Head of Chair

Prof. Dr. Michael Stingl

Chair of Applied Mathematics (Continuous Optimization)

Professors

Address

Cauerstraße 11 91058 Erlangen

Martensstraße 5 a 91058 Erlangen

Contact

• Email: michael.stingl@fau.de

Team Assistant/Secretary

Nicole Güthlein

Chair of Applied Mathematics (Continuous Optimization)

Team assistant/Secretary

Address

Cauerstraße 11 91058 Erlangen

Martensstraße 5 a 91058 Erlangen

Contact

• Email: nicole.guethlein@fau.de
• Phone: +49 173 2177672

Scientific Team

Dr. Fabian Wein

Chair of Applied Mathematics (Continuous Optimization)

Research associates

Address

Cauerstraße 11 91058 Erlangen

Contact

• Email: fabian.wein@fau.de
• Phone: +49 9131 85-67186
• URL: en.www.math.fau.de/continuous-optimization/fabian-wein/

Social Media and Websites

• scholar.google.de/citations
• linkedin.com/in/fabian-wein-044982359/
• orcid.org/0000-0002-3896-6228
• www.researchgate.net/profile/Fabian-Wein

Dr. Lukas Pflug

FAU Competence Center Scientific Computing (FAU CSC)

Research associates

Address

Cauerstraße 11 91058 Erlangen

Martensstraße 5 a 91058 Erlangen

Contact

• Email: lukas.pflug@fau.de

Dr. Dieter Weninger

Chair of Applied Mathematics (Continuous Optimization)

Research associates

Contact

• Email: dieter.weninger@fau.de

Nico Nees

Collaborative Research Center 1411/2 Design of particulate products

Research associates

Address

Cauerstraße 11 91058 Erlangen

Contact

• Email: nico.nees@fau.de

Adeel Muneer

FAU Competence Center Scientific Computing (FAU CSC)

Research associates

Dr. Andrian Uihlein

Chair of Applied Mathematics (Continuous Optimization)

Research associates

Address

Cauerstraße 11 91058 Erlangen

Contact

• Email: andrian.uihlein@fau.de
• Phone: +49 9131 85-67157

Jakob Rodestock

FAU Competence Center Scientific Computing (FAU CSC)

Research associates

Address

Cauerstraße 11 91058 Erlangen

Contact

• Email: jakob.w.rodestock@fau.de

Florian Prohaska

Collaborative Research Center 1411/2 Design of particulate products

Research associates

Address

Cauerstraße 11 91058 Erlangen

Contact

• Email: florian.prohaska@fau.de
• Phone: +49 9131 85-67166

Social Media and Websites

• cris.fau.de/persons/270855888
• scholar.google.de/citations
• matrix.to/
• orcid.org/0009-0004-8034-6366

Max Zetzmann

Research Training Group 2423/2 - Fracture across scales: Integrating mechanics, materials science, mathematics, chemistry, and physics

Research associates

Address

Cauerstraße 11 91058 Erlangen

Contact

• Email: max.zetzmann@fau.de

Dr.-Ing. Sukhminder Singh

Collaborative Research Center 1411/2 Design of particulate products

Research associates

Address

Cauerstraße 11 91058 Erlangen

Contact

• Email: sukhminder.singh@fau.de

Former Members

Current Projects

DFG Research Training Group 2423 FRASCAL
PI, P11: Fracture Control by Material Optimization
Co-PI, P10: Configurational Fracture/Surface Mechanics
GRK 2423: Fracture across scales

Spokesperson: Prof. Dr.-Ing. P. Steinmann (Erlangen)

DFG Collaborative Research Centre 1411
Design of Particulate Products
D05: Topology, material and shape optimisation for particle ensembles (Stingl)
D03: Unifying mathematical framework for synthesis and chromatographic separation of nanoparticles (Pflug)
INF: Information management and computational science support (Spiecker/Stingl)
CRC 1411: Design of Particulate Products

Spokesperson: Prof. Dr. N. Vogel (Erlangen), deputy spokesperson Prof. Dr. M. Hartmann (Erlangen)

The P&G SimCenter (since 2014, extended until the end of 2026)
Master Collaboration Agreement with Procter & Gamble

The collaboration gives rise to a continuous stream of smaller projects with FAU, for example master’s theses. They are organised by the FAU Competence Center Scientific Computing (CSC). Contact person at FAU: Dr. Lukas Pflug.

