Scalable line and plane relaxation in a parallel structured multigrid solver

Journal Article · Tue Oct 20 00:00:00 EDT 2020 · Parallel Computing

DOI:https://doi.org/10.1016/j.parco.2020.102705· OSTI ID:1688768

Reisner, Andrew Ray ^[1]; Moulton, John David ^[1]; Berndt, Markus ^[1]; Olson, Luke N. ^[2]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2. Univ. of Illinois at Urbana-Champaign, IL (United States)

The efficient solution of sparse, linear systems that arise through the discretization of partial differential equations remains a key challenge for a range of high performance scientific simulations. One approach for reducing data movement and improving performance is by exposing and exploiting structure in a problem through the use of robust structured multilevel solvers. By choosing coarsening that preserves the structure of the problem, these methods maintain efficient structured computation and communication throughout the multigrid hierarchy. However, when coarsening is not permitted to be dependent on the operator, anisotropy must be addressed by the smoother — producing error compatible for coarse-grid correction with structured coarsening. Here, the components required in a scalable parallel structured solver are described with a focus on memory and communication efficiency of robust smoothers. While the implementation of communication and memory reduction techniques in smoothers integrated in a complete 3D solver present a significant engineering challenge, a novel approach is proposed that addresses these challenges systematically through a change to the solver’s execution model. Enabled by user-level threading paired with a set of data and communication abstractions, this approach permits seamless aggregation of communication in plane smoothers — directly reusing code for a 2D distributed multilevel cycle. Results show an effective reduction in communication costs for coarse-grid problems, and result in a speedup of 8.7x in smoothing routines shown in Fig. 12 using this approach. This produces a significant improvement to strong scalability while maintaining favorable weak scaling behavior. Finally, a parallel scaling study using a series of refined meshes is included that demonstrates the effectiveness of this approach in an application of interest.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001; AC52-06NA25396; NA0002374
• OSTI ID: 1688768
• Alternate ID(s): OSTI ID: 1776467
• Report Number(s): LA-UR--20-23447
• Journal Information: Parallel Computing, Journal Name: Parallel Computing Vol. 100; ISSN 0167-8191
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
line relaxation
multigrid
parallel
plane relaxation communication
structured