Error Controlled hp-Adaptive Finite Element Methods for the Time-Dependent Maxwell Equations.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2015)
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|Item Type:||Ph.D. Thesis|
|Title:||Error Controlled hp-Adaptive Finite Element Methods for the Time-Dependent Maxwell Equations|
This thesis deals with the development and analysis of a discretization method and the error controlled adaptation of spatial and temporal discretizations in context of the time-dependent Maxwell equations. To this end, a hp space-time Galerkin discretization for Maxwell’s equations, allowing for local adaptation of the polynomial approximation order p as well as the local meshsize h, is developed and analyzed. Furthermore, the developed discretization is extended to problems with waveguide structure, in order to efficiently model waveguide ports. For the purpose of local adaptation and control of the global discretization error, a posteriori error estimates for quantities of interest such as scattering parameters or farfield quantities are derived and employed within an hp-adaptive algorithm. While such adjoint based a posteriori error estimates are available for many other problems, its application to the present problem has been newly developed in this thesis.
|Place of Publication:||Darmstadt|
|Uncontrolled Keywords:||Maxwell's equations, wave propagation, hp adaptivity, error control, space-time finite elements, discontinuous Galerkin|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 510 Mathematik
600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
|Divisions:||18 Department of Electrical Engineering and Information Technology > Institute for Computational Electromagnetics|
|Date Deposited:||29 Jun 2015 10:07|
|Last Modified:||29 Jun 2015 10:07|
|Referees:||Weiland, Prof. Dr. Thomas and Egger, Prof. Dr. Herbert|
|Refereed:||6 March 2015|