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ADI schemes for the time integration of Maxwell equations

Zerulla, Konstantin

This thesis is concerned with the analysis and construction of alternating direction implicit (ADI) splitting schemes for the time integration of linear isotropic Maxwell equations on cuboids.
The work is organized in two major parts.

The first part deals with time discrete approximations to exponentially stable Maxwell equations.
By means of a divergence cleaning technique and artificial damping, we obtain an ADI scheme with approximations that also decay exponentially in time.
The decay rate is here uniform with respect to the time discretization.
One of the main ingredients in the proof of the decay behavior is an observability estimate for the numerical approximations.
This inequality is obtained by means of a discrete multiplier technique.
We also provide a rigorous error analysis for the uniformly exponentially stable ADI scheme, yielding convergence of order one in a space similar to $H^{-1}$.
The error result makes only assumptions on the initial data and the model parameters.

In the second part, we analyze time discrete approximations to linear isotropic Maxwell equations on a heterogeneous cuboid.
In this setting, the domain consists of two different homogeneous subcuboids.
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Volltext §
DOI: 10.5445/IR/1000128718
Veröffentlicht am 25.01.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Hochschulschrift
Publikationsdatum 25.01.2021
Sprache Englisch
Identifikator KITopen-ID: 1000128718
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 220 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Analysis (IANA)
Prüfungsdatum 16.12.2020
Referent/Betreuer Prof. R. Schnaubelt
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Schlagwörter Maxwell equations, ADI schemes, regularity analysis, exponential stability, time integration, splitting method, observability, error estimates
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
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