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

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 fini...

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Bibliographic Details
Published in:Computer physics communications 2016-03, Vol.200, p.50-56
Main Authors: Bauer, Petr, Klement, Vladimír, Oberhuber, Tomáš, Žabka, Vítězslav
Format: Article
Language:English
Subjects:
Approximation
Computational fluid dynamics
Finite element method
Gauss–Seidel
GPU
Incompressible flow
Mathematical analysis
Mathematical models
Mixed finite elements
Multigrid
Navier-Stokes equations
Parallelization
Red–black coloring
Solvers
Vanka-type smoothers
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Summary: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.
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2015.10.021