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FEM-BEM coupling for Maxwell–Landau–Lifshitz–Gilbert equations via convolution quadrature: Weak form and numerical approximation

Bohn, Jan; Feischl, Michael; Kovács, Balázs

Abstract:
The Maxwell equations in the unbounded three dimensional space are coupled to the Landau-Lifshitz-Gilbert equation on a (not necessarily convex) bounded domain. A weak formulation of the whole coupled system is derived based on the boundary integral formulation of the exterior Maxwell equations. We show existence of a weak solution and uniqueness of the Maxwell part of the weak solution. A numerical algorithm is proposed based on finite elements and boundary elements as spatial discretisation and using the backward Euler method and convolution quadratures for the interior domain and the boundary, respectively. Well-posedness and convergence of the numerical algorithm are shown, under minimal assumptions on the regularity of solutions. Numerical experiments illustrate and expand on the theoretical results.

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Volltext (Version 2) §
DOI: 10.5445/IR/1000117889/v2
Veröffentlicht am 15.05.2020
Volltext (Version 1) §
DOI: 10.5445/IR/1000117889
Veröffentlicht am 26.03.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000117889
Verlag KIT, Karlsruhe
Umfang 38 S.
Serie CRC 1173 ; 2020/10
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Abstract/Volltext
Schlagwörter Maxwell-Landau-Lifshitz-Gilbert system, Maxwell equations, linear scheme, ferromagnetism, transparent boundary conditions, boundary elements, convolution quadratures, convergence
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