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A mixed hybrid finite element method for the Helmholtz equation. (English) Zbl 1230.65126

The authors present a novel high-order hybrid mixed finite element method for solving the two-dimensional Helmholtz equation with high wave numbers, which uses a discrete eigenfunction basis for solving the hybrid problem. When uniform rectangular meshes or rectangular meshes with hanging nodes are used, the construction of the eigenfunction basis leads to one-dimensional eigenvalue problems which can be solved efficiently for high order polynomial basis functions on a coarse grid. The effectiveness of the approach is demonstrated with several numerical examples including a large-scale problem.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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