三维数值流形法覆盖系统并行分区生成算法

Parallel Partition Algorithm of Cover System Generation in Three Dimensional Numerical Manifold Method

三维数值流形方法(three dimensional numerical manifold method,3D-NMM)是岩土工程数值模拟中强大的数值方法之一。但一直存在接触判断困难、计算处理数据量大,效率低等问题。将并行计算技术应用于三维数值流形方法覆盖系统生成可以有效提升其覆盖系统的生成效率。详细研究了并行编程模式下三维数值流形法覆盖系统的生成算法。基于MPI(message passing interface)分布式内存编程原理,将分区覆盖生成作为三维数值流形法并行覆盖生成基本思路。先采用规则粗六面体网格覆盖问题域,并利用Metis划分网格形成负载基本均衡的子区域,在原有串行算法的基础上设计了子区域覆盖系统的生成算法。并基于分布式内存存储模式下不同区域间数据传递需求,对本并行算法建立了界面信息传递算法,用以并行计算过程不同区域间中数据交流。最后,使用C++开发了基于布尔运算的三维数值流形单元及覆盖系统并行生成算法。算例表明:此并行覆盖系统生成算法可有效提高三维数值流形法覆盖系统的生成效率及其应用规模。

Three-dimensional numerical manifold method(3D-NMM)is one of the most powerful numerical methods in geotechnical engineering numerical simulation.However,there are many problems such as difficult contact judgment,large amount of data and low efficiency.The parallel computing technique applied to cover system generation by 3D numerical manifold method can effectively improve the efficiency of cover system generation.The generation algorithm of 3D numerical manifold covering system in parallel programming mode was studied in detail.Based on the principle of message passing interface(MPI)distributed memory programming,partition coverage generation was regarded as the basic idea of parallel coverage generation in 3D numerical manifold method.Firstly,the regular coarse hexahedron grid was used to cover the problem area,and Metis was used to divide the grid to form the sub-region of basic load balance.Based on the original serial algorithm,the generation algorithm of sub-region coverage system was designed.Based on the data transfer requirements of different regions in distributed memory storage mode,an interface information transfer algorithm was established for the parallel algorithm to communicate data between different regions in the parallel computing process.Finally,a parallel generation algorithm of three-dimensional numerical manifold element and covering system based on Boolean operation was developed in C++.Numerical examples show that the parallel coverage system generation algorithm can effectively improve the generation efficiency and application scale of the three-dimensional numerical manifold method.