Scientific article

Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems

Published inSIAM journal on scientific computing, vol. 38, no. 4, p. A2173-A2208
Publication date2016-01

We present and analyze a new space-time parallel multigrid method for parabolic equations. The method is based on arbitrarily high order discontinuous Galerkin discretizations in time and a finite element discretization in space. The key ingredient of the new algorithm is a block Jacobi smoother. We present a detailed convergence analysis when the algorithm is applied to the heat equation and determine asymptotically optimal smoothing parameters, a precise criterion for semi-coarsening in time or full coarsening, and give an asymptotic two grid contraction factor estimate. We then explain how to implement the new multigrid algorithm in parallel and show with numerical experiments its excellent strong and weak scalability properties.

Citation (ISO format)
GANDER, Martin Jakob, NEUMÜLLER, Martin. Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems. In: SIAM journal on scientific computing, 2016, vol. 38, n° 4, p. A2173–A2208. doi: 10.1137/15M1046605
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Article (Published version)
ISSN of the journal1064-8275

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