复合材料板时间分数阶对流扩散问题的二阶双尺度计算方法

给出了具有三维周期结构的复合材料板时间分数阶对流扩散问题的二阶双尺度计算方法。首先,从三维的时间分数阶对流扩散问题出发定义局部单胞函数。根据得到的局部单胞函数计算出等效的均匀化参数,进而得到均匀化方程。其次,利用积分投影近似求解均匀化方程的均匀化解。最后,利用均匀化解和局部单胞函数构造出复合材料板时间分数阶对流扩散问题的二阶双尺度近似解。

Second-Order Two-Scale Computational Method for Time-Fractional Diffusion Equation Problems of Composite Plate with 3-D Periodic Configuration

In this paper,we consider the time-fractional diffusion equation of composite plate with 3-D periodic configuration. A second-order two-scale（ SOTS） computational method is designed by means of construction way.First,by 3-D time-fractional diffusion equation,the cell functions which defined on the reference cell are constructed,then the effective homogenization parameters of composites are calculated,and the homogenized plate problem on original domain is defined. Second,based on the integral projection operator method,the homogenization solution is obtained. Finally,the SOTS＇s approximate solution is obtained by the cell functions and the homogenization solution.