周期振荡系数热传导方程的并行多尺度有限元算法  

Parallel multiscale finite element method of heat conduction equation with periodically oscillating coefficients

作　　者：王辛[1] 高洋[1] 段喜亮 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2016年第4期601-617,共17页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11301329)

摘　　要：基于复合材料中具有周期震荡系数的热传导问题的并行多尺度有限元算法,通过构造边界层证明了有界多边形凸区域上的频域方程的多尺度截断误差估计;推导了算法过程中的累积有限元误差;结合逆积分变换给出了整个算法的误差估计.通过三维数值算例验证了算法的正确性与有效性.In this paper, based on the parallel multiscale finite element method （FEM） for the heat conduction equation with periodically oscillating coefficients in composite materials, the mnltiscale truncation error estimate for the frequency equation in the bounded polygon convex region is derived by the method of the boundary layer technique. The accumulative FEM error is analyzed. The full error estimate of the presented algorithm is proved with the inverse integral transformation. The 3D numerical simulations are carried out to validate the presented algorithm.

关 键 词：周期性复合材料结构 均匀化 多尺度渐近分析 有限元方法 

分 类 号：O241.82[理学—计算数学]