GPU implementation of a Helmholtz Krylov Solver preconditioned by a shifted Laplace multigrid method

H. Knibbe, C. W. Oosterlee, C. Vuik
Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
Journal of Computational and Applied Mathematics (July 2011)















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A Helmholtz equation in two dimensions discretized by a second order finite difference scheme is considered. Krylov methods such as Bi-CGSTAB and IDR(s) have been chosen as solvers. Since the convergence of the Krylov solvers deteriorates with increasing wave number, a shifted Laplacian multigrid preconditioner is used to improve the convergence. The implementation of the preconditioned solver on CPU (Central Processing Unit) is compared to an implementation on GPU (Graphics Processing Units or graphics card) using CUDA (Compute Unified Device Architecture). The results show that preconditioned Bi-CGSTAB on GPU as well as preconditioned IDR(s) on GPU is about 30 times faster than on CPU for the same stopping criterion.
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