A comparative study of two numerical approaches for solving Kim–Kim–Suzuki phase-field models

Among the standard multi-phase multi-component phase-field (PF) methods, the Kim–Kim–Suzuki (KKS) method has the advantage of decoupling interfacial energy from bulk energy and solving concentration as the conserved variable. There are two approaches to numerically solving a KKS method: the global solution approach (GSA) solves all variables in a global system simultaneously, and the local solution approach (LSA) solves phase concentrations locally using a Newton solver. This work compares the performance of LSA and GSA for solving four KKS models of increasing complexity with the finite element method using the MOOSE framework. The solution accuracy, degrees of freedom (DOFs), memory usage, and computational efficiency are compared. We find that GSA and LSA generate similar solutions, with a maximum difference of only 0.34%. For each model, LSA has a lower number of DOFs, utilizes less memory, and less wall time. The savings of memory and wall time in LSA increase with increasing mesh density of the same model and are more pronounced in models with higher dimensionality and more nodes. However, GSA is easier to implement in existing codes and can better solve highly nonlinear systems by utilizing sophisticated solvers.