55 citations · 86 across the 24 of their papers we have counts for
27 papers
Total Generalized Variation for Piecewise Constant Functions on Triangular Meshes with Applications in Imaging
Lukas Baumgärtner, Ronny Bergmann, Roland Herzog +2
We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV)…
Preconditioning for a Phase-Field Model with Application to Morphology Evolution in Organic Semiconductors
Kai Bergermann, Carsten Deibel, Roland Herzog +3
The Cahn--Hilliard equations are a versatile model for describing the evolution of complex morphologies. In this paper we present a computational pipeline for the numerical solutio…
Optimal Control of the Kirchhoff Equation
Masoumeh Hashemi, Roland Herzog, Thomas M. Surowiec
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed…
First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
Ronny Bergmann, Roland Herzog, Julián Ortiz López +1
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the cod…
An Optimal Control Problem for Single-Spot Pulsed Laser Welding
Roland Herzog, Dmytro Strelnikov
We consider an optimal control problem for a single-spot pulsed laser welding problem. The distribution of thermal energy is described by a quasilinear heat equation. Our emphasis…
A Discretize-Then-Optimize Approach to PDE-Constrained Shape Optimization
Roland Herzog, Estefanía Loayza-Romero
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admi…
Optimal Prediction using Learning and Shape Optimization
M. Sajjad Edalatzadeh, Roland Herzog
This paper investigates the problem of optimal predictor design for distributed parameter systems using neural networks and shape optimization. Sensors with various shapes are plac…
Fenchel Duality and a Separation Theorem on Hadamard Manifolds
Maurício Silva Louzeiro, Ronny Bergmann, Roland Herzog
In this paper, we introduce a definition of Fenchel conjugate and Fenchel biconjugate on Hadamard manifolds based on the tangent bundle. Our definition overcomes the inconvenience…
Planning of Measurement Series for Thermodynamic Properties based on Optimal Experimental Design
Ophelia Frotscher, Roland Herzog, Markus Richter
Decreasing the time required for accurate thermodynamic property measurements is extremely desirable for model development that can respond to the needs of science and industry wit…
A Manifold of Planar Triangular Meshes with Complete Riemannian Metric
Roland Herzog, Estefanía Loayza-Romero
Shape spaces are fundamental in a variety of applications including image registration, morphing, matching, interpolation, and shape optimization. In this work, we consider two-dim…
Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction
Roland Herzog, Jan-Frederik Pietschmann, Max Winkler
We discuss the control of a human crowd whose dynamics is governed by a regularized version of Hughes' model, cf. Hughes: A continuum theory for the flow of pedestrians. Transporta…
Continuous Galerkin Schemes for Semi-Explicit Differential-Algebraic Equations
Robert Altmann, Roland Herzog
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Ou…
An Extension of the Strain Transfer Principle for Fiber Reinforced Materials
Felix Ospald, Kai Bergermann, Roland Herzog
Fiber optical strain sensors are used to measure the strain at a particular sensor position inside the fiber. In order to deduce the strain in the surrounding matrix material, one…
First-Order Methods for Optimal Experimental Design Problems with Bound Constraints
Roland Herzog, Eric Legler
We consider a class of convex optimization problems over the simplex of probability measures. Our framework comprises optimal experimental design (OED) problems, in which the measu…
Dimensionally Consistent Preconditioning for Saddle-Point Problems
Roland Herzog
The preconditioned iterative solution of large-scale saddle-point systems is of great importance in numerous application areas, many of them involving partial differential equation…
Short note on a relation between the inverse of the cosine and Carlson's elliptic integral
Felix Ospald, Roland Herzog
We prove a simple relation for a special case of Carlson's elliptic integral . The findings are applied to derive explicit formulae for the asymptotics of certain moments of t…
Error estimation for second-order PDEs in non-variational form
Jan Blechschmidt, Roland Herzog, Max Winkler
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman…
Hyper-Differential Sensitivity Analysis of Uncertain Parameters in PDE-Constrained Optimization
Joseph Hart, Bart van Bloemen Waanders, Roland Herzog
Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization…
Discrete Total Variation of the Normal Vector Field as Shape Prior with Applications in Geometric Inverse Problems
Ronny Bergmann, Marc Herrmann, Roland Herzog +2
An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated sur…
Fenchel Duality Theory and A Primal-Dual Algorithm on Riemannian Manifolds
Ronny Bergmann, Roland Herzog, Maurício Silva Louzeiro +2
This paper introduces a new notion of a Fenchel conjugate, which generalizes the classical Fenchel conjugation to functions defined on Riemannian manifolds. We investigate its prop…
Total Variation of the Normal Vector Field as Shape Prior
Ronny Bergmann, Marc Herrmann, Roland Herzog +2
An analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. The analysis of the total variation of the normal vect…
First and Second Order Shape Optimization based on Restricted Mesh Deformations
Tommy Etling, Roland Herzog, Estefanía Loayza +1
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented…
Optimum Experimental Design for Interface Identification Problems
Tommy Etling, Roland Herzog, Martin Siebenborn
The identification of the interface of an inclusion in a diffusion process is considered. This task is viewed as a parameter identification problem in which the parameter space bea…
Discrete Total Variation with Finite Elements and Applications to Imaging
Marc Herrmann, Roland Herzog, Stephan Schmidt +2
The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, di…