Modular hp-FEM system HERMES and its application to Maxwell’s equations. (English) Zbl 1157.78356

Summary: We introduce a multi-physics modular \(hp\)-FEM system HERMES. The code is based on a novel approach where the finite element technology (mesh processing and adaptation, numerical quadrature, assembling and solution of the discrete problems, a-posteriori error estimation, etc.) is fully separated from the physics of the solved problems. The physics is represented via simple modules containing PDE-dependent parameters as well as hierarchic higher-order finite elements satisfying the conformity requirements imposed by the PDE. After describing briefly the modular structure of HERMES and some of its functionality, we focus on its application to the time-harmonic Maxwell’s equations. We present numerical results which illustrate the capability of the \(hp\)-FEM to reduce both the number of degrees of freedom and the CPU time dramatically compared to standard lowest-order FEM.


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