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Efficient Two-Level Preconditionined Conjugate Gradient Method on the GPU

Rohit Gupta, Martin B. van Gijzen, Kees Vuik
Department of Applied Mathematical Analysis, Delft University of Technology
Reports of the Department of Applied Mathematical Analysis, Delft University of Technology, Report 11-15

@article{gupta2011efficient,

   title={Efficient Two-Level Preconditionined Conjugate Gradient Method on the GPU.},

   author={Gupta, R. and van Gijzen, M.B. and Vuik, K.},

   year={2011}

}

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We present an implementation of Two-Level Preconditioned Conjugate Gradient Method for the GPU. We investigate a Truncated Neumann Series based preconditioner in combination with deflation and compare it with Block Incomplete Cholesky schemes. This combination exhibits fine-grain parallelism and hence we gain considerably in execution time. It’s numerical performance is also comparable to the Block Incomplete Cholesky approach. Our method provides a speedup of up to 16 times for a system of one million unknowns when compared to an optimized implementation on the CPU.
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