"978-80-7372-821-2" . "Numerical solution of the Stokes problem using CUDA" . "RIV/68407700:21340/12:00188946!RIV13-MSM-21340___" . "Seminar on Numerical Analysis" . "Numerical solution of the Stokes problem using CUDA"@en . . "Effective numerical solution of incompressible flow problems is essential for, e.g., atmospheric boundary layer simulations. Mixed finite element approximation of the incompressible Stokes or Navier-Stokes equations leads to saddle-point linear systems. Techniques for the efficient solution of large saddle-point systems are often based on an LU factorization of a sparse matrix followed by forward and backward substitutions. However, this approach is difficult to parallelize effectively. We investigate the application of graphics processing units to parallel solution of large saddle-point linear systems arising from the mixed finite element approximation of the two-dimensional Stokes equations. We present an implementation of the Schur complement method in CUDA. It is based entirely on the conjugate gradient method which can be easily parallelized on the GPU. The implementation is tested on the lid-driven cavity flow and compared with a corresponding OpenMP-based CPU implementation. The GPU implementation achieved up to nine times better performance than the 6-threaded CPU implementation and the speedup decreased when smaller systems were solved."@en . . "Numerical solution of the Stokes problem using CUDA" . "[ED11CC936A75]" . . . . "3"^^ . . "3"^^ . "\u017Dabka, V\u00EDt\u011Bzslav" . . "Bauer, Petr" . . . "Numerical solution of the Stokes problem using CUDA"@en . . "Liberec" . . . "Liberec" . . "155087" . "3"^^ . "Effective numerical solution of incompressible flow problems is essential for, e.g., atmospheric boundary layer simulations. Mixed finite element approximation of the incompressible Stokes or Navier-Stokes equations leads to saddle-point linear systems. Techniques for the efficient solution of large saddle-point systems are often based on an LU factorization of a sparse matrix followed by forward and backward substitutions. However, this approach is difficult to parallelize effectively. We investigate the application of graphics processing units to parallel solution of large saddle-point linear systems arising from the mixed finite element approximation of the two-dimensional Stokes equations. We present an implementation of the Schur complement method in CUDA. It is based entirely on the conjugate gradient method which can be easily parallelized on the GPU. The implementation is tested on the lid-driven cavity flow and compared with a corresponding OpenMP-based CPU implementation. The GPU implementation achieved up to nine times better performance than the 6-threaded CPU implementation and the speedup decreased when smaller systems were solved." . "RIV/68407700:21340/12:00188946" . "Technick\u00E1 univerzita v Liberci" . . "Oberhuber, Tom\u00E1\u0161" . "P(LC06052), S, Z(MSM6840770010)" . . . . "2012-01-23+01:00"^^ . . . . "Stokes problem; CUDA"@en . "21340" . .