基于MPI与OpenMP混合编程模型的大型工程结构并行Woodbury非线性分析方法  

Parallel Woodbury nonlinear analysis method for large-scale engineering structures based on MPI and OpenMP hybrid programming model

作　　者：苏璞 余丁浩 李钢[1] SU Pu;YU Dinghao;LI Gang(State Key Laboratory of Costal and Offshore Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024

出　　处：《建筑结构学报》2024年第10期131-143,共13页Journal of Building Structures

基　　金：国家自然科学基金项目(52008075,52225804,52038002);中央高校基本科研业务费专项(DUT23RC(3)030)。

摘　　要：基于Woodbury公式的非线性分析方法避免了结构非线性分析过程中整体刚度矩阵的反复更新和分解,然而,因局限于单机计算,该方法仅适用于中小规模结构的非线性分析。为此,通过两级稀疏近似策略对基于子结构技术的Woodbury法(简称“子结构Woodbury法”)进行改进,结合MPI与OpenMP混合编程模型提出了并行Woodbury非线性分析方法。该方法将整体结构剖分为若干个子结构,其中子结构级别的计算任务通过MPI并行编程模型实现,而每个子结构单元级别的计算任务则嵌套OpenMP并行编程模型完成。所提方法不仅克服了子结构Woodbury法在非线性区域规模较大时变得低效的局限性,也突破了现有Woodbury法的单机性能瓶颈。算例分析结果表明:所提方法能充分利用多个计算节点实现计算效率的大幅提升,其中非线性系数矩阵更新和求解过程降低的计算耗时最为显著,是提升整体分析效率的关键。The nonlinear analysis method based on Woodbury formula avoids the repeated updating and factorization of global stiffness matrix during nonlinear analysis for engineering structures.However,existing Woodbury methods can only be applied to nonlinear analysis of small-and medium-scale structures because they are still limited to single-computer calculation.The Woodbury method based on substructure technique(abbreviated as substructure Woodbury method)is improved through a two-level sparse approximation strategy,and a parallel Woodbury nonlinear analysis method is proposed by combining MPI and OpenMP hybrid programming model.In this method,the whole structure is partitioned into several substructures,and the tasks at the substructure level are computed in parallel by MPI programming model,while the tasks at the element level are computed in parallel by nesting OpenMP programming model.The proposed method not only overcomes the limitation that the substructure Woodbury method becomes inefficient when the nonlinear region is large,but also breaks through the single-machine performance bottleneck of existing Woodbury methods.The numerical example analysis shows that the proposed method can fully utilize multiple computational nodes to improve the algorithm efficiency greatly,among which the nonlinear coefficient matrices updating and solution process reduces most computational time,which is the key of improving the efficiency of the overall analysis.

关 键 词：大型工程结构 子结构技术 Woodbury公式 非线性 并行计算 

分 类 号：TU973.23[建筑科学—结构工程]