A Local Semi-Implicit Level-Set Method for Interface Motion

This paper proposes and implements a novel hybrid level set method which combines the
numerical efficiency of the local level set approach with the temporal stability afforded by a semi-implicit technique. By introducing an extraction/insertion algorithm into the local level set approach, we can accurately capture complicated behaviors such as interface separation and coalescence. This technique solves a well known problem when treating a semi-implicit system with spectral methods, where spurious interface movements emerge when two interfaces are close to each other. Numerical experiments show that the proposed method is stable, efficient and scales up well into three dimensional problems, allowing large scale simulation of nanosystems involving many interfaces and complicated changes.