55 citations · 86 across the 24 of their papers we have counts for
15 papers · 1 filter
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…
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…
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…
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…
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…
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…
Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds
Ronny Bergmann, Roland Herzog
Karush-Kuhn-Tucker (KKT) conditions for equality and inequality constrained optimization problems on smooth manifolds are formulated. Under the Guignard constraint qualification, l…
Fast iterative solvers for an optimal transport problem
Roland Herzog, John W. Pearson, Martin Stoll
Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a parti…
A modified implementation of MINRES to monitor residual subvector norms for block systems
Roland Herzog, Kirk M. Soodhalter
Saddle-point systems, i.e., structured linear systems with symmetric matrices are considered. A modified implementation of (preconditioned) MINRES is derived which allows to monito…