Completed Projects

DFG Transregional Collaborative Research Centre 154 (until 2026)
B06: Robustification of Physical Parameters in Gas Networks
TRR 154: Subprojects, phase 2

Spokesperson: Prof. Dr. A. Martin (Erlangen)

DFG Collaborative Research Centre 814
C2: Robust structural and process optimization in the context of additive manufacturing

Spokesperson: Prof. Dr.-Ing. D. Drummer (Erlangen)

EU ITN Network POEMA (2019–2022)
Polynomial Optimization, Efficiency through Moments and Algebra

Coordinator: Prof. Dr. B. Mourrain (INRIA Sophia Antipolis, Nice)

Additive Manufacturing for Aircraft (ALM2AIR)
Aviation Research Programme (LuFo) 5-2, “Optimization of components for additive manufacturing”

This project aims to advance techniques for lattice optimization in the context of additive manufacturing using titanium alloy (Ti-6Al-4V). We study the full workflow from selection of parametrized base cells for stiffness optimization, the optimization algorithm, the interpretation of optimized results as a macroscopic lattice design including predefined solid and void non-design regions, and the generation of a ready-to-print surface description of the lattice structure. For the field of structural optimization, the SGP (Sequential Global Programming) algorithm is advanced allowing the distinct choice between solid, void and lattice during the optimization process.

DFG Priority Programme 1679
Dynamic simulation of interconnected solids processes: modelling, simulation and optimization of process chains
SPP 1679: DynSim-FP

PI: Prof. Dr. G. Leugering, Coordinator: Prof. Dr. Stefan Heinrich (Hamburg)

Optimization of iron oxide pigments (2012–2017)

The dependency of the optical properties of a pigment film and the shape or shape distribution of the pigment is studied within this project. Further, this dependency is used to identify regions in parameterized shape space which will lead to better color values of the pigment.

Prof. Dr. Günter Leugering (Erlangen), Prof. Dr.-Ing. Wolfgang Peukert (Erlangen), Prof. Dr. Ulf Peschel (Erlangen), Prof. Dr. Robin N. Klupp Taylor (Erlangen), Dr. Lukas Pflug (Erlangen)

Industrial Partners

e.g. Adidas, Airbus, BASF, Lanxess, Procter & Gamble, Schaeffler, Siemens

Projects in CRIS

• SFB/TRR 154 B06: Robust optimization of gas networks (B06)

  
  (Third Party Funds Group – Sub project)
  Overall project: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
  Project leader: Frauke Liers-Bergmann, Michael Stingl
  Term: 01.07.2022 - 30.06.2026
  Acronym: SFB/TRR 154 B06
  Funding source: Deutsche Forschungsgemeinschaft (DFG)
  URL: https://www.trr154.fau.de/
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• SFB 814 (T3): Process strategies for the production of thin-walled components during selective laser beam melting of plastics

  
  (Third Party Funds Group – Sub project)
  Overall project: CRC 814 - Additive Manufacturing
  Project leader: Dietmar Drummer, Michael Stingl
  Term: 01.01.2021 - 31.12.2023
  Acronym: SFB 814 (T3)
  Funding source: DFG / Sonderforschungsbereich (SFB)
  URL: https://www.crc814.research.fau.eu/projekte/t-transferprojekte/transferproject-t3/
  Abstract

  The aim of theproject is the systematic investigation of the process-geometry-interaction ofthin-walled components for the production of locally adapted properties as wellas the modeling of this effect in finite element simulations and structuraloptimization. In experimental tests, the main influencing factors areidentified and mapped in relation to the building position in the process. Newexposure technologies and strategies are used to manipulate the melting pooland homogenize component properties. The findings are incorporated into a wallthickness dependent material model for structural optimization, which isinvestigated in the project. The participating industrial partners willvalidate the results over the course of the project. The experimental findingsand the wall thickness dependent material model will be used to develop amethodology for the product development of thin-walled structures. In thefuture, the product development process can be accelerated, and the economicefficiency increased. Based on these findings, new application areas for theselective laser beam melting of plastics can be opened up in the future.

