To realize the potential of the latest High-Performance-Computing (HPC) architectures for reservoir simulation, scalable linear solvers are necessary. We describe a parallel Algebraic Multiscale Solver (AMS) for the pressure equation of heterogeneous reservoir models. AMS is a two-level algorithm that employs domain decomposition with a localization assumption. In AMS, basis functions, which are local (subdomain) solutions computed during the setup phase, are used to construct the coarse-scale system and grid transfer operators between the fine and coarse levels. The solution phase is composed of two stages: global and local. The global stage involves solving the coarse-scale system and interpolating the solution to the fine grid. The local stage involves application of a smoother on the fine-scale approximation.
The design and implementation of a scalable AMS on multi- and many-core architectures, including the decomposition, memory allocation, data flow, and compute kernels, are described in detail. These adaptations are necessary to obtain good scalability on state-of-the-art HPC systems. The specific methods and parameters, such as the coarsening ratio (
The balance between convergence rate and parallel efficiency as a function of the coarsening ratio (