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

This paper proposes a two-level additive Schwarz preconditioned method for a new immersed interface finite element method for solv-ing the second-order elliptic interface problem proposed in[9].We prove that the condition number of the precoditioned operator is O(H2/δh),where h and H represent the fine mesh size and the coarse mesh size,respectively,and δ represents the size of the overlap-s between the subdomains.Numerical experiments demonstrate the effectiveness of the proposed method.