Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 38, Issue 4, Pages A2173-A2208Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1046605
Keywords
space-time parallel methods; multigrid in space-time; DG-discretizations; strong and weak scalability; parabolic problems
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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.
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