Overview

Many large-scale scientific applications rely heavily on preconditioned iterative solvers for large linear systems. For these solvers to efficiently exploit extreme-scale hardware, both the solver algorithms and the implementations must be redesigned to address challenges like extreme concurrency, complex memory hierarchies, costly data movement, heterogeneous node architectures, and the increasing adoption of low-precision processor technology.

The Production-ready, Exascale-Enabled Krylov Solvers (PEEKS) effort aims to tackle these challenges and advance the capabilities of the ECP software stack by making the new scalable algorithms accessible within the Ginkgo software ecosystem. The PEEKS algorithms focus on communication-minimizing Krylov solvers, parallel incomplete factorization routines, and parallel preconditioning techniques, as these building blocks form the numerical core of many complex application codes. Ginkgo provides native support for NVIDIA GPUs, AMD GPUs, and Intel GPUs to ensure successful delivery of scalable Krylov solvers in robust, production-quality software that can be relied on by ECP applications.
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2018 Poster
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Sponsored By
Exascale Computing Project
National Nuclear Security Administration
The United States Department of Energy

Papers

Anzt, H., Y. M. Tsai, A. Abdelfattah, T. Cojean, and J. Dongarra, Evaluating the Performance of NVIDIA’s A100 Ampere GPU for Sparse and Batched Computations,” 2020 IEEE/ACM Workshop on Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems (PMBS): IEEE, November 2020.  (1.9 MB)
Nayak, P., T. Cojean, and H. Anzt, Evaluating Asynchronous Schwarz Solvers on GPUs,” International Journal of High Performance Computing Applications, August 2020. DOI: 10.1177/1094342020946814
Anzt, H., T. Cojean, Y-C. Chen, F. Goebel, T. Gruetzmacher, P. Nayak, T. Ribizel, and Y-H. Tsai, Ginkgo: A High Performance Numerical Linear Algebra Library,” Journal of Open Source Software, vol. 5, issue 52, August 2020. DOI: 10.21105/joss.02260  (721.84 KB)
Goebel, F., H. Anzt, T. Cojean, G. Flegar, and E. S. Quintana-Orti, Multiprecision Block-Jacobi for Iterative Triangular Solves,” European Conference on Parallel Processing (Euro-Par 2020): Springer, August 2020. DOI: 10.1007/978-3-030-57675-2_34
Tsai, Y. M., T. Cojean, and H. Anzt, Sparse Linear Algebra on AMD and NVIDIA GPUs—The Race is On,” ISC High Performance: Springer, June 2020. DOI: 10.1007/978-3-030-50743-5_16  (5.63 MB)
Anzt, H., T. Cojean, C. Yen-Chen, J. Dongarra, G. Flegar, P. Nayak, S. Tomov, Y. M. Tsai, and W. Wang, Load-Balancing Sparse Matrix Vector Product Kernels on GPUs,” ACM Transactions on Parallel Computing, vol. 7, issue 1, March 2020. DOI: 10.1145/3380930  (5.67 MB)
Gates, M., S. Tomov, H. Anzt, P. Luszczek, and J. Dongarra, Clover: Computational Libraries Optimized via Exascale Research , Houston, TX, 2020 Exascale Computing Project Annual Meeting, February 2020.  (872 KB)
Anzt, H., T. Cojean, Y-C. Chen, F. Goebel, T. Gruetzmacher, P. Nayak, T. Ribizel, Y-H. Tsai, and J. Dongarra, Ginkgo: A Node-Level Sparse Linear Algebra Library for HPC (Poster) , Houston, TX, 2020 Exascale Computing Project Annual Meeting, February 2020.  (699 KB)
Ribizel, T., and H. Anzt, Parallel Selection on GPUs,” Parallel Computing, vol. 91, March 2020, 2019. DOI: 10.1016/j.parco.2019.102588  (1.43 MB)
Anzt, H., G. Flegar, T. Gruetzmacher, and E. S. Quintana-Orti, Toward a Modular Precision Ecosystem for High-Performance Computing,” The International Journal of High Performance Computing Applications, vol. 33, issue 6, pp. 1069-1078, November 2019. DOI: 10.1177/1094342019846547  (1.93 MB)
Anzt, H., T. Cojean, and E. Kuhn, Towards a New Peer Review Concept for Scientific Computing ensuring Technical Quality, Software Sustainability, and Result Reproducibility,” Proceedings in Applied Mathematics and Mechanics, vol. 19, issue 1, November 2019. DOI: 10.1002/pamm.201900490
Yamazaki, I., A. Ida, R. Yokota, and J. Dongarra, Distributed-Memory Lattice H-Matrix Factorization,” The International Journal of High Performance Computing Applications, vol. 33, issue 5, pp. 1046–1063, August 2019. DOI: 10.1177/1094342019861139  (1.14 MB)
Anzt, H., and G. Flegar, Are we Doing the Right Thing? – A Critical Analysis of the Academic HPC Community,” 2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), Rio de Janeiro, Brazil, IEEE, May 2019. DOI: 10.1109/IPDPSW.2019.00122  (622.32 KB)
Bai, Z., J. Dongarra, D. Lu, and I. Yamazaki, Matrix Powers Kernels for Thick-Restart Lanczos with Explicit External Deflation,” International Parallel and Distributed Processing Symposium (IPDPS), Rio de Janeiro, Brazil, IEEE, May 2019.  (480.73 KB)
Anzt, H., T. Ribizel, G. Flegar, E. Chow, and J. Dongarra, ParILUT – A Parallel Threshold ILU for GPUs,” IEEE International Parallel and Distributed Processing Symposium (IPDPS), Rio de Janeiro, Brazil, IEEE, May 2019. DOI: 10.1109/IPDPS.2019.00033  (505.95 KB)
Gruetzmacher, T., T. Cojean, G. Flegar, F. Göbel, and H. Anzt, A Customized Precision Format Based on Mantissa Segmentation for Accelerating Sparse Linear Algebra,” Concurrency and Computation: Practice and Experience, vol. 40319, issue 262, January 2019. DOI: 10.1002/cpe.5418
Jagode, H., A. Danalis, H. Anzt, I. Yamazaki, M. Hoemmen, E. Boman, S. Tomov, and J. Dongarra, Software-Defined Events (SDEs) in MAGMA-Sparse,” Innovative Computing Laboratory Technical Report, no. ICL-UT-18-12: University of Tennessee, December 2018.  (481.69 KB)
Anzt, H., J. Dongarra, G. Flegar, and T. Gruetzmacher, Variable-Size Batched Condition Number Calculation on GPUs,” SBAC-PAD, Lyon, France, September 2018.  (509.3 KB)
Anzt, H., E. Chow, and J. Dongarra, ParILUT - A New Parallel Threshold ILU,” SIAM Journal on Scientific Computing, vol. 40, issue 4: SIAM, pp. C503–C519, July 2018. DOI: 10.1137/16M1079506  (19.26 MB)
Anzt, H., I. Yamazaki, M. Hoemmen, E. Boman, and J. Dongarra, Solver Interface & Performance on Cori,” Innovative Computing Laboratory Technical Report, no. ICL-UT-18-05: University of Tennessee, June 2018.  (188.05 KB)
Anzt, H., and J. Dongarra, A Jaccard Weights Kernel Leveraging Independent Thread Scheduling on GPUs,” SBAC-PAD, Lyon, France, IEEE, 2018.  (237.68 KB)
Anzt, H., T. Gruetzmacher, E. S. Quintana-Orti, and F. Scheidegger, High-Performance GPU Implementation of PageRank with Reduced Precision based on Mantissa Segmentation,” 8th Workshop on Irregular Applications: Architectures and Algorithms, 2018.
Anzt, H., E. Boman, J. Dongarra, G. Flegar, M. Gates, M. Heroux, M. Hoemmen, J. Kurzak, P. Luszczek, S. Rajamanickam, et al., MAGMA-sparse Interface Design Whitepaper,” Innovative Computing Laboratory Technical Report, no. ICL-UT-17-05, September 2017.  (1.28 MB)
Anzt, H., J. Dongarra, G. Flegar, and E. S. Quintana-Orti, Variable-Size Batched LU for Small Matrices and Its Integration into Block-Jacobi Preconditioning,” 46th International Conference on Parallel Processing (ICPP), Bristol, United Kingdom, IEEE, August 2017. DOI: 10.1109/ICPP.2017.18
Yamazaki, I., M. Hoemmen, P. Luszczek, and J. Dongarra, Improving Performance of GMRES by Reducing Communication and Pipelining Global Collectives,” Proceedings of The 18th IEEE International Workshop on Parallel and Distributed Scientific and Engineering Computing (PDSEC 2017), Best Paper Award, Orlando, FL, June 2017. DOI: 10.1109/IPDPSW.2017.65  (453.66 KB)

