平行化迭代自適應多尺度有限元素法：演算法設計，科學計算軟體發展，理論與應用

We propose a new framework of multiscale finite elements (MsFEM) for solving some scalar or system of partial differential equations (PDEs) exhibiting multiscale behavior. The key ingredient of the MsFEMs is a set of multiscale basis functions, which is constructed by solving locally the original PDE problem with some proper boundary conditions. The selection of boundary conditions plays an important role on the overall performance of MsFEM. Finding an appropriate boundary condition setting for some particular application is the current active topic in the area of the MsFEM research. Either using purely local information or purely global information is two popular classes of MsFEMs in the available literature.