Accelerating the Iterative Linear Solver for Reservoir Simulation on Multicore Architectures

Abstract—Modern petroleum reservoir simulation serves as a primary tool for quantitatively managing reservoir production and planning new fields. It involves repeatedly solving the Ja-cobian of a set of strong nonlinear partial differential equations governing the mass and energy conduction and conservation. Most of the existing reservoir simulators adopt iterative solver with multiple stages of preconditioners, in which the incomplete LU (ILU) factorization is an outstanding universal smoother. However, it turns out that when the degree of freedom of each grid grows, ILU usually becomes the bottleneck of the solver. Moreover, ILU is difficult to parallelize due to its inherent data dependency. In this paper, we developed a sparse iterative solver with parallelized ILU and triangular solve using block-wise data structure. Compared with the state of art iterative solver on 14 industrial reservoir simulation matrices, the proposed ILU is 5.2x faster (on average) than the state of art iterative solver because of the block-wise data structure, which leads to 2.2x speedup on the total solver runtime. In addition, parallel ILU and triangular solve are developed to further accelerate the solver. To tackle the strong data dependency in ILU and triangular solve, we first partition the algorithm into separated tasks and construct a data flow graph to represent the data dependency. Then, tasks are scheduled in parallel according to the topological order of the data flow graph. On an 8-thread multicore architecture, we achieved another 3.6x speedup on ILU factorization, and 3.3x on triangular solve with good scalability. Keywords-Iterative solver; sparse matrix; incomplete LU factorization; Multicore architecture I