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UID:submissions.pasc-conference.org_PASC23_sess116_pos128@linklings.com
SUMMARY:P42 - Multigrid in H(curl) on Hybrid Tetrahedral Grids
DESCRIPTION:Poster\n\nDaniel Bauer (Friedrich-Alexander-Universität Erlang
en-Nürnberg)\n\nIn many applications large scale solvers for Maxwell's equ
ations are an indispensable tool. This work presents theory and algorithms
that are relevant to the solution of Maxwell's equations as well as their
implementation in HyTeG. We focus on multigrid methods for the curl-curl-
problem which arises from the time-harmonic formulation of Maxwell's equat
ions. This problem is challenging because it is not elliptic and therefore
standard multigrid smoothers are not effective. We rely on finite element
exterior calculus (FEEC) to explain our choice of discretization: linear
Nédélec edge elements of the first kind. FEEC is a relatively recent theor
y used to design stable finite element discretizations for a wide class of
problems. It is centered around preserving certain structures of chain co
mplexes exactly when going to the discrete level. The techniques introduce
d by FEEC also explain how effective multigrid smoothers in H(curl) can be
designed. These were first introduced by Hiptmair in 1998. HyTeG is a fin
ite element framework designed for massively parallel compute architecture
s. It supersedes the HHG framework which was already capable of solving sy
stems with 1.1e13 unknowns. The key building block to achieve these impres
sive results is a matrix-free implementation of geometric multigrid on hyb
rid tetrahedral grids.
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