Argonne National Laboratory
Mathematics and Computer Science Division
lwang@mcs.anl.gov
Abstract: It is well known that mesoscale material features are very important for the material properties at the macroscale. The phase field method has recently emerged as a powerful computational approach to modeling the defect and the microstructure dynamics in mesoscale materials. We employ coupled Cahn- Hilliard and Allen-Cahn systems with a double-obstacle free energy potential to simulate the physics. Differential Variational Inequality(DVI) is employed in order to guarantee that the discrete solutions satisfy appropriate constraints. We reformulated the DVIs to a complementarity problem, which allows us to use parallel matrix-free solvers such as PETSc and TAO. Several numerical test cases will be shown.