“…However, the method was only applicable to no-flux boundary conditions, and no further extensions to other types of equations or boundary conditions have been reported. Recently, Lowengrub and coworkers [27,28,29,30,31,32,33] developed an alternative formulation for solving partial differential equations with various boundary conditions, based on asymptotic analyses commonly conducted in phase field modeling, which is different from the general derivation of the smoothed boundary method presented in this paper. Although such an implementation for imposing boundary conditions differs from the 'formal' practice suggested by Cahn [17], it dramatically simplifies the formulation, provides a justification of the method, and increases the applicability of the approach.…”