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DTSTAMP:20230831T095746Z
LOCATION:Davos
DTSTART;TZID=Europe/Stockholm:20230627T101300
DTEND;TZID=Europe/Stockholm:20230627T101400
UID:submissions.pasc-conference.org_PASC23_sess110_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.\n\nSession Chair: Jibonananda Sanyal (National Rene
 wable Energy Laboratory)
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