The combination approximation method

Abstract

The purpose of this thesis is to introduce the combination approximation method for the second order elliptic boundary-value problems under certain conditions. This method is developed based on the combination technique and the two-scale finite element discretization scheme. The combination approximation method has improved parallel scalabilities with a bounded resultant sacrifice of accuracy, thus strengthening the potential of grid-based methods in high-dimensional settings. Compare to the combination technique, it also has the flexibility in choosing which parts of the domain are to be partitioned into finer grids and which parts into coarser grids to suit different needs for discretizations. Show more