Industrial processes are currently experiencing their fourth revolution. The entire production process is connected and equipped with sensor technology, which makes huge amounts of data available. Workers are not only supported by technical visualization and information processing, but parts of the decisionmaking processes are even carried out independently with the help of AI systems. The large amount of data and the fully automated process pose new challenges for mathematics, but offer unprecedented opportunities for optimization algorithms, not only in the optimization of individual production steps, but across the entire value chain.
In various application projects at WIAS, simulation and optimal control for various production processes, e.g. in the field of steel production and processing, have been investigated. The focus here is on the efficient simulation of processes and the determination of optimal process parameters, which in practice can usually only be determined with the help of timeconsuming and costintensive experiments. The applications here include: The induction hardening of gears, inductive heating before steel cutting, or inductive welding of tubes.
Steel is also used in new production techniques, such as 3D printing using SLM (Selective Laser Melting). Such additive manufacturing processes enable completely new multiscale structures whose topology must be optimized with regard to strength throughout the entire printing process or with regard to multiscale effects. In the production of roses, natural predators of pests are used as environmentally friendly pesticides. Their optimal control can be modeled by the optimal control of partial differential equations.
Simulatiion and optimization of industrial processes is an integral part of different thirdparty funded projects at WIAS. Within one MATH+ project, the modelling and optimization of weakly coupled minigrids under uncertainty is investigated. In another MATH+ project, anisotropic electrokinetic materials are modelled, analyzed and optimized for the use in socalled "Labonachip" devices, which can help to facilitate the access to laboratory functions.
Research Group 4 coordinates a special interest group in the European Consortium for Mathematics in Industry (ECMI) on "Math for the Digital Factory".
The main objectives are
 reconfigurable, adaptive and evolving factories capable of small scale production
 high performance production, combining flexibility, productivity, precision and zero defect
 energy and resource efficiency in manufacturing.
All of these goals require a thorough modelling of all aspects of the process chain together with a multiscale simulation and optimization of complex production processes.
The following applicationoriented projects dealt with the simulation, optimization and optimal control of production processes in the last years:
 SPP 1886: Multiscale failure analysis with polymorphic uncertainties for optimal design of rotor blades,
duration: 01/01/2017  31/12/2022
Link  MIMESIS: Mathematics and materials science for steel production and manufacturing,
duration: 01/10/2015  30/09/2019
Link
Publications
Monographs

M. Hintermüller, T. Keil, Chapter 3: Optimal Control of Geometric Partial Differential Equations, in: Geometric Partial Differential Equations: Part 2, A. Bonito, R.H. Nochetto, eds., 22 of Handbook of Numerical Analysis, Elsevier, 2021, pp. 213270, (Chapter Published), DOI 10.1016/bs.hna.2020.10.003 .

M. Hintermüller, M. Hinze, J. Sokołowski, S. Ulbrich, eds., Special issue to honour Guenter Leugering on his 65th birthday, 1 of Control & Cybernetics, Systems Research Institute, Polish Academy of Sciences, Warsaw, 2019, (Collection Published).

M. Hintermüller, M. Hinze, Ch. Kahle, T. Keil, Chapter 13: Fully Adaptive and Integrated Numerical Methods for the Simulation and Control of Variable Density Multiphase Flows Governed by Diffuse Interface Models, in: Transport Processes at Fluidic Interfaces, D. Bothe, A. Reusken, eds., Advances in Mathematical Fluid Mechanics, Birkhäuser, Springer International Publishing AG, Cham, 2017, pp. 305353, (Chapter Published), DOI 10.1007/9783319566023 .

L. Ghezzi, D. Hömberg, Ch. Landry, eds., Math for the Digital Factory, 27 of Mathematics in Industry / The European Consortium for Mathematics in Industry, Springer International Publishing AG, Cham, 2017, x+348 pages, (Collection Published), DOI 10.1007/9783319639574 .

P. Deuflhard, M. Grötschel, D. Hömberg, U. Horst, J. Kramer, V. Mehrmann, K. Polthier, F. Schmidt, Ch. Schütte, M. Skutella, J. Sprekels, eds., MATHEON  Mathematics for Key Technologies, 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, 453 pages, (Collection Published).

B. Denkena, D. Hömberg, E. Uhlmann, Mathematik für Werkzeugmaschinen und Fabrikautomatisierung, in: Produktionsfaktor Mathematik. Wie Mathematik Technik und Wirtschaft bewegt, M. Grötschel, K. Lucas, V. Mehrmann, eds., acatech diskutiert, acatech, Springer, Berlin, Heidelberg, 2008, pp. 279299, (Chapter Published).
Articles in Refereed Journals

M. EbelingRump, D. Hömberg, R. Lasarzik, On a twoscale phasefield model for topology optimization, Discrete and Continuous Dynamical Systems  Series S, published online on 26.11.2023, DOI 10.3934/dcdss.2023206 .
Abstract
In this article, we consider a gradient flow stemming from a problem in twoscale topology optimization. We use the phasefield method, where a GinzburgLandau term with obstacle potential is added to the cost functional, which contains the usual compliance but also an additional contribution including a local volume constraint in a penalty term. The minimization of such an energy by its gradientflow is analyzed in this paper. We use an regularization and discretization of the associated statevariable to show the existence of weak solutions to the considered system. 
D. Hömberg, R. Lasarzik, L. Plato, On the existence of generalized solutions to a spatiotemporal predatorprey system with preytaxis, Journal of Evolution Equations, 23 (2023), pp. 20/120/44, DOI 10.1007/s00028023008715 .
Abstract
In this paper we consider a pair of coupled nonlinear partial differential equations describing the interaction of a predatorprey pair. We introduce a concept of generalized solutions and show the existence of such solutions in all space dimension with the aid of a regularizing term, that is motivated by overcrowding phenomena. Additionally, we prove the weakstrong uniqueness of these generalized solutions and the existence of strong solutions at least locallyintime for space dimension two and three. 
D.G. Gahururu, M. Hintermüller, Th.M. Surowiec, Riskneutral PDEconstrained generalized Nash equilibrium problems, Mathematical Programming. A Publication of the Mathematical Programming Society, 198 (2023), pp. 12871337 (published online on 29.03.2022), DOI 10.1007/s1010702201800z .

K. El Karfi, R. Henrion, D. Mentagui, An agricultural investment problem subject to probabilistic constraints, Computational Management Science, 19 (2022), pp. 683701, DOI 10.1007/s10287022004311 .

M. EbelingRump, D. Hömberg, R. Lasarzik, Twoscale topology optimization with heterogeneous mesostructures based on a local volume constraint, Computers & Mathematics with Applications. An International Journal, 126 (2022), pp. 100114, DOI 10.1016/j.camwa.2022.09.004 .
Abstract
A new approach to produce optimal porous mesostructures and at the same time optimizing the macro structure subject to a compliance cost functional is presented. It is based on a phasefield formulation of topology optimization and uses a local volume constraint (LVC). The main novelty is that the radius of the LVC may depend both on space and a local stress measure. This allows for creating optimal topologies with heterogeneous mesostructures enforcing any desired spatial grading and accommodating stress concentrations by stress dependent pore size. The resulting optimal control problem is analysed mathematically, numerical results show its versatility in creating optimal macroscopic designs with tailored mesostructures. 
E. Vorontsova, A. Gasnikov, P. Dvurechensky, A. Ivanova, D. Pasechnyuk, Numerical methods for the resource allocation problem in a computer network, Computational Mathematics and Mathematical Physics, 61 (2021), pp. 297328, DOI 10.1134/S0965542521020135 .

I. Shibaev, P. Dvurechensky, A. Gasnikov, Zerothorder methods for noisy Höldergradient functions, Optimization Letters, published online in April 2021, DOI 10.1007/s1159002101742z .

M.J. Arenas Jaén, D. Hömberg, R. Lasarzik, P. Mikkonen, Th. Petzold, Modelling and simulation of flame cutting for steel plates with solid phases and melting, Journal of Mathematics in Industry, 10 (2020), pp. 18/118/16, DOI 10.1186/s13362020000860 .
Abstract
The goal of this work is to describe in detail a quasistationary state model which can be used to deeply understand the distribution of the heat in a steel plate and the changes in the solid phases of the steel and into liquid phase during the flame cutting process. We use a 3Dmodel similar to previous works from Thiebaud [1] and expand it to consider phases changes, in particular, austenite formation and melting of material. Experimental data is used to validate the model and study its capabilities. Parameters defining the shape of the volumetric heat source and the power density are calibrated to achieve good agreement with temperature measurements. Similarities and differences with other models from literature are discussed. 
J.I. Asperheim, P. Das, B. Grande, D. Hömberg, Th. Petzold, Threedimensional numerical study of heat affected zone in induction welding of tubes, COMPEL. The International Journal for Computation and Mathematics in Electrical and Electronic Engineering. Emerald, Bradford, West Yorkshire. English, English abstracts., 39 (2020), pp. 213219, DOI 10.1108/COMPEL0620190238 .

