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Carnegie Mellon Center for Nonlinear Analysis
Phase Field Modeling for Heterogeneous Materials by Differential Variational Inequality


Lei Wang
Argonne National Laboratory
Mathematics and Computer Science Division

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.