high performance computing on graphics processing units: hgpu.org

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.