23 citations · 37 across the 15 of their papers we have counts for
6 papers · 1 filter
Combining diffuse and sharp interface methods in shape optimisation
Philip J. Herbert, Michael Hinze, Christian Kahle
We develop a concept for the numerical treatment of shape optimization problems based on the combination of phase field and sharp interface methods. On the one hand, phase field me…
Global convergence of -steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space
Klaus Deckelnick, Philip J. Herbert, Michael Hinze
We prove global convergence in function space for the steepest descent method in shape optimisation with semilinear elliptic partial differential equations. Steepest descent is rea…
Shape optimization in with geometric constraints: a study in distributed-memory systems
Philip J. Herbert, Jose A. Pinzon Escobar, Martin Siebenborn
In this paper we present a shape optimization scheme which utilizes the alternating direction method of multipliers (ADMM) to approximate a direction of steepest descent in $W^{1,\…
Shape Optimisation with : A connection between the steepest descent and Optimal Transport
Philip J. Herbert
In this work, we discuss the task of finding a direction of optimal descent for problems in Shape Optimisation and its relation to the dual problem in Optimal Transport. This link…
PDE constrained shape optimisation with first-order and Newton-type methods in the topology
Klaus Deckelnick, Philip J. Herbert, Michael Hinze
We present a general shape optimisation framework based on the method of mappings in the topology. We propose steepest descent and Newton-like minimisation algorithm…
A novel approach to shape optimisation with Lipschitz domains
Klaus Deckelnick, Philip J. Herbert, Michael Hinze
This article introduces a novel method for the implementation of shape optimisation with Lipschitz domains. We propose to use the shape derivative to determine deformation fields w…