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Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid
January 2011 (vol. 22 no. 1)
pp. 22-32
ASCII Text
x 
 
Dominik Göddeke, Robert Strzodka, "Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid," IEEE Transactions on Parallel and Distributed Systems, vol. 22, no. 1, pp. 22-32, January, 2011.
 
 
BibTex
x
 
@article{ 10.1109/TPDS.2010.61,
author = {Dominik Göddeke and Robert Strzodka},
title = {Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid},
journal ={IEEE Transactions on Parallel and Distributed Systems},
volume = {22},
number = {1},
issn = {1045-9219},
year = {2011},
pages = {22-32},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPDS.2010.61},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Parallel and Distributed Systems
TI - Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid
IS - 1
SN - 1045-9219
SP22
EP32
EPD - 22-32
A1 - Dominik Göddeke,
A1 - Robert Strzodka,
PY - 2011
KW - GPU Computing
KW - mixed-precision iterative refinement
KW - multigrid
KW - tridiagonal solvers
KW - cyclic reduction
KW - finite elements
KW - NVIDIA CUDA.
VL - 22
JA - IEEE Transactions on Parallel and Distributed Systems
ER -
 
Dominik Göddeke, TU Dortmund, Dortmund
Robert Strzodka, Max Planck Institut Informatik, Saarbrücken
We have previously suggested mixed precision iterative solvers specifically tailored to the iterative solution of sparse linear equation systems as they typically arise in the finite element discretization of partial differential equations. These schemes have been evaluated for a number of hardware platforms, in particular, single-precision GPUs as accelerators to the general purpose CPU. This paper reevaluates the situation with new mixed precision solvers that run entirely on the GPU: We demonstrate that mixed precision schemes constitute a significant performance gain over native double precision. Moreover, we present a new implementation of cyclic reduction for the parallel solution of tridiagonal systems and employ this scheme as a line relaxation smoother in our GPU-based multigrid solver. With an alternating direction implicit variant of this advanced smoother, we can extend the applicability of the GPU multigrid solvers to very ill-conditioned systems arising from the discretization on anisotropic meshes, that previously had to be solved on the CPU. The resulting mixed-precision schemes are always faster than double precision alone, and outperform tuned CPU solvers consistently by almost an order of magnitude.

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Index Terms:
GPU Computing, mixed-precision iterative refinement, multigrid, tridiagonal solvers, cyclic reduction, finite elements, NVIDIA CUDA.
Citation:
Dominik Göddeke, Robert Strzodka, "Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid," IEEE Transactions on Parallel and Distributed Systems, vol. 22, no. 1, pp. 22-32, Jan. 2011, doi:10.1109/TPDS.2010.61
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