Title: Aggregation algorithms for k-cycle AMG in computational fluid dynamics

Authors: Maximilian Emans

Addresses: Johann Radon Institute for Computational and Applied Mathematics (RICAM), 4040 Linz, Austria; Industrial Mathematics Competence Centre GmbH (IMCC), 4040 Linz, Austria

Abstract: We present a systematic comparison of different aggregation schemes for AMG-based solvers in computational fluid dynamics. Our focus lies on the method of the Krylov-accelerated cycle which has very favourable properties for the applications on 3D unstructured meshed. While on conventional CPUs the k-cycle AMG in its known form with double-pairwise aggregation is shown to be approximately as fast as plain aggregation schemes (and therefore recommendable), the algorithm with plain aggregation becomes significantly more efficient on GPUs since the setup of this aggregation scheme is much leaner. Furthermore, we show that the solution phase of k-cycle AMG has excellent scaling properties on modern cluster hardware with up to 256 cores. However, common coarse-grid treatment techniques such as parallel direct solvers or agglomeration schemes form a bottleneck such that the scaling of the setup phase is considerably worse. Block-iterative methods improve the performance here.

Keywords: algebraic multigrid; k-cycle AMG; Krylov-accelerated cycle; computational fluid dynamics; CFD; GPUs; aggregation schemes; SIMPLE; block iterative methods.

DOI: 10.1504/PCFD.2015.072781

Progress in Computational Fluid Dynamics, An International Journal, 2015 Vol.15 No.6, pp.335 - 351

Published online: 03 Nov 2015 *

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