MGRIT
swMATH ID:  30280 
Software Authors:  Dobrev, V. A.; Kolev, Tz.; Petersson, N. A.; Schroder, J. B. 
Description:  Twolevel convergence theory for multigrid reduction in time (MGRIT). In this paper we develop a twogrid convergence theory for the parallelintime scheme known as multigrid reduction in time (MGRIT), as it is implemented in the opensource package [XBraid: Parallel Multigrid in Time, http://llnl.gov/casc/xbraid]. MGRIT is a scalable and multilevel approach to parallelintime simulations that nonintrusively uses existing timestepping schemes, and in a specific twolevel setting it is equivalent to the widely known parareal algorithm. The goal of this paper is twofold. First, we present a twolevel MGRIT convergence analysis for linear problems where the spatial discretization matrix can be diagonalized, and then apply this analysis to our two basic model problems, the heat equation and the advection equation. One important assumption is that the coarse and fine timegrid propagators can be diagaonalized by the same set of eigenvectors, which is often the case when the same spatial discretization operator is used on the coarse and fine time grids. In many cases, the MGRIT algorithm is guaranteed to converge, and we demonstrate numerically that the theoretically predicted convergence rates are sharp in practice for our model problems. Second, we explore how the convergence of MGRIT compares to the stability of the chosen timestepping scheme. In particular, we demonstrate that a stable timestepping scheme does not necessarily imply convergence of MGRIT, although MGRIT with FCFrelaxation always converges for the diffusion dominated problems considered here. 
Homepage:  https://epubs.siam.org/doi/10.1137/16M1074096 
Keywords:  multigrid; multigridintime; parallelintime; convergence theory; high performance computing 
Related Software:  XBraid; pyParareal; PARAEXP; PARALAAOMPI; RODAS; CHeart; PFASST; ParaDiag; ParaOpt; GitHub; MUMPS; iFEM; TRBDF2; AlexNet; torchdiffeq; ImageNet; TensorFlow; IFISS; Parallel Computing Toolbox; Parareal 
Referenced in:  21 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Twolevel convergence theory for multigrid reduction in time (MGRIT). Zbl 1416.65329 Dobrev, V. A.; Kolev, Tz.; Petersson, N. A.; Schroder, J. B. 
2017

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Referenced by 37 Authors
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Referenced in 13 Serials
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