Extended multiscale finite element method for mechanical analysis of heterogeneous materials

An extended multiscale finite element method （EMsFEM） is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.     

Downscaling data assimilation algorithm with applications to statistical solutions of the Navier–Stokes equations

Based on a previously introduced downscaling data assimilation algorithm, which employs a nudging term to synchronize the coarse mesh spatial scales, we construct a determining map for recovering the full trajectories from their corresponding coarse mesh spatial trajectories, and investigate its properties. This map is then used to develop a downscaling data assimilation scheme for statistical solutions of the two-dimensional Navier–Stokes equations, where the coarse mesh spatial statistics of the system is obtained from discrete spatial measurements. As a corollary, we deduce that statistical solutions for the Navier–Stokes equations are determined by their coarse mesh spatial distributions. Notably, we present our results in the context of the Navier–Stokes equations; however, the tools are general enough to be implemented for other dissipative evolution equations.     

MODIS温度变化率与AMSR-E土壤水分的关系的提出与降尺度算法推广

土壤水分参数是陆面过程与水循环的重要影响因素。不同的遥感平台可提供不同时间和空间尺度的土壤水分,它们分别具有各自的优势与不足。利用被动微波辐射计AMSR-E土壤水分和MODIS地表温度、植被指数产品,作者探讨了地表温度变化率和土壤水分的关系,并借鉴地表温度T_s和归一化植被指数NDVI的特征空间理论,构造了温度变化率和土壤水分的三角形特征空间。随着地表温度变化率的增加,土壤水分的分布范围缩小,同时土壤水分的数值降低。作者由此提出了变温植被指数（TVVI）,并指出该指数与土壤水分呈稳定的幂指数函数关系,建立了土壤水分与温度变化率的经验定量模型。之后作者通过上述函数关系和高分辨率MODIS数据,实现了AMSR-E土壤水分数据的降尺度处理。与地面实测数据的比较表明,该降尺度方法的准确性较高。