P. J. Herbert

activity

20192026

W^{1, \infty}

approach to shape optimisation with Lipschitz domains

23 citations · 37 across the 15 of their papers we have counts for

collaborators

Showing 2023 · math.OCShow all

3 papers · 2 filters

math.OC2023

Shape optimization in $W^{1, \infty}$ 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,\…

math.OC2023

Shape Optimisation with $W^{1, \infty}$ : 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…

math.OC2023★ 5 cited

PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1, \infty}$ topology

Klaus Deckelnick, Philip J. Herbert, Michael Hinze

We present a general shape optimisation framework based on the method of mappings in the $W^{1, \infty}$ topology. We propose steepest descent and Newton-like minimisation algorithm…

Shape optimization in W1,∞ with geometric constraints: a study in distributed-memory systems

Shape Optimisation with W1,∞: A connection between the steepest descent and Optimal Transport

PDE constrained shape optimisation with first-order and Newton-type methods in the W1,∞ topology

Shape optimization in $W^{1, \infty}$ with geometric constraints: a study in distributed-memory systems

Shape Optimisation with $W^{1, \infty}$ : A connection between the steepest descent and Optimal Transport

PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1, \infty}$ topology