Implementation of the Vanka-type multigrid solver for the finite element approximation of the Navier-Stokes equations on GPU

0453384 - ÚT 2016 RIV NL eng J - Journal Article
Bauer, Petr - Klement, V. - Oberhuber, T. - Žabka, V.
Implementation of the Vanka-type multigrid solver for the finite element approximation of the Navier-Stokes equations on GPU.
Computer Physics Communications. Roč. 200, March (2016), s. 50-56. ISSN 0010-4655. E-ISSN 1879-2944
R&D Projects: GA ČR GB14-36566G
Institutional support: RVO:61388998
Keywords : Navier–Stokes equations * mixed finite elements * multigrid * Vanka-type smoothers * Gauss–Seidel * red–black coloring * parallelization * GPU
Subject RIV: BK - Fluid Dynamics
Impact factor: 3.936, year: 2016

We present a complete GPU implementation of a geometric multigrid solver for the numerical solution of the Navier–Stokes equations for incompressible flow. The approximate solution is constructed on a two-dimensional unstructured triangular mesh. The problem is discretized by means of the mixed finite element method with semi-implicit timestepping. The linear saddle-point problem arising from the scheme is solved by the geometric multigrid method with a Vanka-type smoother. The parallel solver is based on the red–black coloring of the mesh triangles. We achieved a speed-up of 11 compared to a parallel (4 threads) code based on OpenMP and 19 compared to a sequential code.
Permanent Link: http://hdl.handle.net/11104/0255903