Scaling Algebraic Multigrid Solvers: On the Road to Exascale

Algebraic Multigrid (AMG) solvers are an essential component of many large-scale scientific simulation codes. Their continued numerical scalability and efficient implementation is critical for preparing these codes for exascale. Our experiences on modern multi-core machines show that significant challenges must be addressed for AMG to perform well on such machines. We discuss our experiences and describe the techniques we have used to overcome scalability challenges for AMG on hybrid architectures in preparation for exascale

Block-asynchronous multigrid smoothers for GPU-accelerated systems

This paper explores the need for asynchronous iteration algorithms as smoothers in multigrid methods. The hardware target for the new algorithms is top-of-the-line, highly parallel hybrid architectures -- multicore-based systems enhanced with GPGPUs. These architectures are the most likely candidates for future high-end supercomputers. To pave the road for their efficient use, challenges related to the established notion that "data movement, not FLOPS, is the bottleneck to performance" must be resolved. Our work is in this direction -- we designed block-asynchronous multigrid smoothers that perform more flops in order to reduce synchronization, and hence data movement. We show that the extra flops are done for "free", while synchronization is reduced and the convergence properties of multigrid with classical smoothers like Gauss-Seidel are preserved

The Open Porous Media Flow Reservoir Simulator

The Open Porous Media (OPM) initiative is a community effort that encourages open innovation and reproducible research for simulation of porous media processes. OPM coordinates collaborative software development, maintains and distributes open-source software and open data sets, and seeks to ensure that these are available under a free license in a long-term perspective. In this paper, we present OPM Flow, which is a reservoir simulator developed for industrial use, as well as some of the individual components used to make OPM Flow. The descriptions apply to the 2019.10 release of OPM.Comment: 43 pages, 22 figure

Parallel Algebraic Multigrid Methods - High Performance Preconditioners

The development of high performance, massively parallel computers and the increasing demands of computationally challenging applications have necessitated the development of scalable solvers and preconditioners. One of the most effective ways to achieve scalability is the use of multigrid or multilevel techniques. Algebraic multigrid (AMG) is a very efficient algorithm for solving large problems on unstructured grids. While much of it can be parallelized in a straightforward way, some components of the classical algorithm, particularly the coarsening process and some of the most efficient smoothers, are highly sequential, and require new parallel approaches. This chapter presents the basic principles of AMG and gives an overview of various parallel implementations of AMG, including descriptions of parallel coarsening schemes and smoothers, some numerical results as well as references to existing software packages