The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...

The Cahn-Hilliard variational inequality is a non-standard
parabolic variational inequality of fourth order for which
straightforward numerical
approaches cannot be applied. We propose a primal-dual active set
method which can be interpreted as a semi-smooth Newton method as
solution technique for the discretized Cahn-Hilliard variational
inequality. A (semi-)implicit Euler discretization is used in time
and a piecewise linear finite element discretization of splitting
type is used in space...

A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where two materials and the void meet. Finally, we present several numerical results for mean compliance...

Download Results (CSV)