Krylov‐accelerated algebraic multigrid for semi‐definite and nonsymmetric systems in computational fluid dynamics

Abstract

SUMMARY This article reports on experiences with aggregation algebraic multigrid relying on Krylov acceleration on each level of the grid hierarchy as preconditioners for linear systems in general purpose fluid flow simulation software. In benchmarks that reflect the requirements of industrial simulations, it is demonstrated that for semi‐definite problems, the performance of recently published algorithms of this type is very attractive but that proposed variants of these algorithms occasionally fail for nonsymmetric problems. A modification leading to reliable solvers is suggested. Copyright © 2012 John Wiley & Sons, Ltd.

Velocity–pressure coupling on GPUs

“…Moreover, our solver must be robust enough for meshes with a quality typical for industrial applications. We prefer therefore to construct our own solver based on the experience we had with both, segregated (elliptic) problems, see Emans [6,8], and coupled problems of another kind, see Emans [11,13].…”

“…Further aspects of the AMG algorithm. Our experience with the velocitypressure coupling has shown that the robustness of GMRES-based k-cycle AMG, see Emans [13], is indispensable in the first iteration of this scheme. Later on, if the current solution is no longer far away from the physical solution, the systems become easier to solve.…”

“…Since the Pairs-of-Pairs scheme is robust and good experience has been reported, e.g. by Emans [13], we use this scheme for the conventional calculations on the CPU. In the GPU-accelerated computation, the solution phase of the R6 scheme is also significantly slower than that of the other schemes, but since the solution phase is efficiently accelerated, its contribution to the total computing time is low and the method with the R6 scheme is in total faster than the method with the Pairs-of-Pairs scheme.…”

Multigrid methods

“…In , Emams reports on experiences with aggregation AMG relying on Krylov acceleration as preconditioners for linear systems in general purpose fluid flow simulation. In benchmarks that reflect the requirements for industrial situations, the performance of recently published algorithms for semi‐definite problems is shown to be very attractive except for proposed variants that occasionally fail for nonsymmetric problems; modifications are suggested to lead to reliable solvers for these situations.…”