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The Maxwell-Landau-Lifshitz-Gilbert System: Mathematical Theory and Numerical Approximation

Bohn, Jan Adam

Abstract (englisch):

This thesis deals with the mathematical theory and numerical approximation of the
Landau--Lifshitz--Gilbert equation coupled to the Maxwell equations without artificial
boundary conditions.
As a starting point, the physical equations are stated on the unbounded three dimensional
space and reformulated in a mathematically precise way to a coupled partial
differential -- boundary integral system.
We derive a weak form of the whole coupled system, state the relation to the strong
form and show uniqueness of the Maxwell part of the solution. A numerical algorithm is
proposed based on the tangent plane scheme for the LLG part and using a finite element
and boundary element coupling as spatial discretization and the backward Euler method
and Convolution Quadrature as time discretization for the interior Maxwell part and the
boundary, respectively. Under minimal assumptions on the regularity of solutions, we
present well-posedness and convergence of the numerical algorithm.
For the pure Maxwell equations without the coupling to the LLG equation, we are
able to show stronger results than in the coupled case. We derive a weak form for the
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Volltext §
DOI: 10.5445/IR/1000133728
Veröffentlicht am 01.07.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Hochschulschrift
Publikationsdatum 01.07.2021
Sprache Englisch
Identifikator KITopen-ID: 1000133728
Verlag Karlsruher Institut für Technologie (KIT)
Umfang x, 225 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 05.05.2021
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Schlagwörter Maxwell, LLG, transparent boundary conditions, Convolution Quadrature, boundary elements, Maxwell-Landau-Lifshitz-Gilbert system, ferromagnetism, convergence
Referent/Betreuer Dörfler, W.
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