摘要
整体代数多重网格(BAMG)法是一种求解偏微分方程组离散系统的高效预条件方法,可用于求解多孔介质中的多相渗流模型.本文针对BAMG方法,面向多相多组分油气藏问题研究了块矩阵粗化中不同范数的选取及基于对角块的经典插值策略对收敛性的影响.针对启动阶段的并行瓶颈,引入了"延迟更新"和"结构保持更新"两种策略,并基于可容忍迭代增长阈值的判据设计了一种自适应启动BAMG预条件方法.进一步,对求解阶段中的磨光算子与残量计算等热点进行了深度优化与向量化.数值实验表明,所提出方法在收敛性、高效性及并行可扩展性方面具有优势;例如,在亿级网格规模的测试中,当使用8192个CPU核时,提出方法的计算时间相比于传统方法减少了57.6%,并行效率提升了38.1%.
The block algebraic multigrid(BAMG)method is an efficient preconditioning technique for solving discretized systems of partial differential equations and can be applied to multiphase flow models in porous media.In this work,we investigate the impact of different norm selections in block-matrix coarsening and a diagonal-block-based classical interpolation strategy on the convergence behavior of the BAMG method for multiphase,multicomponent reservoir simulations.To address the parallel bottleneck during the setup phase,we introduce the“delayed update”and“structure-preserving update”strategies,and develop an adaptive-setup-based BAMG algorithm guided by a tolerable iteration growth threshold criterion.Furthermore,we perform in-depth optimization and vectorization of performancecritical components in the solve phase,including the smoother and residual computation.Numerical experiments demonstrate the proposed method’s advantages in terms of convergence,efficiency,and parallel scalability.For example,in tests involving grids with over one hundred million elements,the proposed method reduces computation time by 57.6%and improves parallel efficiency by 38.1%when using 8192 CPU cores compared to the traditional method.
作者
赵梨
李研研
王宝华
张晨松
Zhao Li;Li Yanyan;Wang Baohua;Zhang Chensong(Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of Science,Hunan University of Technology,Zhuzhou 412007,China;Research Institute of Petroleum Exploration and Development,Beijing 100190,China)
出处
《数值计算与计算机应用》
2025年第4期321-345,共25页
Journal on Numerical Methods and Computer Applications
基金
中国科学院战略性先导科技专项课题(XDB0640000)
中国石油勘探开发研究院合作项目(RIPED-2025-d-1665)资助.
关键词
油气藏数值模拟
整体代数多重网格法
自适应预条件方法
单指令多数据流方法
并行计算.
Petroleum reservoir simulation
Block algebraic multigrid methods
Adaptive preconditioners
Single instruction multiple data methods
Parallel computing.
