Shifted inverse iteration based multigrid methods for the quad-curl eigenvalue problem. (English) Zbl 1433.65332
Summary: This paper is devoted to multgrid methods for solving the quad-curl eigenvalue problem. The multgrid methods based on the Rayleigh quotient iteration and the inverse iteration with fixed shift are proposed. We prove the error estimates for both methods. Numerical experiments confirm our theoretical analysis and validate the efficiency of both methods.
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
Software:
iFEMReferences:
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