Novel Finite Difference Discretization of Interface Boundary Conditions for Stablized Explicit-Implicit Domain Decomposition Methods

Stabilized explicit-implicit domain decomposition is a group of methods for solving time-dependent partial difference equations of the parabolic type on parallel computers. They are efficient, stable, and highly parallel, but suffer from a restriction that the interface boundaries must not intersect inside the domain. Various techniques have been proposed to handle this restriction. In this paper, we present finite difference schemes for discretizing the equation spatially, which is of high simplicity, easy to implement, attains second-order spatial accuracy, and allows interface boundaries to intersect inside the domain.