An efficient GPU implementation of the alternating direction implicit (ADI) numerical method in 3D domains is proposed. An application of the ADI method to fluid flow simulation by solving the full Navier-Stokes equations and some implementation details of a fast tridiagonal matrix solver on CUDA are discussed. The performances of GPU and CPU implementations are compared for a modeling problem to illustrate how GPU outperforms the latest multicore CPUs by an order of magnitude in the double precision mode.

Keywords: alternating direction implicit method, parallel computing, GPU, Navier-Stokes equations

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