An implicit multigrid solver for high-order compressible flow simulations on GPUs

V. Esfahanian, M. Hedayat, B. Baghapour, M. Torabzadeh, S.J. Hosseini
Vehicle, Fuel and Environment Research Institute, University of Tehran, Iran
5th Asia Pacific Congress on Computational Mechanics and 4th International Symposium on Computational Mechanics (APCOM2013), 2013


   title={An implicit multigrid solver for high-order compressible flow simulations on GPUs},

   author={Esfahanian, V and Hedayat, M and Baghapour, B and Torabzadeh, M and Hosseini, SJ},



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The multigrid method has proved to be effective for a large class of numerical methods. In this study, a strategy based on Full Approximation Storage (FAS) scheme is implemented together with Full Multigrid Algorithm (FMG) to accelerate convergence of steady state solutions of the two-dimensional compressible Euler equations on Graphics Processing Unit (GPU). The Beam and Warming linearization scheme in curvilinear coordinates is used to discretize the governing equation. The second-order central and the fourth-order compact finite-difference schemes are applied for spatial discretization. A high-performance GPU-implemented block-tridiagonal solver based on Block Cyclic Reduction (BCR) algorithm is utilized. The proposed BCR solver is applied to finite-difference discretization on structured grids via Alternating Direction Implicit (ADI) scheme. Attention is directed towards the computational performance of the V-cycle and W-cycle multigrid strategies in two and three grid levels using the NVIDIA GTX480 graphics card. Speedups between 2x-5.2x are achieved in comparison to the Intel Core i7-920 2.67GHz CPU for different grid sizes.
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