Multigrid discretization and iterative algorithm for mixed variational formulation of the eigenvalue problem of electric field. (English) Zbl 1256.78001

Summary: This paper discusses highly finite element algorithms for the eigenvalue problem of an electric field. Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of an electric field. Theoretical analysis and numerical results show that the computational schemes established in the paper have high efficiency.


78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
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