Title: Solving phase field equations using a meshless method

Authors: J X Zhou and M E Li

Source: Communications in numerical methods in engineering, Vol. 22, Issue 11, pp. 1109-1115.


The phase field equation is solved by using a meshless reproducing kernel particle method (RKPM) for the very first time. The 1D phase field equation is solved using different grid sizes and various time steps at a given grid size. The method can give accurate solutions across the interface, and allows a larger time step than explicit finite-difference method. The 2D phase field equation is computed by the present method and a classic shrinking of a circle is simulated. This shows the powerfulness and the potential of the method to treat more complicated problems.