P. Nestler, N. Schlömer, O. Klein, J. Sprekels, F. Tröltzsch, Optimal control of semiconductor melts by traveling magnetic fields, Vietnam Journal of Mathematics, 47 (2019), pp. 793812, DOI 10.1007/s10013019003555 .
Abstract
In this paper, the optimal control of traveling magnetic fields in a process of crystal growth from the melt of semiconductor materials is considered. As controls, the phase shifts of the voltage in the coils of a heatermagnet module are employed to generate Lorentz forces for stirring the crystal melt in an optimal way. By the use of a new industrial heatermagnet module, the Lorentz forces have a stronger impact on the melt than in earlier technologies. It is known from experiments that during the growth process temperature oscillations with respect to time occur in the neighborhood of the solidliquid interface. These oscillations may strongly influence the quality of the growing single crystal. As it seems to be impossible to suppress them completely, the main goal of optimization has to be less ambitious, namely, one tries to achieve oscillations that have a small amplitude and a frequency which is sufficiently high such that the solidliquid interface does not have enough time to react to the oscillations. In our approach, we control the oscillations at a finite number of selected points in the neighborhood of the solidification front. The system dynamics is modeled by a coupled system of partial differential equations that account for instationary heat condution, turbulent melt flow, and magnetic field. We report on numerical methods for solving this system and for the optimization of the whole process. Different objective functionals are tested to reach the goal of optimization. 
D. Hömberg, K. Krumbiegel, N. Togobytska, Optimal control of multiphase steel production, Journal of Mathematics in Industry, 9 (2019), pp. 132, DOI 10.1186/s133620190063x .
Abstract
An optimal control problem for the production of multiphase steel is investigated, where the state equations are a semilinear heat equation and an ordinary differential equation, which describes the evolution of the ferrite phase fraction. The optimal control problem is analyzed and the firstorder necessary and secondorder sufficient optimality conditions are derived. For the numerical solution of the control problem reduced sequential quadratic programming (rSQP) method with a primaldual active set strategy (PDAS) was applied. The numerical results were presented for the optimal control of a cooling line for production of hot rolled MoMn dual phase steel. 
N. Alia, V. John, S. Ollila, Revisiting the singlephase flow model for liquid steel ladle stirred by gas, Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems. Elsevier Science Inc., New York, NY. English, English abstracts., 67 (2019), pp. 549556 (published online on 21.11.2018), DOI 10.1016/j.apm.2018.11.005 .

L. Adam, M. Hintermüller, Th.M. Surowiec, A PDEconstrained optimization approach for topology optimization of strained photonic devices, Annali di Matematica Pura ed Applicata. Serie Quarta. Fondazione Annali di Matematica Pura ed Applicata, c/o Dipartimento di Matematica ``U. Dini'', Firenze; SpringerVerlag, Heidelberg. English, French, German, Italian, English abstracts., 19 (2018), pp. 521557, DOI 10.1007/s1108101893945 .
Abstract
Recent studies have demonstrated the potential of using tensilestrained, doped Germanium as a means of developing an integrated light source for (amongst other things) future microprocessors. In this work, a multimaterial phasefield approach to determine the optimal material configuration within a socalled GermaniumonSilicon microbridge is considered. Here, an “optimal" configuration is one in which the strain in a predetermined minimal optical cavity within the Germanium is maximized according to an appropriately chosen objective functional. Due to manufacturing requirements, the emphasis here is on the crosssection of the device; i.e. a socalled aperture design. Here, the optimization is modeled as a nonlinear optimization problem with partial differential equation (PDE) and manufacturing constraints. The resulting problem is analyzed and solved numerically. The theory portion includes a proof of existence of an optimal topology, differential sensitivity analysis of the displacement with respect to the topology, and the derivation of first and secondorder optimality conditions. For the numerical experiments, an array of first and secondorder solution algorithms in functionspace are adapted to the current setting, tested, and compared. The numerical examples yield designs for which a significant increase in strain (as compared to an intuitive empirical design) is observed. 
K. Sturm, M. Hintermüller, D. Hömberg, Distortion compensation as a shape optimisation problem for a sharp interface model, Computational Optimization and Applications. An International Journal, 64 (2016), pp. 557588.
Abstract
We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface. 
D. Hömberg, Q. Liu, J. MontalvoUrquizo, D. Nadolski, Th. Petzold, A. Schmidt, A. Schulz, Simulation of multifrequencyinductionhardening including phase transitions and mechanical effects, Finite Elements in Analysis and Design, 121 (2016), pp. 86100.
Abstract
Induction hardening is a well known method for the heat treatment of steel components. With the concept of multifrequency hardening, where currents with two different frequency components are provided on a single inductor coil, it is possible to optimize the hardening zone to follow a given contour, e.g. of a gear. In this article, we consider the simulation of multifrequency induction hardening in 3D. The equations to solve are the vector potential formulation of Maxwell's equations describing the electromagnetic fields, the balance of momentum to determine internal stresses and deformations arising from thermoelasticity and transformation induced plasticity, a rate law to determine the distribution of different phases and the heat equation to determine the temperature distribution in the workpiece. The equations are solved using adaptive finite element methods. The simulation results are compared to experiments for discs and for gears. A very good agreement for the hardening profile and the temperature is observed. It is also possible to predict the distribution of residual stresses after the heat treatment. 
TH. Petzold, D. Hömberg, D. Nadolski, A. Schulz, H. Stiele, Adaptive FiniteElementeSimulation des MehrfrequenzInduktionshärtens, HTM Journal for Heat Treatment and Materials, 70 (2015), pp. 3339.

D. Hömberg, Th. Petzold, E. Rocca, Analysis and simulations of multifrequency induction hardening, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 22 (2015), pp. 8497.
Abstract
We study a model for induction hardening of steel. The related differential system consists of a time domain vector potential formulation of the Maxwell's equations coupled with an internal energy balance and an ODE for the volume fraction of austenite, the high temperature phase in steel. We first solve the initial boundary value problem associated by means of a Schauder fixed point argument coupled with suitable apriori estimates and regularity results. Moreover, we prove a stability estimate entailing, in particular, uniqueness of solutions for our Cauchy problem. We conclude with some finite element simulations for the coupled system. 
W. Bleck, D. Hömberg, U. Prahl, P. Suwanpinij, N. Togobytska, Optimal control of a cooling line for production of hot rolled dual phase steel, Steel Research International, 85 (2014), pp. 13281333.
Abstract
In this article, the optimal control of a cooling line for production of dual phase steel in a hot rolling process is discussed. In order to achieve a desired dual phase steel microstructure an optimal cooling strategy has to be found. The cooling strategy should be such that a desired final distribution of ferrite in the steel slab is reached most accurately. This problem has been solved by means of mathematical control theory. The results of the optimal control of the cooling line have been verified in hot rolling experiments at the pilot hot rolling mill at the Institute for Metal Forming (IMF), TU Bergakademie Freiberg. 
A. Fügenschuh, B. Geissler, Ch. Hayn, R. Henrion, B. Hiller, J. Humpola, Th. Koch ET AL., Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets, Energy Systems, 5 (2014), pp. 449473.

