基于多重网格法的三维有限元程序设计

Design of Three-dimensional FEM Program Based on Multigrid Method

为了提高普通有限元方法在解决大型工程计算问题时的收敛性和准确性.文中在普通有限元方法的网格信息预处理过程和迭代求解过程中加入了多重网格方法的迭代方法和校正技术,使其与有限元方法有机地结合在一起,成功地构造了一种多重网格有限元法,并用FORTRAN95语言编写了面向对象的源代码SAFEM.数值验证表明,此方法收敛稳定、快速,且具有很高的精度,在加密网格与ABAQUS网格同样的条件下,能使其数值解与理论解的相对误差在1%之内,比ABAQUS解的相对误差稍低,而计算时间远远短于ABAQUS的求解时间,显示出极大的工程实用价值.

For improvement of astringency and accuracy in large-scale project problems by using ordinary FEM, multigrid method is introduced into 3D structural analysis of finite method during pretreatment of net message and iterative computation using ordinary FEM. A new multigrid method for FEM is constructed systematically. Furthermore, the code has been written in Fortran 95 . It＇s indicated that convergence of multigrid method is not only stable but also fast,and it has high precision. If it is the same conditions of finest net and ABAQUS net, relative error between numerical solution and theoretic solution is less than 1% which is less than that of ABAQUS, and computation time is greatly less than that of ABAQUS. This new method is proved tremendous engineering value.