基于PETSc的有限元高性能求解方法  

Finite element high-performance solution based on PETSc

作　　者：高怀玉[1] 张峰 秦忠国[1] 

机构地区：[1]河海大学力学与材料学院,江苏南京210098 [2]南京市水利规划设计院有限责任公司工程分院,江苏南京210006

出　　处：《河海大学学报（自然科学版）》2013年第4期365-370,共6页Journal of Hohai University(Natural Sciences)

摘　　要：基于科学计算工具箱PETSc提供的应用开发平台,针对单机多核计算机开发出一种线性并行求解器。用C++类的形式封装求解线性有限元问题必需的数据和操作,并行使用迭代法求解线性有限元问题。算例测试结果表明,在内存为3G的四核计算机上可以计算节点数达80万的三维线性有限元问题;在运行2个进程计算时加速比达到1.81,4个进程计算时为3.24;求解器对于病态方程组有良好的适应能力;对于材料弹性模量相差10万倍的有限元模型,迭代也能收敛。Based on the application and development platform provided by the calculation toolbox PETSc,a parallel linear solver was developed for single multi-core computers.Data and operations that are necessary for an FEM analysis were packaged in the form of a class provided by C＋＋,and the linear FEM iteration method was used to solve problems in parallel.Test results show that 3G memory and four nuclear computers can compute a 3D linear FEM with a number of nodes of 800 000.The speedup ratio was up to 1.81 for two processes and 3.24 for four processes.The solver has a good ability to adapt to morbid equations.Iteration can converge for the finite element model with elastic modulus of materials differing by 100 000 times.

关 键 词：有限元 线性方程组 并行计算 PETSC 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]