An Adaptive Coloring Scheme for Graphics Processing Unit Preconditioners

Abstract

A single modern graphics processing unit (GPU) typically has the memory bandwidth equivalent to many central processing unit (CPU) nodes. This makes GPU hardware appealing for linear solvers that tend to require high memory bandwidth and fast inter-core communication. Reservoir simulators are designed to handle a wide range of simulation models, and to obtain peak performance the linear solver must be well suited to the resulting linear systems. This fact can lead to disappointing performance when shifting the linear solver from CPU to GPU. To fully utilize the capabilities of the latest GPU devices, we must transition from coarse-grained to fine-grained parallel preconditioners. To enable such high levels of parallelism in the linear solver a common approach is to employ a multicolor reordering of the linear system. Depending on the specific properties of the simulation model, this process can cause a significant weakening of the parallel preconditioner, resulting in much slower convergence. In some situations, this slow convergence can cause an order of magnitude increase in the linear iteration count, and result in the GPU linear solver performing worse than the CPU version. In this paper we analyze the impact on performance of employing different coloring schemes for different simulation models and we identify how the coloring can be automatically adapted for the properties of each simulation model. In this way, the performance improvements expected on the GPU can be realized for a wider range of simulations.