eigenvalue problem, for n -> infinity, is the same as for Arnoldi's method for standard eigenvalue problems. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/15M1044667 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
nonlinear eigenvalue problems,iterative methods,Krylov methods,Helmholtz equation,Arnoldi's method | Discretization,Mathematical optimization,Tensor,Arnoldi iteration,Iterative method,Mathematical analysis,Divide-and-conquer eigenvalue algorithm,Partial differential equation,Eigenvalues and eigenvectors,Mathematics,Inverse iteration | Journal |
Volume | Issue | ISSN |
39 | 3 | 1064-8275 |
Citations | PageRank | References |
2 | 0.39 | 15 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jarlebring Elias | 1 | 84 | 11.48 |
| giampaolo mele | 2 | 2 | 0.39 |
| Olof Runborg | 3 | 34 | 6.66 |