Comparison of solvers for two formulations of Cahn-Hilliard equations

Abstract

Two different formulations of the Cahn-Hilliard equations implemented in modern PETIGA library for isogeometric analysis simulations are dealt with. In the first formulation, fourth order strong form resulting in weak second-order formulation with cubic B-splines used for discretization is used. In the second formulation, a system of two-second order equations resulting in a first order weak formulation with quadratic B-splines used for discretization is used. The second formulation requires twofold unknowns but lower order B-splines. The computational costs of iterative solvers from PETSc library, showing that the two-field formulation, even with the larger number of unknowns, can be solved in lower computational cost are tested.