Efficient Two-Level Preconditioned Conjugate Gradient Method on the GPU

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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