D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Parameter identification in nonisothermal nucleation and growth processes, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 30 (2014), pp. 035003/1035003/24.
Abstract
We study nonisothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation. 
K. Chełminski, D. Hömberg, O. Rott, On a thermomechanical milling model, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 12 (2011), pp. 615632.
Abstract
This paper deals with a new mathematical model to characterize the interaction between machine and workpiece in a milling process. The model consists of a harmonic oscillator equation for the dynamics of the cutter and a linear thermoelastic workpiece model. The coupling through the cutting force adds delay terms and further nonlinear effects. After a short derivation of the governing equations it is shown that the complete system admits a unique weak solution. A numerical solution strategy is outlined and complemented by numerical simulations of stable and unstable cutting conditions. 
A. Fasano, D. Hömberg, D. Naumov, On a mathematical model for laserinduced thermotherapy, Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems. Elsevier Science Inc., New York, NY. English, English abstracts., 34 (2010), pp. 38313840.
Abstract
We study a mathematical model for laserinduced thermotherapy, a minimally invasive cancer treatment. The model consists of a diffusion approximation of the radiation transport equation coupled to a bioheat equation and a model to describe the evolution of the coagulated zone. Special emphasis is laid on a refined model of the applicator device, accounting for the effect of coolant flow inside. Comparisons between experiment and simulations show that the model is able to predict the experimentally achieved temperatures reasonably well. 
D. Hömberg, Ch. Meyer, J. Rehberg, W. Ring, Optimal control for the thermistor problem, SIAM Journal on Control and Optimization, 48 (2010), pp. 34493481.
Abstract
This paper is concerned with the stateconstrained optimal control of the twodimensional thermistor problem, a quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Existence, uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity. By similar arguments the linearized state system is discussed, while the adjoint system involving measures is investigated using a duality argument. These results allow to derive firstorder necessary conditions for the optimal control problem. 
A. Fasano, D. Hömberg, L. Panizzi, A mathematical model for case hardening of steel, Mathematical Models & Methods in Applied Sciences, 19 (2009), pp. 21012126.
Abstract
A mathematical model for the case hardening of steel is presented. Carbon is dissolved in the surface layer of a lowcarbon steel part at a temperature sufficient to render the steel austenitic, followed by quenching to form a martensitic microstructure. The model consists of a nonlinear evolution equation for the temperature, coupled with a nonlinear evolution equation for the carbon concentration, both coupled with two ordinary differential equations to describe the evolution of phase fractions. We investigate questions of existence and uniqueness of a solution and finally present some numerical simulations. 
D. Hömberg, D. Kern, The heat treatment of steel  A mathematical control problem, Materialwissenschaft und Werkstofftechnik, 40 (2009), pp. 438442.
Abstract
The goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machinebased control. 
D. Hömberg, N. Togobytska, M. Yamamoto, On the evaluation of dilatometer experiments, Applicable Analysis. An International Journal, 88 (2009), pp. 669681.
Abstract
The goal of this paper is a mathematical investigation of dilatometer experiments to measure the kinetics of solidsolid phase transitions in steel upon cooling from the high temperature phase. Usually, the data are only used for measuring the start and end temperature of the phase transition. In the case of several coexisting product phases, lavish microscopic investigations have to be performed to obtain the resulting fractions of the different phases. In contrast, we show that the complete phase transition kinetics including the final phase fractions are uniquely determined by the dilatometer data and present some numerical identification results. 
K. Chełminski, D. Hömberg, D. Kern, On a thermomechanical model of phase transitions in steel, Advances in Mathematical Sciences and Applications, 18 (2008), pp. 119140.

P. Suwanpinij, N. Togobytska, Ch. Keul, W. Weiss, U. Prahl, D. Hömberg, W. Bleck, Phase transformation modeling and parameter identification from dilatometric investigations, Steel Research International, 79 (2008), pp. 793799.
Abstract
The goal of this paper is to propose a new approach towards the evaluation of dilatometric results, which are often employed to analyse the phase transformation kinetics in steel, especially in terms of continuous cooling transformation (CCT) diagram. A simple task of dilatometry is deriving the start and end temperatures of the phase transformation. It can yield phase transformation kinetics provided that plenty metallographic investigations are performed, whose analysis is complicated especially in case of several coexisting product phases. The new method is based on the numerical solution of a thermomechanical identification problem. It is expected that the phase transformation kinetics can be derived by this approach with less metallographic tasks. The first results are remarkably promising although further investigations are required for the numerical simulations. 
H. Alder, D. Hömberg, W. Weiss, Simulationsbasierte Regelung der Laserhärtung von Stahl, HTM Zeitschrift für Werkstoffe. Wärmebehandlung. Fertigung, 61 (2006), pp. 103108.

D. Hömberg, W. Weiss, PID control of laser surface hardening of steel, IEEE Transactions on Control Systems Technology, 14 (2006), pp. 896904.

D. Hömberg, A mathematical model for induction hardening including mechanical effects, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 5 (2004), pp. 5590.

D. Hömberg, J. Sokolowski, Optimal shape design of inductor coils for induction hardening, SIAM Journal on Control and Optimization, 42 (2003), pp. 10871117.

D. Hömberg, S. Volkwein, Control of laser surface hardening by a reducedorder approach using proper orthogonal decomposition, Mathematical and Computer Modelling, 38 (2003), pp. 10031028.
Contributions to Collected Editions

G. Thiele, Th. Johanni, D. Sommer, M. Eigel, J. Krüger, OptTopo: Automated setpoint optimization for coupled systems using topology information, in: 2022 8th International Conference on Control, Decision and Information Technologies (CoDIT), IEEE, 2022, pp. 224229, DOI 10.1109/CoDIT55151.2022.9803985 .

G. Thiele, A. Fey, D. Sommer, J. Krüger, System identification of a hysteresiscontrolled pump system using SINDy, in: 2020 24th International Conference on System Theory, Control and Computing (ICSTCC), IEEE, 2020, pp. 457464, DOI 10.1109/ICSTCC50638.2020.9259776 .
Abstract
Hysteresiscontrolled devices are widely used in industrial applications. For example, cooling devices usually contain a twopoint controller, resulting in a nonlinear hybrid system with two discrete states. Dynamic models of systems are essential for optimizing such industrial supply technology. However, conventional system identification approaches can hardly handle hysteresiscontrolled devices. Thus, the new identification method Sparse Identification of Nonlinear Dynamics (SINDy) is extended to consider hybrid systems. SINDy composes models from basis functions out of a customized library in a datadriven manner. For modeling systems that behave dependent on their own past as in the case of natural hysteresis, Ferenc Preisach introduced the relay hysteron as an elementary mathematical description. In this new method (SINDyHybrid), tailored basis functions in form of relay hysterons are added to the library which is used by SINDy. Experiments with a hysteresis controlled water basin show that this approach correctly identifies state transitions of hybrid systems and also succeeds in modeling the dynamics of the discrete system states. A novel proximity hysteron achieves the robustness of this method. The impacts of the sampling rate and the signal noise ratio of the measurement data are examined accordingly. 
M. Hintermüller, N. Strogies, On the consistency of RungeKutta methods up to order three applied to the optimal control of scalar conservation laws, in: Numerical Analysis and Optimization, M. AlBaali, L. Grandinetti, A. Purnama, eds., 235 of Springer Proceedings in Mathematics & Statistics, Springer Nature Switzerland AG, Cham, 2019, pp. 119154.
Abstract
Higherorder RungeKutta (RK) time discretization methods for the optimal control of scalar conservation laws are analyzed and numerically tested. The hyperbolic nature of the state system introduces specific requirements on discretization schemes such that the discrete adjoint states associated with the control problem converge as well. Moreover, conditions on the RKcoefficients are derived that coincide with those characterizing strong stability preserving RungeKutta methods. As a consequence, the optimal order for the adjoint state is limited, e.g., to two even in the case where the conservation law is discretized by a thirdorder method. Finally, numerical tests for controlling Burgers equation validate the theoretical results. 
M. Hintermüller, T. Keil, Some recent developments in optimal control of multiphase flows, in: Shape Optimization, Homogenization and Optimal Control. DFGAIMS Workshop held at the AIMS Center Senegal, March 1316, 2017, V. Schulz, D. Seck, eds., 169 of International Series of Numerical Mathematics, Birkhäuser, Springer Nature Switzerland AG, Cham, 2018, pp. 113142, DOI 10.1007/9783319904696_7 .

L. Capone, Th. Petzold, D. Hömberg, D. Ivanov, A novel integrated tool for parametric geometry generation and simulation for induction hardening of gears, in: Heat Treat 2017: Proceedings of the 29th AMS Heat Treating Society Conference, October 2426, 2017, Columbus, Ohio, USA, ASM International, Materials Park, Ohio, 2017, pp. 234242.

P. Das, J.I. Asperheim, B. Grande, Th. Petzold, D. Hömberg, Simulation of temperature profile in longitudinal welded tubes during highfrequency induction (HFI) welding, in: Heat Treat 2017: Proceedings of the 29th AMS Heat Treating Society Conference, October 2426, 2017, Columbus, Ohio, USA, ASM International, Materials Park, Ohio, 2017, pp. 534538.

