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Habilitation
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Numerical Methods for Fluid Flow: High Order SBP Schemes, IMEX Advection-Diffusion Splitting and Positivity Preservation for Production-Destruction PDEs
(2021-01)
The current demands regarding the numerical simulation of fluid flow often require highly accurate computations to obtain a detailed resolution of the occurring physical phenomena. The basic concept for the construction of a fluid solver is to transfer the physical model into a numerical scheme which complies with the underlying physical principles such as conservation and balances of certain quantities. In addition, the numerical methods are required to be stable and efficient. Again, stability is often determined ...
Dissertation
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Mathematical Modelling and Adaptive Finite Element Simulation of Viscoelastic Fluid-Structure Interaction Systems and Chemical Processes with Applications to Ophthalmology
(2023)
The aim of this thesis is the numerical analysis of nonlinear coupled partial differential equations and their application to ophthalmology. Firstly, we consider fluid-structure interaction problems where the fluid is either Newtonian or viscoelastic. The structure is modelled as a hyperelastic material. The application to ophthalmology lies in the interaction of the vitreous with its surrounding elastic structures like the sclera and the lens. The underlying flow in the vitreous is modelled by a viscoelastic Burgers ...
Lehrmaterial
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Skriptum zur Linearen Algebra und Analytischen Geometrie
(2020-07)
Vorlesungsskript zur Vorlesung „Lineare Algebra und Analytische Geometrie“ an der Universität Kassel im Sommersemester 2020. Es handelt sich um die Druckversion.
Preprint
Identifying critical demand scenarios for the robust capacitated network design problem using principal component analysis
(2021-11-30)
In this paper, we consider the single-commodity robust network design problem. Given an undirected graph with capacity installation costs on its edges and a set S of scenarios with associated flow balance vectors that represent different scenarios of node supplies and demands, the goal is to find integer edge capacities that minimize the total installation cost and permit a feasible single commodity flow for each scenario. This problem arises, for example, in the design of power networks, which are dimensioned to ...
Dissertation
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Optimal control of a rate-independent system constrained to parameterized balanced viscosity solutions
(2022)
In this dissertation, we analyze an optimal control problem governed by a rate-independent system in an abstract infinite-dimensional setting. The rate-independent system is characterized by a nonconvex stored energy functional, which depends on time via a time-dependent external loading, and by a convex dissipation potential, which is assumed to be bounded and positively homogeneous of degree one.
The optimal control problem uses the external load as control variable and is constrained to normalized ...
Dissertation
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Development of a Preconditioning Scheme for Real Gases using Asymptotic Expansions
(2022)
Bei der Beschreibung von Strömungen wird klassischerweise zwischen inkompressiblen und kompressiblen Bereichen unterschieden. Während inkompressible Strömungen durch ein divergenzfreies Geschwindigkeitsfeld charakterisiert werden, sind kompressible Strömungsfelder durch Expansionsfächer, Kontaktunstetigkeiten und Stoßwellen gekennzeichnet. Die beiden Bereiche werden damit durch stark unterschiedliche Systeme partieller Differentialgleichungen beschrieben. Diese Unterscheidung zeigt sich auch in der numerischen ...