Before revision:  To resolve the instability issue of Yee's scheme (staircasing) caused by discontinuous permittivity across the interface, our algorithm revises the permittivities and makes some corrections to the scheme for the cells around the interface. It is also an improvement over the contour-path effective permittivity algorithm by including some extra terms in the formulas.
After revision:  It is an improvement over the contour-path effective permittivity algorithm by including some extra terms in the formulas.