Secod-order two-scale method for time-fractional diffusion equation in composite plate

Abstract

In this paper, a second-order two-scale(SOTS) method for time-fractional diffusion equation in composite plate is presented by means of construction way. First, by 3-D composite plate model, 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. Based on the integral projection operator, the homogenization solution on the median plane of the plate is obtained. Second, the approximation of the SOTS's solution in pointwise sense is analyzed. Finally, the procedure of SOTS's method is given. A set of numerical results are demonstrated. It shows that SOTS's method can capture the 3-D local behaviors caused by 3-D micro-structures well.