21 citations · 65 across the 33 of their papers we have counts for
5 papers · 1 filter
Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields
Patrick Dondl, Matteo Novaga, Benedikt Wirth +1
We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional…
Optimizing Bone Scaffold Porosity Distributions
Patrina S. P. Poh, Dvina Valainis, Kaushik Bhattacharya +2
We consider a simple one-dimensional time-dependent model for bone regeneration in the presence of a bio-resorbable polymer scaffold. Within the framework of the model, we optimize…
Simultaneous elastic shape optimization for a domain splitting in bone tissue engineering
Patrick Dondl, Patrina S. P. Poh, Martin Rumpf +1
This paper deals with the simulateneous optimization of a subset of some domain and its complement both co…
Keeping it together: a phase field version of path-connectedness and its implementation
Patrick Dondl, Stephan Wojtowytsch
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the pha…
A gradient system with a wiggly energy and relaxed EDP-convergence
Patrick Dondl, Thomas Frenzel, Alexander Mielke
If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic effects. We introduce a noti…