Exposing Fine-Grained Parallelism in Sequential Gaussian Simulation

The implementation of computationally demanding algorithms on GPU architectures is becoming inevitable nowadays. In the geoscience domain, reverse time migration based on the wave equation provides the most evident example. Problems related to modeling of flow and transport of black-oil or compositional fluids in the subsurface have also been successfully addressed. However, less attention has been drawn to the population of petrophysical properties, where geostatistical simulation algorithms, such as Sequential Gaussian Simulation (SGS), are also computationally expensive. The path level parallelism approach in SGS assumes the simultaneous simulation of several values along a randomly chosen path, which traverses the simulation grid. The values simulated further down the path may depend on previously simulated values, hence efficient operation requires scheduling the simulation of each cell to maximize parallelism while avoiding race conditions. This can be tackled by relaxing the accuracy of the initial algorithm and ignoring a few dependencies leading to conflicts, however, the solution will diverge from the exact algorithm and the level of differences is difficult to control. The exact path-level parallelization strategy can be implemented using multi-coloring schemes, as it has been shown for a limited number of CPU threads. In our work, we demonstrate that fine-grained parallelism in sequential Gaussian simulation can be exposed to sufficient degree for efficient use of GPU architectures even for an exact strategy. We discuss several implementations of multi-coloring algorithms applied to path-level parallelism and benchmark the overall performance of the GPU implementations against CPU standards.