A dimension by dimension splitting immersed interface method for heat conduction equation with interfaces

The numerical method proposed in this paper is an improvement of the ADI method by Li and Mayo (1994). The proposed method is unconditionally stable for both two and three-dimensional heat conduction interface problems, while Li’s ADI method is only stable for two-dimensional problems. The method is a modification of a Locally One-Dimensional (LOD) difference scheme, with correction term added to the right-hand side of the standard LOD difference scheme at irregular points. The correction term is determined so that the local truncation error is of order O(h)O(h) at irregular points. Then the method is two-order convergent in both time and space directions. Numerical examples show good agreement with exact solutions and confirm the order of convergence and stability.