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Original Articles

GPU-accelerated preconditioned GMRES method for two-dimensional Maxwell's equations

, , , &
Pages 2122-2144 | Received 15 Aug 2016, Accepted 01 Nov 2016, Published online: 03 Feb 2017
 

ABSTRACT

In this study, for two-dimensional Maxwell's equations, an efficient preconditioned generalized minimum residual method on the graphics processing unit (GPUPGMRES) is proposed to obtain numerical solutions of the equations that are discretized by a multisymplectic Preissmann scheme. In our proposed GPUPGMRES, a novel sparse matrix–vector multiplication (SpMV) kernel is suggested while keeping the compressed sparse row (CSR) intact. The proposed kernel dynamically assigns different number of rows to each thread block, and accesses the CSR arrays in a fully coalesced manner. This greatly alleviates the bottleneck of many existing CSR-based algorithms. Furthermore, the vector-operation and inner-product decision trees are automatically constructed. These kernels and their corresponding optimized compute unified device architecture parameter values can be automatically selected from the decision trees for vectors of any size. In addition, using the sparse approximate inverse technique, the preconditioner equation solving falls within the scope of SpMV. Numerical results show that our proposed kernels have high parallelism. GPUPGMRES outperforms a recently proposed preconditioned GMRES method, and a preconditioned GMRES implementation in the AmgX library. Moreover, GPUPGMRES is efficient in solving the two-dimensional Maxwell's equations.

2010 AMS SUBJECT CLASSIFICATIONS:

Acknowledgments

We gratefully acknowledge the comments from the anonymous reviewers, which greatly helped us to improve the contents of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research has been supported by the Chinese Natural Science Foundation under grant number [61379017], and the Natural Science Foundation of Zhejiang Province, China under grant number [LY17F020021].

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