An Adaptive, Multilevel Scheme for the Implicit Solution of Three-Dimensional Phase-Field Equations

Phase-field models, consisting of a set of highly nonlinear coupled parabolic partial differential equations, are widely used for the simulation of a range of solidification phenomena. This paper focuses on the numerical solution of one such model, representing anisotropic solidification in three space dimensions. The main contribution of the work is to propose a solution strategy that combines hierarchical mesh adaptivity with implicit time integration and the use of a nonlinear multigrid solver at each step. This strategy is implemented in a general software framework that permits parallel computation in a natural manner. Results are presented which provide both qualitative and quantitative justifications for these choices.