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3D Helmholtz Krylov Solver Preconditioned by a Shifted Laplace Multigrid Method on Multi-GPUs

Abstract

We are focusing on an iterative solver for the three-dimensional Helmholtz equation on multi-GPU using CUDA (Compute Unified Device Architecture). The Helmholtz equation discretized by a second order finite difference scheme is solved with Bi-CGSTAB preconditioned by a shifted Laplace multigrid method. Two multi-GPU approaches are considered: data parallelism and split of the algorithm. Their implementations on multi-GPU architecture are compared to a multi-threaded CPU and single GPU implementation. The results show that the data parallel implementation is suffering from communication between GPUs and CPU, but is still a number of times faster compared to many-cores. The split of the algorithm across GPUs limits communication and delivers speedups comparable to a single GPU implementation.

Keywords

  • Helmholtz Equation
  • Multiple GPUs
  • Coarse Grid Correction
  • Krylov Solver
  • Realistic Problem Size

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Notes

  1. 1.

    During the work on this paper, the newer version of CUDA 4.0 has been released. It was not possible to have the newer version installed on all systems for our experiments. That is why for consistency and comparability of experiments, we use the previous version

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Correspondence to H. Knibbe .

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Knibbe, H., Oosterlee, C.W., Vuik, C. (2013). 3D Helmholtz Krylov Solver Preconditioned by a Shifted Laplace Multigrid Method on Multi-GPUs. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_69

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