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Speaker: Dr. Huangxin Chen
School of Mahtematical Sciences, Xiamen University
Title: Local Multigrid Methods
for the Time-Harmonic Maxwell Equation
Time: Thursday Aut. 08, 16:00 pm -
17:00pm
Venue: B703
Abstract:
For the efficient numerical solution of indefinite linear systems
arising from curl conforming edge element approximations of the
time-harmonic Maxwell equation, we will discuss local multigrid
methods (LMM) on adaptively refined meshes in this talk. The LMM
features local hybrid Hiptmair smoothers of Jacobi and Gauss-Seidel
type which are performed only on basis functions associated with
newly created edges/nodal points or those edges/nodal points where
the support of the corresponding basis function has changed during
the refinement process. Using the abstract Schwarz theory of
multilevel iterative schemes, quasi-optimal convergence of the LMM
is shown, i.e., the convergence rates are independent of mesh sizes
and mesh levels provided that the coarsest mesh is chosen
sufficiently fine. The theoretical findings are illustrated by the
results of some numerical examples.