Massively Parallel Algebraic Multiscale Linear Solver

We analyze the parallel performance of the Algebraic Multiscale Solver (AMS) for the heterogeneous pressure system that arises from incompressible flow in porous media. We propose special modifications to the algorithm to improve its computational efficiency on massively parallel architectures. AMS is a two-level linear solver algorithm, based on the idea of non-overlapping domain-decomposition with a localization assumption, where the local solutions in each domain are used to construct the coarse operator. The overall scalability of AMS is strongly tied to the choice of parameters and algorithms involved. These choices additionally impact the convergence properties of the solver. We focus on the basis-function kernel, which dominates the setup phase, and on the local smoother, which dominates the solution phase. We carefully consider the balance of computational scalability and convergence rate to ensure high overall performance while maintaining robustness. We present test results for highly heterogeneous problems derived from the SPE10 benchmark, and ranging in size from millions to tens of millions of cells. The parallel AMS code is run two different architectures: a multi-core architecture and a massively parallel Knights Corner architecture. We also compare the performance and robustness of AMS with the widely-used SAMG solver, running on the multi-core architecture.