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

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • H. Knibbe

    (Delft University of Technology)

  • C. W. Oosterlee

    (Delft University of Technology, Dutch National Research Centre for Mathematics and Computer Science (CWI))

  • C. Vuik

    (Delft University of Technology)

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.

Suggested Citation

  • H. Knibbe & C. W. Oosterlee & C. Vuik, 2013. "3D Helmholtz Krylov Solver Preconditioned by a Shifted Laplace Multigrid Method on Multi-GPUs," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 653-661, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_69
    DOI: 10.1007/978-3-642-33134-3_69
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