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Article

Sparse matrix solvers on the GPU: conjugate gradients and multigrid

Authors:

Eitan Grinspun,

Peter SchröderAuthors Info & Claims

SIGGRAPH '03: ACM SIGGRAPH 2003 Papers

Pages 917 - 924

https://doi.org/10.1145/1201775.882364

Published: 01 July 2003 Publication History

Abstract

Many computer graphics applications require high-intensity numerical simulation. We show that such computations can be performed efficiently on the GPU, which we regard as a full function streaming processor with high floating-point performance. We implemented two basic, broadly useful, computational kernels: a sparse matrix conjugate gradient solver and a regular-grid multigrid solver. Real time applications ranging from mesh smoothing and parameterization to fluid solvers and solid mechanics can greatly benefit from these, evidence our example applications of geometric flow and fluid simulation running on NVIDIA's GeForce FX.

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Index Terms

Sparse matrix solvers on the GPU: conjugate gradients and multigrid
1. Computing methodologies
  1. Computer graphics
    1. Graphics systems and interfaces
      1. Graphics processors
  2. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Partial differential equations
    2. Numerical analysis
      1. Computations on matrices

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Published In

cover image ACM Conferences

SIGGRAPH '03: ACM SIGGRAPH 2003 Papers

July 2003

683 pages

ISBN:1581137095

DOI:10.1145/1201775

Conference Chair:
Alyn P. Rockwood
Colorado School of Mines

Copyright © 2003 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 July 2003

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SIGGRAPH03: Special Interest Group on Computer Graphics and Interactive Techniques

July 27 - 31, 2003

California, San Diego

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SIGGRAPH '03 Paper Acceptance Rate 81 of 424 submissions, 19%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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https://dl.acm.org/doi/10.1145/3687911
Chen ALiu ZYang YYuksel C(2024)Vertex Block DescentACM Transactions on Graphics10.1145/365817943:4(1-16)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658179
Adabag EAtal MGerard WPlancher B(2024)MPCGPU: Real-Time Nonlinear Model Predictive Control through Preconditioned Conjugate Gradient on the GPU2024 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA57147.2024.10611212(9787-9794)Online publication date: 13-May-2024
https://doi.org/10.1109/ICRA57147.2024.10611212
Bu XPlancher B(2024)Symmetric Stair Preconditioning of Linear Systems for Parallel Trajectory Optimization2024 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA57147.2024.10610386(9779-9786)Online publication date: 13-May-2024
https://doi.org/10.1109/ICRA57147.2024.10610386
Guo JLiu JWang QZhu X(2024)Optimizing CSR-Based SpMV on a New MIMD Architecture Pezy-SC3sAlgorithms and Architectures for Parallel Processing10.1007/978-981-97-0801-7_2(22-39)Online publication date: 1-Mar-2024
https://doi.org/10.1007/978-981-97-0801-7_2
Kim JJang MNam HKim S(2023)HARP: Hardware-Based Pseudo-Tiling for Sparse Matrix Multiplication AcceleratorProceedings of the 56th Annual IEEE/ACM International Symposium on Microarchitecture10.1145/3613424.3623790(1148-1162)Online publication date: 28-Oct-2023
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Pérez PGangnet MBlake A(2023)Poisson Image EditingSeminal Graphics Papers: Pushing the Boundaries, Volume 210.1145/3596711.3596772(577-582)Online publication date: 2-Aug-2023
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Lan LLi MJiang CWang HYang Y(2023)Second-order Stencil Descent for Interior-point HyperelasticityACM Transactions on Graphics10.1145/359210442:4(1-16)Online publication date: 26-Jul-2023
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Giannoula CFernandez ILuna JKoziris NGoumas GMutlu O(2022)SparsePProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/35080416:1(1-49)Online publication date: 28-Feb-2022
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Walden AZubair MStone CNielsen E(2021)Memory Optimizations for Sparse Linear Algebra on GPU Hardware2021 IEEE/ACM Workshop on Memory Centric High Performance Computing (MCHPC)10.1109/MCHPC54807.2021.00010(25-32)Online publication date: Nov-2021
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