An adaptive P1 finite element method for two-dimensional transverse magnetic time harmonic Maxwell’s equations with general material properties and general boundary conditions

• Verfasst von: Brenner, Susanne C. [VerfasserIn]
• Verfasst von: Gedicke, Joscha [VerfasserIn]
• Verfasst von: Sung, L.-Y. [VerfasserIn]
• Titel: An adaptive P1 finite element method for two-dimensional transverse magnetic time harmonic Maxwell’s equations with general material properties and general boundary conditions
• Verf.angabe: S.C. Brenner, J. Gedicke, L.-Y. Sung
• E-Jahr: 2016
• Jahr: 01 February 2016
• Umfang: 16 S.
• Fussnoten: Im Titel ist die Zahl "1" tief gestellt ; Gesehen am 19.05.2020
• Titel Quelle: Enthalten in: Journal of scientific computing
• Ort Quelle: New York, NY [u.a.] : Springer Science + Business Media B.V., 1986
• Jahr Quelle: 2016
• Band/Heft Quelle: 68(2016), 2, Seite 848-863
• ISSN Quelle: 1573-7691
• DOI: doi:10.1007/s10915-015-0161-x
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1698528507

Abstract

We present an adaptive P1 finite element method for two-dimensional transverse magnetic time harmonic Maxwell’s equations with general material properties and general boundary conditions. It is based on reducing the boundary value problems for Maxwell’s equations to standard second order scalar elliptic problems through the Hodge decomposition. We allow inhomogeneous and anisotropic electric permittivity, sign changing magnetic permeability, and both the perfectly conducting boundary condition and the impedance boundary condition. The optimal convergence of the adaptive finite element method is demonstrated by numerical experiments. We also present results for a semiconductor simulation, a cloaking simulation and a flat lens simulation that illustrate the robustness of the method.