Q. Liu, Th. Petzold, D. Nadolski, R. Pulch, Simulation of thermomechanical behavior subjected to induction hardening, in: Scientific Computing in Electrical Engineering, SCEE 2014, Wuppertal, Germany, July 2014, A. Bartel, M. Clemens, M. Günther, E.J.W. TER Maten, eds., 23 of Mathematics in Industry, Springer International Publishing Switzerland, Cham, 2016, pp. 133142.

CH. Landry, M. Gerdts, R. Henrion, D. Hömberg, W. Welz, Collisionfree path planning of welding robots, in: Progress in Industrial Mathematics at ECMI 2012, M. Fontes, M. Günther, N. Marheineke, eds., 19 of Mathematics in Industry, Springer, Cham et al., 2014, pp. 251256.

T. Bosse, R. Henrion, D. Hömberg, Ch. Landry, H. Leövey ET AL., C2  Nonlinear programming with applications to production processes, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 171187.

C. Carstensen, M. Hintermüller, D. Hömberg, F. Tröltzsch, C  Production, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 151153.

M. Hintermüller, D. Hömberg, O. Klein, J. Sprekels, F. Tröltzsch, C4  PDEconstrained optimization with industrial applications, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 207222.

D. Hömberg, E. Rocca, Th. Petzold, Multifrequency induction hardening  A challenge for industrial mathematics, in: The Impact of Applications on Mathematics  Proceedings of the Forum of Mathematics for Industry 2013, M. Wakayama, ed., 1 of Mathematics for Industry, Springer, Tokyo et al., 2014, pp. 257264.

D. Hömberg, Th. Petzold, Modelling and simulation of multifrequency induction hardening of steel parts, in: Proceedings of the International Scientific Colloquium ``Modelling for Electromagnetic Processing'', MEP 2014, E. Baake, B. Nacke, eds., Leibniz University of Hannover, 2014, pp. 245250.

D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Nucleation rate identification in binary phase transition, in: The Impact of Applications on Mathematics  Proceedings of the Forum of Mathematics for Industry 2013, M. Wakayama, ed., 1 of Mathematics for Industry, Springer, Tokyo et al., 2014, pp. 227243.

L. Panizzi, A. Fasano, D. Hömberg, Modeling, analysis and simulations of case hardening of steel, in: Progress in Industrial Mathematics at ECMI 2008, A. Fitt, J. Norbury, H. Ockendon, E. Wilson, eds., 15 of Mathematics in Industry, Springer, Berlin et al., 2010, pp. 965970.

P. Rasper, O. Rott, D. Hömberg, E. Uhlmann, Analysis of uncertainties in the stability prediction for milling processes, in: Conference Proceedings, CIRP 2nd International Conference ``Process Machine Interactions'', June 1011, 2010, Vancouver (CD), Y. Altintas, B. Denkena, Ch. Brecher, eds., 2010, pp. M18/1M18/12.

D. Hömberg, O. Rott, Modeling, analysis and stability of milling processes including workpiece effects, in: Progress in Industrial Mathematics at ECMI 2008, A. Fitt, J. Norbury, H. Ockendon, E. Wilson, eds., 15 of Mathematics in Industry, Springer, Berlin et al., 2010, pp. 493498.

O. Rott, P. Rasper, D. Hömberg, E. Uhlmann, A milling model with thermal effects including the dynamics of machine and work piece, B. Denkena, ed., Proceedings, 1st International Conference on Process Machine Interactions, Hannover, September 34, 2008, PZH Produktionstechnisches Zentrum GmbH, Garbsen, 2008, pp. 369378.
Abstract
This paper deals with the development of a new mathematical model that characterizes the structureprocess interaction for a complex milling system. The structure is divided into a work piece and a machine part, which are represented by different models. While the machine dynamics is characterized by a standard multibody system, the work piece is described as a linear thermoelastic continuum. The coupling of both parts is carried out by an empirical process model permitting an estimate of heat and coupling forces occurring during milling. This work reports the derivation of the governing equations emphasizing the coupling and summarizes the numerical algorithms being applied to solve the coupled equation system. The results of numerical simulations that show the dynamics of the complex thermomechanical system are presented at the end. 
D. Hömberg, D. Kern, The heat treatment of steel  A mathematical control problem, in: Proceedings of the 2nd International Conference on Distortion Engineering  IDE 2008, 1719 September 2008, Bremen, Germany, H.W. Zoch, Th. Lübben, eds., IWT, Bremen, 2008, pp. 201209.

CH. Meyer, D. Hömberg, J. Rehberg, W. Ring, Optimal control of the thermistor problem, in: Optimal Control of Coupled Systems of PDE, Workshop, March 28, 2008, 5 of Oberwolfach Reports, Mathematisches Forschungsinstitut Oberwolfach, 2008, pp. 624626.

D. Hömberg, D. Kern, W. Weiss, Die Wärmebehandlung von Stahl  ein Optimierungsproblem, in: Distortion Engineering  Verzugsbeherrschung in der Fertigung III , 3 of Sonderforschungsbereich 570, Universität Bremen, Kolloquium, 2006, pp. 3955.

M. Anthonissen, D. Hömberg, W. Weiss, Realtime control of surface remelting, in: Progress in Industrial Mathematics at ECMI 2004, A. Di Bucchianico, R.M.M. Mattheij, M.A. Peletier, eds., 8 of Mathematics in Industry, Springer, 2005, pp. 356360.

D. Hömberg, S. Volkwein, W. Weiss, Optimal control strategies for the surface hardening of steel, in: Proceedings of the 2nd International Conference on Thermal Process Modelling and Computer Simulation, S. Denis, P. Archambault, J.M. Bergheau, R. Fortunier, eds., 120 of J. Physique IV, EDP Sciences, 2004, pp. 325335.
Preprints, Reports, Technical Reports

M.J. Arenas, D. Hömberg, R. Lasarzik, Optimal beam forming for laser materials processing, Preprint no. 3080, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3080 .
Abstract, PDF (2441 kByte)
We investigate an optimal control problem related to laser material treatments such as welding, remelting, hardening, or the 3D printing of metal components. The mathematical model leads to the investigation of a quasilinear elliptic state system with additional nonmonotone loweroder terms. We analyze the state system, derive first order optimality conditions and show first results for beam shaping. 
N. Ouanes, T. González Grandón, H. Heitsch, R. Henrion, Optimizing the economic dispatch of weaklyconnected minigrids under uncertainty using joint chance constraints, Preprint no. 3069, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3069 .
Abstract, PDF (1681 kByte)
In this paper, we deal with a renewablepowered minigrid, connected to an unreliable main grid, in a Joint Chance Constrained (JCC) programming setting. In several rural areas in Africa with low energy access rates, gridconnected minigrid system operators contend with four different types of uncertainties: forecasting errors of solar power and load; frequency and outages duration from the maingrid. These uncertainties pose new challenges to the classical power system's operation tasks. Three alternatives to the JCC problem are presented. In particular, we present an Individual Chance Constraint (ICC), ExpectedValue Model (EVM) and a so called regular model that ignores outages and forecasting uncertainties. The JCC model has the capability to guarantee a high probability of meeting the local demand throughout an outage event by keeping appropriate reserves for Diesel generation and battery discharge. In contrast, the easier to handle ICC model guarantees such probability only individually for different time steps, resulting in a much less robust dispatch. The even simpler EVM focuses solely on average values of random variables. We illustrate the four models through a comparison of outcomes attained from a real minigrid in Lake Victoria, Tanzania. The results show the dispatch modifications for battery and Diesel reserve planning, with the JCC model providing the most robust results, albeit with a small increase in costs.
Talks, Poster

R. Henrion, Turnpike phenomenon in discretetime optimal control with probabilistic constraint, 2nd Vienna Workshop on Computational Optimization, March 15  17, 2023, Universität Wien, Austria, March 15, 2023.

M. Hintermüller, A descent algorithm for the optimal control of ReLU neural network Informed PDEs based on approximate directional derivatives, FoCM 2023  Foundations of Computational Mathematics, Session II.2: ``Continuous Optimization'', June 12  21, 2023, Sorbonne University, Paris, France, June 15, 2023.

M. Hintermüller, Learninginformed and PINNbased multi scale PDE models in optimization, Conference on Deep Learning for Computational Physics, July 4  6, 2023, UCL  London's Global University, UK, July 6, 2023.

