Stephen Thomas, Arielle Carr, Paul Mullowney, Katarzyna Świrydowicz, Marcus Day
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引用次数: 0
Abstract
Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) -cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has demonstrated the advantages of Jacobi iteration as an alternative to direct solution of these systems. Depending on the threshold and fill-level parameters chosen, the factors can be highly nonnormal and Jacobi is unlikely to converge in a low number of iterations. We demonstrate that row scaling can reduce the departure from normality, allowing us to replace the inherently sequential solve with a rapidly converging Richardson iteration. There are several advantages beyond the lower compute time. Scaling is performed locally for a diagonal block of the global matrix because it is applied directly to the factor. Further, an ILUT Schur complement smoother maintains a constant GMRES iteration count as the number of MPI ranks increases, and thus parallel strong-scaling is improved. Our algorithms have been incorporated into hypre, and we demonstrate improved time to solution for linear systems arising in the Nalu-Wind and PeleLM pressure solvers. For large problem sizes, GMRESAMG executes at least five times faster when using iterative triangular solves compared with direct solves on massively parallel GPUs.
期刊介绍:
The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction.
Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review.
The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.