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Locally Implicit Time Integration for Linear Maxwell's Equations

Sturm, Andreas

Abstract (englisch):
This thesis is concerned with the full discretization of Maxwell's equations in cases where the spatial discretization has to be carried out with a locally refined grid. In such situations locally implicit time integrators are an appealing choice for the time discretization since they overcome the grid-induced stiffness of these problems. We analyze such a locally implicit time integrator in the case where the space discretization stems from a central fluxes discontinuous Galerkin method. In fact, we prove its stability under a CFL condition which solely depends on the coarse part of the spatial grid and give a rigorous error analysis showing that the integrator is second order convergent. Moreover, we extend this time integrator so that it can be applied to an upwind fluxes discontinuous Galerkin space discretization. We show that this novel integrator preserves the second order temporal convergence and that it inherits the improved properties of an upwind fluxes discretization (better stability, higher spatial convergence rate) compared to the central fluxes case.

Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Hochschulschrift
Jahr 2017
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000069341
URN: urn:nbn:de:swb:90-693411
KITopen ID: 1000069341
Verlag Karlsruhe
Umfang 170 S.
Abschlussart Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 26.04.2017
Referent/Betreuer Prof. M. Hochbruck
Projektinformation GRK 1294 (DFG, DFG KOORD, GRK 1294/2)
SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagworte Maxwell's equations, discontinuous Galerkin finite elements, locally implicit time integration, grid-induced stiffness, energy technique, error analysis, evolution equations, component splitting, Crank-Nicolson, Verlet, leap frog,
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