A Two-level Additive Schwarz Method For The Second-order Elliptic Interface Problem

In this dissertation, we study the two-level additive Schwarz method for the immersed interface finite element method for the second-order elliptic interface problem.First of all, we briefly introduce the immersed interface finite el-ement method for the second-order elliptic interface problem. Then we propose a two-level additive Schwarz preconditioner and inter-grid transfer operator between a coarse grid space and a fine grid space, and prove the stability and approximation of the intergrid transfer operator. Furthermore we estimate the upper bound of the condition number of the preconditioned operator. Finally, numerical experiments are presented to conform our theoretical results.