Details

Autor(en) / Beteiligte

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

Titel

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

Ist Teil von

• SIAM journal on scientific computing, 2023-01, Vol.45 (4), p.A1890-A1916

Ort / Verlag

United States: Society for Industrial and Applied Mathematics (SIAM)

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.