基于区域分解算法的岩土大规模高性能并行有限元系统研究

LARGE-SCALE HIGH PERFORMANCE PARALLEL FINITE ELEMENT SYSTEM BASED ON DOMAIN DECOMPOSITIOIN METHOD IN GEOMECHANICS

岩土工程规模大,加上岩土介质复杂的特性,使得当前有限元数值模拟在时间和精确度上很难达到工程要求。研究了在普通 PC 机群上实现的大规模并行有限元方法,以更好地发挥有限元在岩土工程中的应用。组建了Windows 下 PC 机群并行系统。采用“分而治之”的并行策略实现有限元并行,并实现了存储局部化。采用基于区域分解预处理技术的并行共轭梯度法来实现方程组的求解。集成以上方法,用 C++开发了并行有限元程序ParallelGeoFEM。对水布垭地下厂房进行了三维有限元并行模拟,得到了较好的加速比。结果表明,基于区域分解的并行有限元方法可以实现岩土工程大规模快速精细的模拟。

The finite element (FE) simulation often finds itself difficult to meet the time and accuracy requirements due to the large scales of projects and complexity of rock properties. To fully utilize the potential of FEM,large-scale parallel FEM are investigated on Windows. PC cluster on Windows operating system is built up. The‘Divide and Conquer’strategies are used to parallel the FEM,and locality of storage is implemented. The equations are solved using the parallel preconditioned conjugate gradient method by domain decomposition method. Integrated with the above-mentioned methods,a parallel FE system,ParallelGeoFEM is developed in C++. A 3D FE underground powerhouses model is simulated,and good speedup ratio is obtained. The results show that the parallel FEM based on domain decomposition method can be used to achieve accurate and good geotechnical simulation within a reasonable short time.