GPU Parallelization Nested Decomposition Method for Solving Large Linear Systems in Reservoir Numerical Simulation

Abstract

This paper designs a highly parallel Nested Factorization (NF) to solve large linear equations generated in reservoir numerical simulation problems. The NF method is a traditional linear solution preprocessing method for reservoir numerical simulation problems, and has regained attention in recent years due to its potential to extend to parallel architectures such as GPUs (Graphics Processor Units). The parallel algorithm of this paper is based on the MPNF (Massively Parallel Nested Factorization) framework proposed by Appleya (Appleyard, Appleyard, Wakefield, & Desitter, 2011). The MPNF algorithm designed in this paper focuses on its efficient implementation on the GPU parallel architecture. Its features include: using a custom matrix structure to achieve merge access, improving access bottlenecks and improving the efficiency of the SpMV algorithm. It is also applicable to the two-stage preprocessing method CPR. (Constrain Pressure Residual) pressure solution and global preprocessing stage; the MPNF method is extended to the solution of 2.5-dimensional unstructured grid problem. The parallel algorithm in this paper has been integrated into the reservoir numerical simulator. For the SPE10 (million grid, highly heterogeneous) standard example, the GPU-based parallel NF algorithm is in the structured grid model and the equivalent 2.5-dimensional non- On the structured grid model, compared with the serial version of the NF method, the acceleration ratios of 19.8 and 17.0 times were obtained respectively; compared with the mainstream serial solution method, the efficiency was also improved by 2 to 3 times.

Keywords

• nested decomposition
• gpu parallel
• linear solution
• cpr