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Keeping it together - phase field methods for problems with a connectedness constraint

Banff International Research Station for Mathematical Innovation and Discovery

Phase field models are often used in situations where sharp interface simulations are difficult, in particular where topological changes can occur. While these are a feature in many applications, we may want to control at least the connectedness of either the phase transition regions or the phases. We present a method which allows us to approximate a relaxation of the perimeter functional under a connectedness constraint in two dimensions and Willmore's curvature energy at connected surfaces in three dimensions. We will give numerical evidence of the effectiveness of the method and describe how it can be implemented in an efficient manner.

Mathematics; Calculus of variations and optimal control; optimization; Partial differential equations

video/mp4

Author affiliation: Carnegie-Mellon University

2019-03-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69005

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/