8 papers
A Local Discontinuous Galerkin Method for Dirichlet Boundary Control Problems
Peter Benner, Michael Hinze, Hamdullah Yücel
In this paper, we consider control constrained Dirichlet boundary control of a convection-diffusion equation on a two dimensional convex polygonal domain. We discretize the c…
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…
Long-time behavior of solutions to a fluid dynamic shape optimization problem via phase-field method
Michael Hinze, Christian Kahle, John Sebastian H. Simon
We investigate the long time behavior of solutions to a shape and topology optimization problem with respect to the time-dependent Navier--Stokes equations. The sought topology is…
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…
A reduced basis method for parabolic PDEs based on a space-time least squares formulation
Michael Hinze, Christian Kahle, Michael Stahl
In this work, we present a POD-greedy reduced basis method for parabolic partial differential equations (PDEs), based on the least squares space-time formulation proposed in [Hinze…
Layerwise goal-oriented adaptivity for neural ODEs: an optimal control perspective
Michael Hintermüller, Michael Hintermüller, Michael Hinze +1
In this work, we propose a novel layerwise adaptive construction method for neural network architectures. Our approach is based on a goal--oriented dual-weighted residual technique…