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• SFB 1411 - INF: Information management and computational science support

  
  (Third Party Funds Group – Sub project)
  Overall project: SFB 1411: Design of particulate products
  Project leader: Michael Stingl, Erdmann Spiecker
  Term: 01.01.2020 - 31.12.2023
  Acronym: SFB 1411 - INF
  Funding source: DFG / Sonderforschungsbereich (SFB)
  
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• SFB 1411 - D05: Topology, material and shape optimisation for particle ensembles

  
  (Third Party Funds Group – Sub project)
  Overall project: SFB 1411: Design of particulate products
  Project leader: Michael Stingl
  Term: 01.01.2020 - 31.12.2023
  Acronym: SFB 1411 - D05
  Funding source: DFG / Sonderforschungsbereich (SFB)
  
  Abstract

  The objective is the development of a mathematical framework which allows to conclude from desired optical properties to a corresponding optimised configuration of single particles as well as particle assemblies. A structural optimisation approach based on discrete dipole approximations is explored to allow for a design space with sufficiently high resolution and enabling the prediction of structure-property relations of individual particles. For particle assemblies a structural optimisation method based on a generalised hybrid finite element approach is established. Finally, dispersity and angle independency are taken into account by a new stochastic optimisation method.
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• GRK2423 - P11: Teilprojekt P11 - Fracture Control by Material Optimization

  
  (Third Party Funds Group – Sub project)
  Overall project: Skalenübergreifende Bruchvorgänge: Integration von Mechanik, Materialwissenschaften, Mathematik, Chemie und Physik (FRASCAL)
  Project leader: Michael Stingl, Julia Mergheim
  Term: 02.01.2019 - 31.12.2027
  Acronym: GRK2423 - P11
  Funding source: DFG / Graduiertenkolleg (GRK)
  URL: https://www.frascal.research.fau.eu/home/research/p-11-fracture-control-by-material-optimization/
  Abstract

  In previous works, the dependence of failure mechanisms in composite materials like debonding of the matrix-fibre interface or fibre breakage have been discussed.  The underlying model was based on specific cohesive zone elements, whose macroscopic properties could be derived from DFT. It has been shown that the dissipated energy could be increased by appropriate choices of cohesive parameters of the interface as well as aspects of the fibre. However due to the numerical complexity of applied simulation methods the crack path had to be fixed a priori. Only recently models allow computing the full crack properties at macroscopic scale in a quasi-static scenario by the solution of a single nonlinear variational inequality for a given set of material parameters and thus model based optimization of the fracture properties can be approached.

  The goal of the project is to develop an optimization method, in the framework of which crack properties (e.g. the crack path) can be optimized in a mathematically rigorous way. Thereby material properties of matrix, fibre and interfaces should serve as optimization variables.

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• GRK2423 - P10: Teilprojekt P10 - Configurational Fracture/Surface Mechanics

  
  (Third Party Funds Group – Sub project)
  Overall project: Fracture across Scales: Integrating Mechanics, Materials Science, Mathematics, Chemistry, and Physics (FRASCAL)
  Project leader: Paul Steinmann, Michael Stingl
  Term: 02.01.2019 - 31.12.2027
  Acronym: GRK2423 - P10
  Funding source: DFG / Graduiertenkolleg (GRK)
  URL: https://www.frascal.research.fau.eu/home/research/p-10-configurational-fracture-surface-mechanics/
  Abstract

  In a continuum the tendency of pre-existing cracks to propagate through the ambient material is assessed based on the established concept of configurational forces. In practise crack propagation is however prominently affected by the presence and properties of either surfaces and/or interfaces in the material. Here materials exposed to various surface treatments are mentioned, whereby effects of surface tension and crack extension can compete. Likewise, surface tension in inclusion-matrix interfaces can often not be neglected. In a continuum setting the energetics of surfaces/interfaces is captured by separate thermodynamic potentials. Surface potentials in general result in noticeable additions to configurational mechanics. This is particularly true in the realm of fracture mechanics, however its comprehensive theoretical/computational analysis is still lacking.

  The project aims in a systematic account of the pertinent surface/interface thermodynamics within the framework of geometrically nonlinear configurational fracture mechanics. The focus is especially on a finite element treatment, i.e. the Material Force Method [6]. The computational consideration of thermodynamic potentials, such as the free energy, that are distributed within surfaces/interfaces is at the same time scientifically challenging and technologically relevant when cracks and their kinetics are studied.

