Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

De Sterck, Hans; Falgout, Robert D.; Krzysik, Oliver A.

doi:10.1137/22m1486522

Title: Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

Journal Article · Mon Jul 24 00:00:00 EDT 2023 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/22m1486522· OSTI ID:1995057

De Sterck, Hans ^[1]; Falgout, Robert D. ^[2];

^[1]

Univ. of Waterloo, ON (Canada)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs) but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the application of the multigrid reduction-in-time (MGRIT) algorithm to linear advection PDEs. Here, the key to efficient time integration with this method is using a coarse-grid operator that provides a sufficiently accurate approximation to the so-called ideal coarse-grid operator. For certain classes of semi-Lagrangian discretizations, we present a novel semi-Lagrangian-based coarse-grid operator that leads to fast and scalable multilevel time integration of linear advection PDEs. The coarse-grid operator is composed of a semi-Lagrangian discretization followed by a correction term, with the correction designed so that the leading-order truncation error of the composite operator is approximately equal to that of the ideal coarse-grid operator. Parallel results show substantial speed-ups over sequential time integration for variable-wave-speed advection problems in one and two spatial dimensions, and using high-order discretizations up to order five. The proposed approach establishes the first practical method that provides small and scalable MGRIT iteration counts for advection problems.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1995057

Report Number(s):: LLNL-JRNL-833088; 1050937

Journal Information:: SIAM Journal on Scientific Computing, Vol. 45, Issue 4; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

97 MATHEMATICS AND COMPUTING
parallel-in-time
MGRIT
parareal
hyperbolic PDE
advection equation
multigrid

Title: Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

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