M. Hintermüller, Optimal control of (quasi)variational inequalities: Stationarity, riskaversion, and numerical solution, Workshop on Optimization, Equilibrium and Complementarity, August 16  19, 2023, The Hong Kong Polytechnic University, Department of Applied Mathematic, August 19, 2023.

M. Hintermüller, PDEconstrained optimization with nonsmooth learninginformed structures, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), Minisymposium 00711 ``Recent Advances in Optimal Control and Optimization'', August 20  25, 2023, Waseda University, Tokyo, Japan, August 21, 2023.

D. Hömberg, On twoscale topology optimization for AM, The Fourth International Conference on Simulation for Additive Manufacturing (SimAM 2023), IS14 ``Advanced Methods and Innovative Technologies for the Optimal Design of Structures and Materials II'', July 26  28, 2023, Galileo Science Congress Center MunichGarching, Garching, July 27, 2023.

D. Hömberg, Phasefield based topology optimization, Norwegian Workshop on Mathematical Optimization, Nonlinear and Variational Analysis 2023, April 26  28, 2023, Norwegian University of Science and Technology, Trondheim, Norway, April 27, 2023.

D. Hömberg, Twoscale topology optimization  A phase field approach, 22nd European Conference on Mathematics for Industry (ECMI2023), MS17 ``ECMI SIG: Mathematics for the Digital Factory'', June 26  30, 2023, Wrocław University of Science and Technology Congress Centre, Poland, June 26, 2023.

M. Hintermüller, A descent algorithm for the optimal control of ReLU neural network informed PDEs based on approximate directional derivatives (online talk), Workshop 2: Structured Optimization Models in HighDimensional Data Analysis, December 12  16, 2022, National University of Singapore, Institute for Mathematical Sciences, December 15, 2022.

M. Hintermüller, Optimization subject to learning informed PDEs, International Conference on Continuous Optimization  ICCOPT/MOPTA 2022, Cluster ``PDEConstrained Optimization'', July 23  28, 2022, Lehigh University, Bethlehem, Pennsylvania, USA, July 27, 2022.

M. Hintermüller, Optimization with learninginformed differential equation constraints (online talk), Workshop on Control Problems (Online Event), October 17  20, 2022, Technische Universität Dortmund, October 17, 2022.

M. Hintermüller, PDEconstrained optimization with learninginformed structures (online talk), Optimization in Oslo (OiO) Seminar, Simula Research Laboratory, Norway, December 7, 2022.

P. Farrell, Modelling and simulation of the lateral photovoltage scanning method (online talk), European Conference on Mathematics for Industry (ECMI2021), MSOEE: ``Mathematical Modeling of Charge Transport in Graphene and Low dimensional Structures'' (Online Event), April 13  15, 2021, Bergische Universität Wuppertal, April 13, 2021.

D. Sommer, Robust nonlinear model predictive control using tensor networks (online talk), European Conference on Mathematics for Industry (ECMI2021), MS23: ``DataDriven Optimization'' (Online Event), April 13  15, 2021, Bergische Universität Wuppertal, April 14, 2021.

M. Hintermüller, Optimal control of quasivariational inequalities (online talk), SIAM Conference on Optimization (OP21) (Online Event), Minisymposium MS93 ``Nonsmooth Problems and Methods in Largescale Optimization'', July 20  23, 2021, July 23, 2021.

M. Hintermüller, Optimization with learninginformed differential equation constraints and its applications, Online Conference ``Industrial and Applied Mathematics'', January 11  15, 2021, The Hong Kong University of Science and Technology, Institute for Advanced Study, January 13, 2021.

M. Hintermüller, Optimization with learninginformed differential equation constraints and its applications (online talk), One World Optimization Seminar, Universität Wien, Fakultät für Mathematik, Austria, May 10, 2021.

M. Hintermüller, Semismooth Newton methods: Theory, numerical algorithms and applications I (online talk), International Forum on Frontiers of Intelligent Medical Image Analysis and Computing 2021 (Online Forum), Xidian University, Southeastern University, and Hong Kong Baptist University, China, July 19, 2021.

M. Hintermüller, Semismooth Newton methods: Theory, numerical algorithms and applications II (online talk), International Forum on Frontiers of Intelligent Medical Image Analysis and Computing 2021 (Online Forum), Xidian University, Southeastern University, and Hong Kong Baptist University, China, July 26, 2021.

D. Hömberg, Mathematics for steel production and manufacturing (online talk), Cardiff University, School of Mathematics, UK, March 2, 2021.

D. Hömberg, Modelling and simulation of highfrequency induction welding (online talk), European Conference on Mathematics for Industry (ECMI2021), MS08: ``Modelling, Simulation and Optimization in Electrical Engineering'' (Online Event), April 13  15, 2021, Bergische Universität Wuppertal, April 13, 2021.

H. Nguyen, A shape optimization problem for stationary NavierStokes flows in threedimensional tubes, Model Order Reduction Summer School 2020 (MORSS 2020), September 7  10, 2020, École polytechnique fédérale de Lausanne (EPFL), Lausanne, Switzerland, September 7, 2020.

C. Löbhard, Spacetime discretization for parabolic optimal control problems with state constraints, ICCOPT 2019  Sixth International Conference on Continuos Optimization, Session ``Optimal Control and Dynamical Systems (Part VI)'', August 5  8, 2019, Berlin, August 7, 2019.

M. Hintermüller, Lecture Series: Optimal control of nonsmooth structures, Thematic Programme ``Modern Maximal Monotone Operator Theory: From Nonsmooth Optimization to Differential Inclusions'', February 4  7, 2019, Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland, December 3, 2019.

D. Hömberg, MSO for steel production and manufacturing, 9th International Congress on Industrial and Applied Mathematics (ICIAM), Minisymposium IM FT42 1 ``AcademiaIndustry Case Studies from MINET and ECMI'', July 15  19, 2019, Valencia, Spain, July 15, 2019.

D. Hömberg, Mathematics for steel production and manufacturing, Conference ``Dynamics, Equations and Applications (DEA 2019)'', Session ``D442 Complex Systems in Material Science'', September 16  20, 2019, AGH University of Science and Technology, Kraków, Poland, September 17, 2019.

D. Hömberg, Mathematics for steel production and manufacturing, Sondierungsworkshop MPIE/WIAS ``Elektrochemie, Halbleiternanostrukturen und Metalle'', October 14  15, 2019, MaxPlanckInstitut für Eisenforschung GmbH Düsseldorf, October 14, 2019.

D. Hömberg, Maths for digital factory, Polytechnic of Leiria, Center for Rapid and Sustainable Product Development, Marinha Grande, Portugal, October 10, 2019.

N. Alia, Modeling and optimization of a gasstirred liquid flow for steelmaking processes, The 20th European Conference on Mathematics for Industry (ECMI), MS27: MSO for steel production and manufacturing, June 18  22, 2018, University Budapest, Institute of Mathematics at Eötvös Loránd, Hungary, June 19, 2018.

M. Hintermüller, Nonsmooth structures in PDE constrained optimization, Mathematisches Kolloquium, Universität Bielefeld, Fakultät für Mathematik, June 7, 2018.

M. Hintermüller, Recent advances in nonsmooth and complementaritybased distributed parameter systems, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Session PP07 ``DFG Priority Program 1962'', March 19  23, 2018, Technische Universität München, March 20, 2018.

M. Hintermüller, Semismooth Newton methods in PDE constrained optimization, Advanced Training in Mathematics Schools ``New Directions in PDE Constrained Optimisation'', March 12  16, 2018, National Centre for Mathematics of IIT Bombay and TIFR, Mumbai, Bombay, India.

D. Hömberg, European collaboration in industrial and applied mathematics, Conference ``Mathematical Modelling in Metallurgical Industry'', September 17  18, 2018, Kristiansand, Norway, September 18, 2018.

D. Hömberg, European collaboration in industrial and applied mathematics, Salzburg Mathematics Colloquium, Universität Salzburg, Fachbereich Mathematik, Austria, May 17, 2018.

D. Hömberg, European collaboration in industrial and applied mathematics, Inderprastha Engineering College, Ghaziabad, India, January 5, 2018.

D. Hömberg, Knowledge exchange in mathematics  The European perspective, 1st IMA Conference on Knowledge Exchange in the Mathematical Sciences, December 3  4, 2018, Aston University, Birmingham, UK, December 3, 2018.

