Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements

A few years ago, Costabel and Dauge proposed a variational setting, which allows one to solve numerically the time-harmonic Maxwell equations in 3D polyhedral geometries, with the help of a continuous approximation of the electromagnetic field. In order to remove spurious eigenmodes, their method re...

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Veröffentlicht in:Numerische Mathematik Jg. 113; H. 4; S. 497 - 518
Hauptverfasser: Buffa, Annalisa, Ciarlet, Patrick, Jamelot, Erell
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer-Verlag 01.10.2009
Springer
Springer Verlag
Schlagworte:
Exact sciences and technology
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical analysis. Scientific computation
Numerical and Computational Physics
Sciences and techniques of general use
Simulation
Theoretical
65N25 (Numerical analysis, eigenvalue problems)
78M10 (Optics & EM theory, finite element methods)
35Q60 (PDEs, Eqs of EM theory and optics)
Geometry
Finite element method
Numerical analysis
Approximation
Three-dimensional calculations
Numerical solution
Eigenvalue
Electromagnetic field
Eigenvalue problem
Parameterization
Maxwell equation
ISSN:0029-599X, 0945-3245
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Beschreibung
Zusammenfassung:A few years ago, Costabel and Dauge proposed a variational setting, which allows one to solve numerically the time-harmonic Maxwell equations in 3D polyhedral geometries, with the help of a continuous approximation of the electromagnetic field. In order to remove spurious eigenmodes, their method required a parameterization of the variational formulation. In order to avoid this difficulty, we use a mixed variational setting instead of the parameterization, which allows us to handle the divergence-free constraint on the field in a straightforward manner. The numerical analysis of the method is carried out, and numerical examples are provided to show the efficiency of our approach.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-009-0246-2