SPAI Preconditioners for HPC Applications
Version of Record online: 3 DEC 2012
Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Special Issue: 83rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Darmstadt 2012; Editors: H.-D. Alber, N. Kraynyukova and C. Tropea
Volume 12, Issue 1, pages 651–652, December 2012
How to Cite
Sawyer, W., Vanini, C., Fourestey, G. and Popescu, R. (2012), SPAI Preconditioners for HPC Applications. Proc. Appl. Math. Mech., 12: 651–652. doi: 10.1002/pamm.201210314
- Issue online: 3 DEC 2012
- Version of Record online: 3 DEC 2012
Iterative methods to solve systems of linear equations Ax = b usually require preconditioners M to speed convergence. But the calculation of many preconditioners can be notoriously sequential. The sparse approximate inverse preconditioner (SPAI) has particular potential for high performance computing . We have ported the SPAI algorithm to graphical processing units (GPUs) within NVIDIA's CUSP library  for sparse linear algebra. GPUs perform well on dense linear algebra problems where data resides for long periods on the device. Since the underlying minimization problems are independent, they are mapped to separate thread-blocks, and an optimized QR algorithm implemented using NVIDIA's CUBLAS library is employed on each.
Traditionally the challenge has been to determine a sparsity pattern Sp(M) of the preconditioner dynamically , which reduces the condition number of MA to a degree where a preconditioned iterative solver such as GMRES becomes computationally viable. Due to the extremely high performance of the GPU, it is possible to consider initial sparsity patterns much denser than have been previously considered. We therefore consider a fixed sparsity patterns to simplify the GPU implementation.
We evaluate the performance of the resulting preconditioner on a standard set of sparse matrices, and compare SPAI to other preconditioners. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)