26 citations · 164 across the 38 of their papers we have counts for
56 papers
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…
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…
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…
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…
Layerwise goal-oriented adaptivity for neural ODEs: an optimal control perspective
Michael Hintermüller, Michael Hinze, Denis Korolev
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…
Finite element approximation to the non-stationary quasi-geostrophic equation
Dohyun Kim, Amiya K. Pani, Eun-Jae Park
In this paper, C1-conforming element methods are analyzed for the stream function formulation of a single layer non-stationary quasi-geostrophic equation in the ocean circulation m…
A least-squares space-time approach for parabolic equations
Michael Hinze, Christian Kahle, Michael Stahl
We propose a least squares formulation for abstract parabolic equations in the natural norm which only relies on natural regularity assumptions on the da…
An Incremental Singular Value Decomposition Approach for Large-Scale Spatially Parallel & Distributed but Temporally Serial Data -- Applied to Technical Flows
Niklas Kühl, Hendrik Fischer, Michael Hinze +1
The paper presents a strategy to construct an incremental Singular Value Decomposition (SVD) for time-evolving, spatially 3D discrete data sets. A low memory access procedure for r…
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…
Two-Phase Flow Simulations of Surface Waves in Wind-Forced Conditions
Malte Loft, Niklas Kühl, Marc P. Buckley +4
The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn-Hilliard Volume-of-Fluid model to capture the dynamics of the air-sea…
Variational discretization of one-dimensional elliptic optimal control problems with BV functions based on the mixed formulation
Evelyn Herberg, Michael Hinze
We consider optimal control of an elliptic two-point boundary value problem governed by functions of bounded variation (BV). The cost functional is composed of a tracking term for…
A Novel -Harmonic Descent Approach Applied to Fluid Dynamic Shape Optimization
Peter Marvin Müller, Niklas Kühl, Martin Siebenborn +3
We introduce a novel method for the implementation of shape optimziation in fluid dynamics applications, where we propose to use the shape derivative to determine deformation field…
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…
Adjoint Complement to the Volume-of-Fluid Method for Immiscible Flows
Niklas Kühl, Jörn Kröger, Martin Siebenborn +2
The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering…
Time adaptivity in model predictive control
Alessandro Alla, Carmen Gräßle, Michael Hinze
The core of the Model Predictive Control (MPC) method in every step of the algorithm consists in solving a time-dependent optimization problem on the prediction horizon of the MPC…
A space-time certified reduced basis method for quasilinear parabolic partial differential equations
Michael Hinze, Denis Korolev
In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems. The method is based on a space-time variational formulation. We provide a residu…
Cahn-Hilliard Navier-Stokes Simulations for Marine Free-Surface Flows
Niklas Kühl, Michael Hinze, Thomas Rung
The paper is devoted to the simulation of maritime two-phase flows of air and water. Emphasis is put on an extension of the classical Volume-of-Fluid (VoF) method by a diffusive co…
Variational discretization approach applied to an optimal control problem with bounded measure controls
Evelyn Herberg, Michael Hinze
We consider a parabolic optimal control problem with an initial measure control. The cost functional consists of a tracking term corresponding to the observation of the state at fi…
Reduced basis methods for quasilinear elliptic PDEs with applications to permanent magnet synchronous motors
Michael Hinze, Denis Korolev
In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the lat…
Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data
Abramo Agosti, Pasquale Ciarletta, Harald Garcke +1
Parameters in mathematical models for glioblastoma multiforme (GBM) tumour growth are highly patient specific. Here we aim to estimate parameters in a Cahn-Hilliard type diffuse in…
Simulation and Control of a Nonsmooth Cahn-Hilliard Navier-Stokes System
Carmen Gräßle, Michael Hintermüller, Michael Hinze +1
We are concerned with the simulation and control of a two phase flow model governed by a coupled Cahn-Hilliard Navier-Stokes system involving a nonsmooth energy potential. We estab…
Model Order Reduction by Proper Orthogonal Decomposition
Carmen Gräßle, Michael Hinze, Stefan Volkwein
We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as a…
Decoupling of Control and Force Objective in Adjoint-Based Fluid Dynamic Shape Optimization
Niklas Kühl, Peter M. Müller, Arthur Stück +2
We discuss exterior and classical interior alternatives for evaluating fluid flow induced forces on bodies. The discussion aims at a reduction of the total shape derivative, achiev…