P42 - Multigrid in H(curl) on Hybrid Tetrahedral Grids
DescriptionIn many applications large scale solvers for Maxwell's equations 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 equations. 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 theory used to design stable finite element discretizations for a wide class of problems. It is centered around preserving certain structures of chain complexes exactly when going to the discrete level. The techniques introduced 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 finite element framework designed for massively parallel compute architectures. It supersedes the HHG framework which was already capable of solving systems with 1.1e13 unknowns. The key building block to achieve these impressive results is a matrix-free implementation of geometric multigrid on hybrid tetrahedral grids.
TimeTuesday, June 2710:13 - 10:14 CEST