GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Preconditioning and boundary conditions
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
How fast are nonsymmetric matrix iterations
SIAM Journal on Matrix Analysis and Applications
Applied numerical linear algebra
Applied numerical linear algebra
The Parallel Algorithm of Conjugate Gradient Method
IWCC '01 Proceedings of the NATO Advanced Research Workshop on Advanced Environments, Tools, and Applications for Cluster Computing-Revised Papers
Cg: a system for programming graphics hardware in a C-like language
ACM SIGGRAPH 2003 Papers
Sparse matrix solvers on the GPU: conjugate gradients and multigrid
ACM SIGGRAPH 2003 Papers
OpenGL(R) Shading Language
LU-GPU: Efficient Algorithms for Solving Dense Linear Systems on Graphics Hardware
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
GMRES Method on Lightweight GRID System
ISPDC '05 Proceedings of the The 4th International Symposium on Parallel and Distributed Computing
Proceedings of the 44th annual Design Automation Conference
Efficient gather and scatter operations on graphics processors
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
GPU acceleration of cutoff pair potentials for molecular modeling applications
Proceedings of the 5th conference on Computing frontiers
Relational joins on graphics processors
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
Sparse matrix computations on manycore GPU's
Proceedings of the 45th annual Design Automation Conference
Numerical Mathematics and Computing
Numerical Mathematics and Computing
Solving Sparse Linear Systems on NVIDIA Tesla GPUs
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
GCMS '09 Proceedings of the 2009 Grand Challenges in Modeling & Simulation Conference
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We have used Graphics Processing Units (GPUs) to accelerate the solution of the types of equations typically encountered in dynamic system simulators. Compared to commercial matrix solvers that run on a CPU, we realized speedups ranging from 5 (for system size ≈ 700) to 460 (for system size ≈ 5800). While calculation time for the commercial matrix solver increased with matrix size ≈ O(N)2.3, our new GPU-based Preconditioned Generalized Minimal Residual (PGM-RES) technique yielded scaling as ≈ O(N)1.2. A significant component of this performance was achieved by development of new Basic Linear Algebra routines for the NVIDIA Tesla GPU that directly address characteristics typical of matrices that describe the time domain response of naturally-coupled dynamic systems.