D. Hömberg, Mathematical challenges in steel manufacturing, Second International Conference on Modern Mathematical Methods and High Performance Computing in Science and Technology (M3HPCST 2018), January 4  6, 2018, Inderprastha Engineering College (IPEC), Ghaziabad, India, January 4, 2018.

D. Hömberg, Maths for digital factory, University of Southern Denmark, The Maersk McKinney Moller Institute, Odense, Denmark, October 12, 2018.

D. Hömberg, Temporal homogenization of a nonlinear parabolic system, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 15 ``Electromagnetic Problems Arising in Industry: Modelling and Numerical Techniques'', June 18  22, 2018, Budapest, Hungary, June 18, 2018.

C. Löbhard, A function space based solution method with spacetime adaptivity for parabolic optimal control problems with state constraints, PGMO Days 2017, November 13  14, 2017, EDF Lab Paris Saclay, France, November 14, 2017.

C. Löbhard, An ddaptive discontinuous Galerkin method for a parabolic optimal control problem with state constraints . . ., Workshop on Optimization of Infinite Dimensional NonSmooth Distributed Parameter Systems, October 4  6, 2017, Darmstadt, October 4, 2017.

C. Löbhard, Spacetime discretization of a parabolic optimal control problem with state constraints, 18th FrenchGermanItalian Conference on Optimization, September 25  28, 2017, Paderborn, September 26, 2017.

R. Henrion, On Mstationary condition for a simple electricity spot market model, Workshop ``Variational Analysis and Applications for Modelling of Energy Exchange'', May 4  5, 2017, Université Perpignan, France, May 4, 2017.

M. Hintermüller, Adaptive finite element solvers for MPECs in function space, SIAM Conference on Optimization, Minisymposium MS122 ``Recent Trends in PDEConstrained Optimization'', May 22  25, 2017, Vancouver, British Columbia, Canada, May 25, 2017.

M. Hintermüller, Nonsmooth structures in PDE constrained optimization, Optimization Seminar, Chinese Academy of Sciences, State Key Laboratory of Scientific and Engineering Computing, Beijing, China, June 6, 2017.

M. Hintermüller, Optimal control of multiphase fluids based on non smooth models, 14th International Conference on Free Boundary Problems: Theory and Applications, Theme Session 8 ``Optimization and Control of Interfaces'', July 9  14, 2017, Shanghai Jiao Tong University, China, July 10, 2017.

D. Hömberg, From dilatometer experiments to distortion compensation  Optimal control problems related to solidsolid phase transitions, Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, Norway, November 3, 2017.

D. Hömberg, MSO for steel production and manufacturing, Workshop ``Future and Emerging Mathematical Technologies in Europe'', December 11  15, 2017, Lorentz Center, Leiden, Netherlands, December 11, 2017.

D. Hömberg, Mathematical aspects of multifrequency induction heating, Universidade Técnica de Lisboa, Instituto Superior Técnico, Portugal, February 2, 2017.

D. Hömberg, On a robust phase field approach to topology optimization, Università degli Studi di Pavia, Dipartimento di Matematica, Italy, April 28, 2017.

TH. Petzold, The MIMESIS project  An example for an interdisciplinary research project, LeibnizKolleg for Young Researchers: Chances and Challenges of Interdisciplinary Research, Thematic Workshop ``Models and Modelling'', November 9  11, 2016, LeibnizGemeinschaft, Berlin, November 9, 2016.

M.H. Farshbaf Shaker, AllenCahn MPECs, WIASPGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10  12, 2016, WIAS Berlin, May 11, 2016.

M. Hintermüller, Optimal control of multiphase fluids and droplets, Salzburg Mathematics Colloquium, Universität Salzburg, Fachbereich Mathematik, Austria, June 9, 2016.

M. Hintermüller, Recent trends in optimal control problems with nonsmooth structures, Computational Methods for Control of Infinitedimensional Systems, March 14  18, 2016, Institute for Mathematics and its Applications, Minneapolis, USA, March 14, 2016.

D. Hömberg, Analysis and simulation of Joule heating problems, Mathematisches Kolloquium, Bergische Universität Wuppertal, Fachgruppe Mathematik und Informatik, June 21, 2016.

D. Hömberg, European Industrial Doctorates  A funding opportunity for collaboration with industry, Math Meets Industry, September 22  23, 2016, Trondheim, Norway, September 22, 2016.

D. Hömberg, European collaboration in Industrial and Applied Mathematics, The 19th European Conference on Mathematics for Industry (ECMI 2016), Minisymposium 38 ``Maths in HORIZON 2020 and Beyond'', June 13  17, 2016, Universidade de Santiago de Compostela, Spain, June 15, 2016.

D. Hömberg, Math for steel production and manufacturing, MACSI10  Empowering Industrial Mathematical and Statistical Modelling for the Future, December 8  9, 2016, University of Limerick, Ireland, December 9, 2016.

D. Hömberg, Modelling and simulation of multifrequency induction hardening, Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2016), January 11  15, 2016, Universidad de Concepción, Chile, January 14, 2016.

D. Hömberg, Multifrequency induction hardening  Modelling and simulation, FraunhoferInstitut für Techno und Wirtschaftsmathematik, Kaiserslautern, May 17, 2016.

D. Hömberg, Modelling, analysis and simulation of multifrequency induction hardening, XXIV Congress on Differential Equations and Applications (CEDYA)/XIV Congress on Applied Mathematics (CMA), June 8  12, 2015, Universidad de Cádiz, Spain, June 11, 2015.

D. Hömberg, Nucleation, growth, and grain size evolution in multiphase materials, INdAM Workshop ``Special Materials in Complex Systems  SMaCS 2015'', May 18  22, 2015, Rome, Italy, May 21, 2015.

D. Hömberg, Optimal coefficient control for semilinear parabolic equations, Fudan University, School of Mathematical Sciences, Shanghai, China, March 10, 2015.

D. Hömberg, The digital factory  A perspective for a closer cooperation between math and industry, Workshop ``Mathematics and Computer Science in Practice: Potential and Reality'', December 9  11, 2015, Prague, Czech Republic, December 9, 2015.

TH. Petzold, Adaptive FiniteElementeSimulation des MehrfrequenzInduktionshärtens in 3D, HärtereiKongress, October 22  24, 2014, Köln, October 23, 2014.

TH. Petzold, Finite element simulations and experiments for multifrequency induction hardening, IUTAM Symposium on ThermomechanicalElectromagnetic Coupling in Solids: Microstructural and Stability Aspect, June 16  18, 2014, Paris, France, June 18, 2014.

TH. Petzold, Modelling and simulation of multifrequency induction hardening of steel parts, 7th International Scientific Colloquium ``Modelling for Electromagnetic Processing'' (MEP 2014), September 16  19, 2014, Leibniz Universität Hannover, September 19, 2014.

TH. Petzold, Modelling and simulation of multifrequency induction hardening for gear components, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium ``Recent Trends in Modelling, Analysis, and Simulation of Induction Heat Treatments'', June 9  13, 2014, Taormina, Italy, June 13, 2014.

D. Hömberg, Modelling and simulation of multifrequency induction hardening, Ecole Polytechnique, Laboratoire de Mécanique des Solides, Palaiseau, France, March 13, 2014.

D. Hömberg, Modelling, analysis and simulation of multifrequency induction hardening, Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, October 21, 2014.

D. Hömberg, Modelling, simulation and control of surface heat treatments, Norwegian University of Science and Technology, Department of Physics, Trondheim, October 31, 2014.

D. Hömberg, Models of induction hardening  An FK limited approach, RIPE60  Rate Independent Processes and Evolution Workshop, June 24  26, 2014, Prague, Czech Republic, June 25, 2014.

D. Hömberg, Multifrequency induction hardening  Modelling, analysis, and simulation, Fudan University, School of Mathematical Sciences, Shanghai, China, March 4, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Workshop ``Recent Developments and Challenges in Interface and Free Boundary Problems'', March 25  28, 2014, University of Warwick, UK, March 26, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium 37: Simulation and Control of Hotrolling, June 9  13, 2014, Taormina, Italy, June 9, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Wrocław University of Technology, Institute of Mathematics and Computer Science, Poland, July 1, 2014.

