A domain decomposition method for solving thin film elliptic interface problems with variable coefficients

A domain decomposition method is developed for solving thin "lm elliptic interface problems with variable coe$cients. In this study, the elliptic equation with variable coe$cients is discretized using second-order "nite di!erences while a discrete interface equation is obtained using the immersed interface method in order to obtain a second-order global accuracy. The obtained linear system is solved using a preconditioned Richardson iteration, which is shown to converge fast when the grid size in the thickness direction is much smaller than the grid sizes in both the length and width directions. To simplify the computation, a domain decomposition algorithm is obtained based on a parallel Gaussian elimination procedure. The method is illustrated by a numerical example.