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A uniformly exponentially stable ADI scheme for Maxwell equations

Zerulla, Konstantin

A modified alternating direction implicit scheme for the time integration of linear isotropic Maxwell equations with strictly positive conductivity on cuboids is constructed. A key feature of the proposed scheme is its uniform exponential stability, being achieved by coupling the Maxwell system with an additional damped PDE and adding artificial damping to the scheme. The implicit steps in the resulting time integrator further decouple into essentially one-dimensional elliptic problems, requiring only linear complexity. The convergence of the scheme to the solution of the original Maxwell system is analyzed in the abstract time-discrete setting, providing an error bound in a space related to $H^{−1}$.

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DOI: 10.5445/IR/1000098268
Veröffentlicht am 13.09.2019
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2019
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000098268
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 40 S.
Serie CRC 1173 ; 2019/15
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Schlagwörter Maxwell equations, splitting method, exponential stability, observability, error bound, divergence cleaning
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