Preparing sparse solvers for exascale computing.

Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'

Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs

We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the algorithm uses a parallel maximal independent set algorithm in forming aggregates and the resulting coarse level hierarchy is then used in a K-cycle iteration solve phase with a $\ell^1$-Jacobi smoother. Numerical tests of a parallel implementation of the method for graphics processors are presented to demonstrate its effectiveness.Comment: 18 pages, 3 figure

Multi-Level Parallelism for Incompressible Flow Computations on GPU Clusters

We investigate multi-level parallelism on GPU clusters with MPI-CUDA and hybrid MPI-OpenMP-CUDA parallel implementations, in which all computations are done on the GPU using CUDA. We explore efficiency and scalability of incompressible flow computations using up to 256 GPUs on a problem with approximately 17.2 billion cells. Our work addresses some of the unique issues faced when merging fine-grain parallelism on the GPU using CUDA with coarse-grain parallelism that use either MPI or MPI-OpenMP for communications. We present three different strategies to overlap computations with communications, and systematically assess their impact on parallel performance on two different GPU clusters. Our results for strong and weak scaling analysis of incompressible flow computations demonstrate that GPU clusters offer significant benefits for large data sets, and a dual-level MPI-CUDA implementation with maximum overlapping of computation and communication provides substantial benefits in performance. We also find that our tri-level MPI-OpenMP-CUDA parallel implementation does not offer a significant advantage in performance over the dual-level implementation on GPU clusters with two GPUs per node, but on clusters with higher GPU counts per node or with different domain decomposition strategies a tri-level implementation may exhibit higher efficiency than a dual-level implementation and needs to be investigated further

Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond

In this and a set of companion whitepapers, the USQCD Collaboration lays out a program of science and computing for lattice gauge theory. These whitepapers describe how calculation using lattice QCD (and other gauge theories) can aid the interpretation of ongoing and upcoming experiments in particle and nuclear physics, as well as inspire new ones.Comment: 44 pages. 1 of USQCD whitepapers