GAMPACK (GPU Accelerated Algebraic Multigrid Package). In reservoir simulation, the elliptic character of the pressure subsystem and the inhomogeneous permeability field result in extremely slow convergence for conventional iterative solvers. Algebraic multigrid (AMG) methods address this challenge by constructing a multilevel hierarchy of matrices that naturally adapts to the permeability channels of the underlying geology. Preconditioning with AMG allows difficult cases with millions of unknowns to be solved in just a few iterations. In just a few years, graphical processing units (GPUs) have progressed from a research curiosity to a productivity workhorse by reducing time-to-solution and overall hardware cost. The highly irregular computation patterns of AMG, however, require new approaches to adapt to the many-core paradigm. The construction of the coarse matrix hierarchy and grid transfer operators poses a particular challenge for GPU acceleration. We show that by carefully selecting algorithms with sufficient fine-grained parallelism, and implementing them with novel approaches, it is possible to substantially accelerate both the setup and solve stages. We present GAMPACK, a library for accelerated AMG, and show that on a single GPU it can typically reduce the total setup and solve time by a factor of over 5, when compared to a widely-used AMG solver running on 8 Xeon cores.

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