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Stable and convergent fully discrete interior-exterior coupling of Maxwell’s equations

Kovács, Balázs; Lubich, Christian

Maxwell's equations are considered with transparent boundary conditions, with initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The proposed computational scheme only involves the interior domain and its boundary. The transparent boundary conditions are imposed via a time-dependent boundary integral operator that is shown to satisfy a coercivity property. The stability of the numerical method relies on this coercivity. The method proposed here uses a discontinuous Galerkin method and the leapfrog scheme in the interior and is coupled to boundary elements and convolution quadrature on the boundary. The method is explicit in the interior
and implicit on the boundary. Stability and convergence of the spatial semidiscretization are proven, and with a computationally simple stabilization term, this is also shown for the full discretization.

Zugehörige Institution(en) am KIT Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000054663
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-546631
KITopen ID: 1000054663
Verlag KIT, Karlsruhe
Umfang 25 S.
Serie CRC 1173 ; 2016/12
Schlagworte transparent boundary conditions, Calderon operator, discontinuous Galerkin, boundary elements, leapfrog scheme, convolution quadrature
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