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• Robustification of Physics Parameters in Gas Networks (B06) (2018 - 2022)

  
  (Third Party Funds Group – Sub project)
  Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
  Project leader: Frauke Liers, Michael Stingl
  Term: 01.07.2018 - 30.06.2022
  Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
  
  Abstract

  The goal of this research project is to study uncertain optimization problems using robust optimization methods. Focusing on transport networks, we aim at the development of tractable robust counterparts for uncertain optimization problems and an analysis of the problem structure. For the arising adjustable robust optimization tasks, good relaxations as well as effective branch-and-bound implementations shall be developed.

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• Robustification of Physics Parameters in Gas Networks (B06) (2014 - 2018)

  
  (Third Party Funds Group – Sub project)
  Overall project: TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks
  Project leader: Frauke Liers-Bergmann, Michael Stingl
  Term: since 01.07.2014
  Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
  URL: https://en.www.math.fau.de/edom/projects-edom/energy/robustification-of-physical-parameters-in-gas-networks/
  Abstract

  The goal of this research project is to study uncertain optimization problems using robust optimization methods. Focusing on transport networks, we aim at the development of tractable robust counterparts for uncertain optimization problems and an analysis of the problem structure. For the arising adjustable robust optimization tasks, good relaxations as well as effective branch-and-bound implementations shall be developed.
  →More information

• SFB 814 (C2): Robust Structure-Process-Optimization (C2)

  
  (Third Party Funds Group – Sub project)
  Overall project: CRC 814 - Additive Manufacturing
  Project leader: Michael Stingl
  Term: 01.07.2011 - 30.06.2023
  Acronym: SFB 814 (C2)
  Funding source: DFG / Sonderforschungsbereich (SFB)
  
  Abstract

  Sub-project C2 is concerned with material and topologyoptimization in the context of additive manufacturing (AM). Based on a newflexible multi-material optimization concept developed in the second phase,which allows to consider process dependent materials, the focus will be now onmultifunctional components. The multifunctionality will be enabled by theintegration of graded lattice structures, which are known to exhibit astabilizing effect w.r.t. buckling and can provide exceptional dynamicproperties, such as the suppression of undesired vibrations. By this, thedesign freedom of AM shall be ultimately exploited.

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Master’s theses

Multiscale Elasto-dynamics

Description

Nowadays, considerable progress is being made in the design of composite materials which can exhibit properties that are not found in naturally occurring materials. Numerical homogenization techniques are used in order to find effective properties of periodic microstructures at the macro-scale. In conventional homogenization methods, the material properties are averaged over a repeating Representative Volume Element (RVE) in order to calculate those effective properties. But in the case of elastodynamics, uniform volume averaging can lead to a loss of phase information which is necessary to accurately describe the elastodynamic material at the macro-scale. Such limitations can be overcome by transferring the microscale information to the Fourier space and then projecting the frequency modes to a reduced space composing a few selected Floquet-Bloch eigenmodes, thereby reducing the degrees of freedom at the macro-scale. The homogenized parameters can then be utilized in a material optimization setting, thus optimizing the dynamic properties of the structure.

Objective

To develop a multiscale method for elasto-dynamic simulation using homogenization in the Fourier domain.

Prerequisites

Good knowledge of numerics of partial differential equations, mathematical optimization, programming in MATLAB/Python/C++ and a lot of enthusiasm.
Language: English or German

Tasks

• Literature research
• Model development
• Numerical experimentation
• Writing thesis and dissemination of the results

Optimization of a Mechatronic Sensor

Maximizing the sensitivity and robustness of a mechatronic sensor through structural optimization.
In cooperation with a regional industry partner.

Tooth Root Optimization

Topology optimization of a tooth root. Attempt to compare evolution against structural optimization. For CE students who aren’t afraid of the dentist. 🙂

Solar Air Heater

Solar air heaters are fascinatingly simple, cheap and efficient devices for environmentally friendly ventilation and heating. Yet, solar air heaters are widely unknown in western countries.

Based on an existing numerical setup for a coupled flow/heat model, certain properties can be structurally optimized by means of gradient-based optimization.

HiWi jobs

We are constantly looking for dedicated students starting from Bachelor level to work on small scientific projects in our group. If you are interested in optimization, numerics and challenging applications and would like some income on a regular basis, please contact us. For students of mathematics and computational engineering.