裂隙岩体三维并行自适应扩展有限元模拟与验证

With regard to the numerical computation of large scale rock engineering, three-dimensional parallel adaptive extended finite element method is suggested to solve the issues of geological structures' description and simulation, the control of computational errors, and the bottleneck problems of memory limitations and computing time, and efforts will be made to solve the problems emerged in the method. Level set method is adopted to represent mathmatically the cracks and its propogation. After analyzing the discontinity and sigularity of fractured rock masses, proper error estimation method and hp adatptive strategies will be proposed and implementation will be made.FETI-type domain decomposition method is used to achieve high performance parallel extended finite element method. Preconditioners of the interface equations in FETI will be defined and fast convergent iterative method will be accomplished. Load monitoring, load adjustment and load transfer algorithms will be proposed to fulfill dynamic load balancing in adaptive extended finite elment method. Efficient data structures for adaptive mesh refinement, FETI algorithm, and dynamic load balancing will be constructed. On the basis of the 2D code written by the principal investigator, 3D adaptive parallel extended finite element code will be developed using object-oriented programming technique and message passing interface(MPI). Verfication and validation will be done by means of classic benchmarking problems, laboratary tests and pratical engineering problems. The objective of this research is to achieve the simulation and stability analysis of large-scale rock engineering by means of parallel adaptive extended finite element on supercomputers like Shengteng7000. Besides, this reseach will help to apply the high performance computing in more scientifical areas.

针对大型岩体工程三维数值分析中的结构面描述与模拟、计算误差控制、存储瓶颈和时间瓶颈等问题，提出采用三维并行自适应扩展有限元(XFEM)的求解方法，解决方法中遇到的问题。采用水平集方法描述空间裂纹及其扩展轨迹。针对裂隙岩体非连续性和奇异性等特点，提出并实现高精度的XFEM后验误差估计方法和hp型网格自适应策略。采用FETI型区域分解算法实现高性能并行扩展有限元，构造界面方程预条件子，实现快速收敛的迭代算法。提出自适应扩展有限元的负载监测、负载调整和负载转移等算法，实现计算中动态负载平衡。建立描述自适应网格、FETI算法和动态负载平衡算法的高效数据结构。采用面向对象并行编程技术和消息传递界面（MPI），在已有程序基础上扩展，开发三维自适应扩展有限元并行程序。采用多种手段调试和验证程序，最终实现大型岩土工程在深腾7000等超级并行机上计算，为稳定性分析和安全评价提供技术支撑，推广高性能并行计算。

模拟裂隙岩体从连续到非连续变形过程是岩土工程一个关键科学问题。开展了裂隙岩体模拟的扩展有限元方法研究，开发了弹塑性扩展有限元程序，并对含裂隙的边坡问题进行了分析。针对裂隙岩体的非连续性和奇异性、裂纹尖端应力集中等特点，提出了一种数值流形T 样条局部加密方法，并将适合分析的T 样条引入数值流形方法中来建立高阶数值流形方法的分析格式，提高了计算精度。采用FETI型区域分解算法实现高性能并行计算，基于图论理论建立了子区域间的通讯拓扑关系，实现了子区域间点对点通讯，避免速度慢、通信量大的全局通讯。在自主开发程序基础上，增加相应模块，采用面向对象编程技术和MPI 消息传递库开发程序。对一个一亿多单元的隧道工程实例运用5 000 核并行计算，得到较高的并行效率。计算结果在专用图形工作站上进行后处理，显示和交互操作速度良好。研究在两方面实现了突破：一是将模型规模提高到了一亿多单元；二是同时调用了5000 个计算核来并行运算，并得到了很高效率。本项目将有力推广高性能并行计算在岩土工程中的应用，对同类基于网格的数值方法的并行计算具有很强的指导意义。