Presentations

Gates, M., S. Tomov, H. Anzt, P. Luszczek, and J. Dongarra, Clover: Computational Libraries Optimized via Exascale Research , Houston, TX, 2020 Exascale Computing Project Annual Meeting, February 2020.  (872 KB)
Anzt, H., T. Cojean, Y-C. Chen, F. Goebel, T. Gruetzmacher, P. Nayak, T. Ribizel, Y-H. Tsai, and J. Dongarra, Ginkgo: A Node-Level Sparse Linear Algebra Library for HPC (Poster) , Houston, TX, 2020 Exascale Computing Project Annual Meeting, February 2020.  (699 KB)
Hoemmen, M., and I. Yamazaki, Production Implementations of Pipelined & Communication-Avoiding Iterative Linear Solvers , Tokyo, Japan, SIAM Conference on Parallel Processing for Scientific Computing, March 2018.  (2.34 MB)
Anzt, H., G. Collins, J. Dongarra, G. Flegar, and E. S. Quintana-Orti, Flexible Batched Sparse Matrix Vector Product on GPUs , Denver, Colorado, ScalA'17: 8th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, November 2017.  (16.8 MB)
Yamazaki, I., M. Hoemmen, P. Luszczek, and J. Dongarra, Comparing performance of s-step and pipelined GMRES on distributed-memory multicore CPUs , Pittsburgh, Pennsylvania, SIAM Annual Meeting, July 2017.  (748 KB)

ICL Team Members

Hartwig Anzt
Consultant
Natalie Beams
Research Scientist I
Sebastien Cayrols
Research Scientist I
Jack Dongarra
University Distinguished Professor
Stanimire Tomov
Research Assistant Professor

In Collaboration With

Sandia National Laboratories

Exascale Computing Project

PEEKS is part of ICL's involvment in the Exascale Computing Project (ECP). The ECP was established with the goals of maximizing the benefits of high-performance computing (HPC) for the United States and accelerating the development of a capable exascale computing ecosystem. Exascale refers to computing systems at least 50 times faster than the nation’s most powerful supercomputers in use today.

The ECP is a collaborative effort of two U.S. Department of Energy organizations – the Office of Science (DOE-SC) and the National Nuclear Security Administration (NNSA).