| Abstract: |
| Phase-field models are a popular choice in computational physics to describe complex dynamics of substances with multiple phases and are widely used in applications including solidification of materials. In this talk, I will present nonlocal phase-field models of Cahn-Hilliard and Allen-Cahn types involving a nonsmooth double-well obstacle potential. Mathematically, in a weak form, the models translate to systems of variational inequalities, which are additionally coupled to a temperature evolution equation. I will demonstrate that under appropriate conditions on the nonlocal operator and the kernel we obtain a model that allows for sharp interfaces in the solution compared to a diffuse-interface local model. I will present an implicit-explicit time-stepping formulation for the model, well-posedness analysis and development of appropriate discretization methods that can be realized efficiently. Finally, several numerical experiments will be presented to support theoretical findings. |
|