D. Hömberg, Oberflächenbearbeitung mit Mathematik, Opel Innovation Day, Rüsselsheim, November 7, 2014.

D. Hömberg, Optimal control and shape design problems in thermomechanics, BMSWIAS Summer School ``Applied Analysis for Materials'', August 25  September 5, 2014, Berlin Mathematical School, Technische Universität Berlin, September 1, 2014.

J. Rehberg, Maximal parabolic regularity on strange geometries and applications, Joint Meeting 2014 of the German Mathematical Society (DMV) and the Polish Mathematical Society (PTM), September 17  20, 2014, Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Poznan, Poland, September 18, 2014.

TH. Petzold, Modelling and simulation of multifrequency induction hardening of steel parts, sc Matheon Multiscale Seminar, Technische Universität Berlin, Institut für Mathematik, January 24, 2013.

D. Hömberg, Modelling, analysis and simulation of multifrequency induction hardening, Forum MathforIndustry 2013 ``The Impact of Applications on Mathematics'', November 4  8, 2013, Kyushu University, Fukuoka, Japan, November 7, 2013.

TH. Petzold, Finite element simulations of induction hardening of steel parts, University of Tokyo, Graduate School of Mathematical Sciences, Japan, March 6, 2012.

CH. Landry, Timeoptimal control for robot motion planning, Universität Bayreuth, Lehrstuhl für Ingenieurmathematik, June 6, 2011.

N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, 9. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und analyse in der Umformtechnik'', Siegen, April 6, 2011.

N. Togobytska, Simulation, optimisation and control of microstructure evolution and mechanical properties during hot rolling of multiphase steels, 10. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und analyse in der Umformtechnik'', Freiberg, November 8, 2011.

CH. Landry, A minimum time control problem for the collisionfree robot motion planning, 82th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2011), Session on Optimal Control and Applications, April 18  21, 2011, Technische Universität Graz, Austria, April 20, 2011.

CH. Landry, A backface culling to speed up the resolution of an optimal control problem in robot motion planning, ENUMATH 2011, September 5  9, 2011, University of Leicester, UK, September 5, 2011.

CH. Landry, Pathplanning with collision avoidance in automotive industry, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12  16, 2011, Technische Universität Berlin, September 16, 2011.

CH. Landry, How to avoid collisions between translating robots, Summer School ``Optimal Control of Partial Differential Equations'', July 12  17, 2010, Cortona, Italy, July 15, 2010.

O. Rott, An iterative method for the multipliers of periodic delaydifferential equations and the analysis of a PDE milling model, 9th IFAC Workshop on Time Delay Systems, June 7  9, 2010, Czech Technical University, Prague, Czech Republic, June 8, 2010.

O. Rott, Analysis of uncertainties in the stability prediction for milling processes, 2nd International Conference ``Process Machine Interactions'', June 10  11, 2010, The University of British Columbia, Vancouver, Canada, June 11, 2010.

N. Togobytska, An inverse problem for laserinduced thermotherapy arising in tumor tissue imaging, Chemnitz Symposium on Inverse Problems 2010, September 23  24, 2010, September 24, 2010.

N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, 8. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und analyse in der Umformtechnik'', Aachen, November 10, 2010.

D. Hömberg, Coupling of process, machine, and workpiece in production processes  A challenge for industrial mathematics, Warsaw Seminar on Industrial Mathematics (WSIM'10), March 18  19, 2010, Warsaw University of Technology, Poland, March 19, 2010.

D. Hömberg, Modelling, simulation and control of phase transformations in steel, Nippon Steel Corporation, Chiba, Japan, September 10, 2010.

D. Hömberg, Multiphase steels, heat treatment and distortion  Mathematical challenges in steel production and manufacturing, Summer School ``High Performance Computing'' (organizer: TU Ilmenau), September 29  October 2, 2010, Upstalsboom Hotel Friedrichshain, Berlin, September 30, 2010.

D. Hömberg, Steel manufacturing  A challenge for applied mathematics, Universität DuisburgEssen, Fachbereich Mathematik, May 11, 2010.

D. Kern, Optimal control of a thermomechanical model including transformation induced plasticity, SIAM Conference on Control and its Applications, July 6  8, 2009, Denver, USA, July 8, 2009.

N. Togobytska, Parameter identification for the phase transformations in steel, Conference on Applied Inverse Problems 2009, July 20  24, 2009, University of Vienna, Austria, July 21, 2009.

N. Togobytska, Parameter identification from dilatometric investigations, SIAM Conference on Control and its Applications, July 6  8, 2009, Denver, USA, July 8, 2009.

N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, 8. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und analyse in der Umformtechnik'', WIAS Berlin, June 23, 2009.

D. Hömberg, Coupling of process, machine, and workpiece in production processes  A challenge for industrial mathematics, Workshop ``Industrial Mathematics and its Practice'', February 23  24, 2009, University of Tokyo, Japan, February 23, 2009.

D. Hömberg, Die Wärmebehandlung von Stahl  Thermomechanische Modellierung, Simulation und Optimierung, Technische Universität Dortmund, Fakultät Maschinenbau, January 22, 2009.

D. Hömberg, Direct and inverse problems related to phase transitions and distortion in modern multiphase steels, Workshop ``Mathematical Models and Analytical Problems for Special Materials'', July 9  11, 2009, Università degli Studi di Brescia, Italy, July 9, 2009.

D. Hömberg, Distortion compensation  An optimal control approach, 24th IFIP TC 7 Conference on System Modelling and Optimization, July 27  31, 2009, Buenos Aires, Argentina, July 27, 2009.

D. Hömberg, Interactions between machine, workpiece, and process dynamics in milling machines, SIAM Conference on Mathematics for Industry: Challenges and Frontiers (MI09), October 9  10, 2009, San Francisco, USA, October 9, 2009.

D. Hömberg, Optimal control of heat treatments and stability of milling processes  Two case studies from industrial mathematics, Worcester Polytechnic Institute, Mechanical Engineering Department, USA, October 7, 2009.

D. Hömberg, The mathematics of distortion, University of Delaware, Department of Mathematical Sciences, Newark, USA, October 6, 2009.

O. Rott, A milling model with thermal effects including the dynamics of machine and workpiece, 1st International Conference on Process Machine Interactions (PMI 2008), September 3  4, 2008, Leibniz Universität Hannover, September 3, 2008.

O. Rott, Modeling, analysis and stability of milling processes including workpiece effects, The European Consortium for Mathematics in Industry (ECMI 2008), June 30  July 4, 2008, University College, London, UK, July 3, 2008.

O. Rott, Numerical solution of a milling model including thermoelastic workpiece effects, Universität Dortmund, Fachbereich für Mathematik, June 23, 2008.

O. Rott, Parameter für ein MKSModell einer Fräsmaschine, DFG SPP 1180 Workshop ``Parameteridentifikation bei Werkzeugmaschinen'', February 21  22, 2008, WIAS Berlin, February 22, 2008.

O. Rott, Semiimplizite Zeitintegration eines gekoppelten Systems aus partiellen und gewöhnlichen Differentialgleichungen mit Retardierung, DFG SPP 1180 Workshop ``Modellierungstechnologien'', May 29  30, 2008, Dresden, May 30, 2008.

N. Togobytska, On the evaluation of the dilatometer experiments, Chemnitz Symposium on Inverse Problems 2008, September 25  26, 2008, September 25, 2008.

N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, Antragskolloquium zum DFG Schwerpunktprogramm 1204/2, Bonn, May 20, 2008.

W. Bleck, D. Hömberg, Ch. Keul, U. Prahl, P. Suwanpinij, N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, Workshop ``MEFORM 2008: Simulation von Umformprozessen'', Freiberg, March 26  28, 2008.

D. Hömberg, Modellierung und Optimierung der Gefügeumwandlung in niedrig legierten Stählen und Anwendungen, Salzgitter Mannesmann Forschung GmbH, February 19, 2008.

D. Hömberg, On a mathematical model for highspeed milling including the dynamics of machine and workpiece, Conference ``Direct, Inverse and Control Problems for PDE's'' (DICOP 08), September 22  26, 2008, Cortona, Italy, September 26, 2008.

D. Hömberg, Prozesskette Stahl, Workshop of scshape Matheon with Siemens AG (Industry Sector) in cooperation with Center of Knowledge Interchange (CKI) of Technische Universität (TU) Berlin and Siemens AG, TU Berlin, September 29, 2008.

D. Hömberg, Solidsolid phase transitions  Analysis, optimal control and industrial application, Warsaw University of Technology, Faculty of Mathematics and Information Science, Poland, February 14, 2008.

