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URN: urn:nbn:de:swb:90-418093

Convergence of an ADI splitting for Maxwell's equations

Hochbruck, Marlis; Jahnke, Tobias; Schnaubelt, Roland

Abstract The convergence of an alternating direction implicit method for Maxwell's equations on product domains is investigated. Unlike the classical Yee scheme and most other integrators proposed in the literature, this method is both unconditionally stable and computationally cheap. We prove second-order convergence of the time-discretization in the framework of operator semigroup theory. In contrast to formal considerations based on Taylor expansions, our convergence analysis respects the unboundedness of the involved differential operators. The proofs are based on results concerning the regularity of the Cauchy problems, which then allow to apply an abstract convergence proof by Hansen and Ostermann.

Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Zeitschriftenaufsatz
Jahr 2014
Sprache Englisch
Identifikator ISSN: 0029-599X
KITopen ID: 1000041809
Erschienen in Numerische Mathematik
Band 129
Heft 3
Seiten 535-561
Schlagworte Maxwell's equations, alternating direction implicit method, Peaceman-Rachford splitting, well-posedness, regularity, error analysis, time integration, semigroups
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