D. Hömberg, The heat treatment of steel  A mathematical control problem, 2nd International Conference on Distortion Engineering 2008, September 17  19, 2008, Bremen, September 19, 2008.

D. Kern, Optimal control of a thermomechanical model of phase transitions in steel, 13th CzechFrenchGerman Conference on Optimization, September 17  21, 2007, Heidelberg, September 20, 2007.

W. Weiss, Control of laser surface hardening, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16  20, 2007, ETH Zürich, Switzerland, July 19, 2007.

W. Weiss, Simulationsbasierte Regelung der Laserhärtung von Stahl, RuhrUniversität Bochum, Institut für Werkstoffe, May 30, 2007.

D. Hömberg, D. Kern, Optimal control of a thermomechanical model of phase transitions in steel, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16  20, 2007, ETH Zürich, Switzerland, July 19, 2007.

D. Hömberg, Mathematical tools for the simulation and control of heat treatments, Delphi, Puerto Real, Spain, January 16, 2007.

D. Hömberg, Mathematics for complex production processes, Comau, Turin, Italy, March 23, 2007.

D. Hömberg, Mathematics for steel production and manufacturing, Nippon Steel, Kimitsu, Japan, March 1, 2007.

D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Universidad de Cádiz, Departamento de Matemáticas, Puerto Real, Spain, January 15, 2007.

D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Fudan University, Department of Mathematics, Shanghai, China, March 5, 2007.

D. Hömberg, Optimal control of semilinear parabolic equations and an application to laser material treatments (part I), University of Tokyo, Department of Mathematical Sciences, Japan, February 21, 2007.

D. Hömberg, Optimal control of semilinear parabolic equations and an application to laser material treatments (part II), University of Tokyo, Department of Mathematical Sciences, Japan, February 22, 2007.

D. Hömberg, Phase transition models for multiphase steels, Industrial and Interdisciplinary Workshop ``Problems Related to the Manufacture of Multiphase Steels'', University of Oxford, Oxford Centre for Industrial and Applied Mathematics, UK, November 2, 2007.

D. Hömberg, Solidsolid phase transitions in steel  modeling, simulation and optimal control, Universitá di Pavia, Dipartimento di Matematica, Italy, March 27, 2007.

D. Hömberg, Thermomechanical phase transition models  analysis, optimal control and industrial applications, University of Oxford, Oxford Centre for Industrial and Applied Mathematics, UK, October 11, 2007.

D. Hömberg, Die Wärmebehandlung von Stahl  ein Optimierungsproblem, Universität Bremen, SFB 570 ``Distortion Engineering'', March 2, 2006.

D. Hömberg, Laser surface hardening  modelling, simulation and optimal control, 4th KoreanGerman Seminar on Applied Mathematics and Physics, September 24  October 1, 2006, Erlangen, September 26, 2006.

D. Hömberg, Modellierung, Simulation und Optimierung der Wärmebehandlung von Stahl, Endress+Hauser Flowtec AG, Reinach, Switzerland, May 15, 2006.

D. Hömberg, Optimal control of a thermomechanical phase transition model, 12th IEEE International Conference on Methods and Models in Automation and Robotics, August 28  31, 2006, Miedzyzdroje, Poland, August 29, 2006.

D. Hömberg, Optimal control of laser material treatments, 21st European Conference on Operational Research (EURO XXI), July 3  5, 2006, Reykjavik, Iceland, July 3, 2006.

D. Hömberg, Phasenübergänge in Stahl, Summer School ``Simulation und Anwendungen von Mikrostrukturen'', August 14  18, 2006, Föhr.

D. Hömberg, Thermomechanical models of phase transitions  modelling, control and industrial applications, Escuela Politécnica Nacional, Departamento de Matématica, Quito, Ecuador, November 13, 2006.

D. Hömberg, A thermomechanical phase transition model for the surface hardening of steel, International Conference ``Free Boundary Problems: Theory and Applications'', June 7  12, 2005, Coimbra, Portugal, June 11, 2005.

D. Hömberg, Control of laser material treatments, SIAM Conference on Mathematics for Industry, October 24  26, 2005, Detroit Marriott Renaissance Center, USA, October 25, 2005.

D. Hömberg, Die Laserhärtung von Stahl  Modellierung, Analysis und optimale Steuerung, Universität Bayreuth, Mathematisches Institut, June 30, 2005.

D. Hömberg, Entwicklung eines Prognosetools zur Identifizierung von stabilen Fräsprozessen, DFG SPP 1180, Garbsen, May 19, 2005.

D. Hömberg, Laser material treatments  modeling, simulation, and optimal control, Michigan State University, Department of Mathematics, East Lansing, USA, October 27, 2005.

D. Hömberg, Modelling, simulation and control of laser material treatments, Scuola Normale Superiore, Pisa, Italy, November 22, 2005.

D. Hömberg, On a thermomechanical model of surface heat treatments, EQUADIFF 11 International conference on differential equations, July 25  29, 2005, Comenius University, Bratislava, Slovakia, July 28, 2005.

D. Hömberg, Optimal control of solidsolid phase transitions including mechanical effects, Workshop ``Optimal Control of Coupled Systems of PDE'', April 17  23, 2005, Mathematisches Forschungsinstitut Oberwolfach, April 22, 2005.

D. Hömberg, Von der Stahlhärtung bis zur Krebstherapie  Simulations und Optimierungsaufgaben in Lehre und Forschung, FEMLAB Konferenz 2005, November 3  4, 2005, Frankfurt am Main, November 3, 2005.

D. Hömberg, Modellierung, Analysis und optimale Steuerung der Lasermaterialbearbeitung, Kolloquium der Angewandten Mathematik, Universität Münster, December 3, 2004.

D. Hömberg, Modelling, simulation and control issues in laserinduced thermotherapy, 13th European Conference on Mathematics for Industry (ECMI 2004), June 21  25, 2004, Eindhoven University of Technology, Eindhoven, Netherlands, June 22, 2004.

D. Hömberg, On a thermomechanical model of phase transitions in steel, INdAM Workshop ``Dissipative Models in Phase Transitions'', September 5  11, 2004, Cortona, Italy, September 10, 2004.

D. Hömberg, On a thermomechanical model of surface heat treatments, University of Tokyo, Department of Mathematical Sciences, Japan, October 14, 2004.

D. Hömberg, Optimal control of laser surface hardening, University of Chiba, Department of Mathematics and Informatics, Japan, October 19, 2004.

D. Hömberg, Simulation und Optimierung der Lasermaterialbearbeitung, Seminar des Forschungsschwerpunktes Photonik, Technische Universität Berlin, Optisches Institut, June 18, 2004.

D. Hömberg, The induction hardening of steel  Modelling, analysis and optimal design of inductor coils, University of Kyoto, Department of Mathematics, Japan, October 21, 2004.

D. Hömberg, Thermoelastische Phasenübergänge in Stahl, HumboldtUniversität zu Berlin, Institut für Mathematik, May 13, 2004.

D. Hömberg, Widerstandsschweißen und Oberflächenhärtung von Stahl  Modellierung, Analysis und optimale Steuerung, Colloquium of Sfb 393, Technische Universität Chemnitz, Institut für Mathematik, February 13, 2004.

D. Hömberg, A mathematical model for capacitor resistance welding, 5th International Congress on Industrial and Applied Mathematics (ICIAM 2003), July 7  11, 2003, Sydney, Australia, July 10, 2003.

D. Hömberg, Optimal design of inductor coils, 5th International Congress on Industrial and Applied Mathematics (ICIAM 2003), July 7  11, 2003, Sydney, Australia, July 10, 2003.

D. Hömberg, Surface hardening of steel  Part I: Optimal design of inductor coils, 9th IEEE International Conference on Methods and Models in Automation and Robotics, August 25  28, 2003, Miedzyzdroje, Poland, August 26, 2003.
Contact
Contributing Groups of WIAS
Mathematical Context
 Algorithms for the generation of 3D boundary conforming Delaunay meshes
 Analysis of Partial Differential Equations and Evolutionary Equations
 Direct and inverse problems for the Maxwell equations
 Direct and inverse problems in thermomechanics
 Functional analysis and operator theory
 Numerical Methods for PDEs with Stochastic Data
 Optimal control of partial differential equations and nonlinear optimization
 Systems of partial differential equations: modeling, numerical analysis and simulation