Photo of Lukas  Pflug

Dr. Lukas Pflug

Mathematische Optimierung
Cauerstr. 11
91058 Erlangen
Room: 03.332

Phone: +49 9131 85-67139
Fax: +49 9131 85-67134


DAAD Indo-German Partnership in Higher Education Program (2016-2020)
Partners: FAU Erlangen-Nürnberg, IIT Delhi
Adaptive Wavelet-Methods for Optimal Control of Quasilinear Balance Laws on Networks


The project concerns theoretical aspects of Wavelet-Galerkin approximations in the context of controllability, stabilizability as well as optimal control for dynamics in networks with applications in energy networks, structural mechanics, fluid mechanics, medicine and traffic networks. Similar to moment theory that has been developed earlier and depends on the Eigen elements of the underlying differential operators, such methods for networks provide a challenging question in particular from the multi-resolution point of view. The theoretical contributions will be complemented via a numerical realization of the wavelet-based simulations. More information about DAAD DIP 2016

FAU Coordinator: Prof. Dr. G. Leugering, IIT Coordinator: Prof. Dr. M. Mehra

DFG Schwerpunktprogramm 1679

Dynamische Simulation vernetzter Feststoffprozesse
Modellierung, Simulation und Optimierung von Prozessketten

SPP1679: DynSim-FP

PI: Prof. Dr. G. Leugering, Coordinator: Opens external link in new windowProf. 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.


The interaction of electromagnetic waves and material is mathematically described by Maxwell's equations. Under the assumption of a time-harmonic incident light - which holds in the studied regime - this equations can be transformed to the well known curl-curl formulation of Maxwell's equation.
This complex vector valued equation can be solved numerically in 3D with the Nédélec FEM but, due to the high resolution one needs, it is only possible for single particles or small clusters of particles. The size of the pigment particles is in the sub micron range and the wavelength range we are interested in is 400 to 700 nm. In order to derive optical properties of a film with randomly oriented particles from single particle simulations we use a model which lies in-between the 2-Flux model derived by Kubelka and Munk and the radiative transfer equation.
With this method we are able to compute the reflectance spectra of a pigment color film with a known particle size distribution. These computed spectra show a good agreement with experimental data.
The project is funded by the DFG and the Opens external link in new windowLANXESS GmbH

Prof. Dr. Günter Leugering (Erlangen), Opens external link in new windowProf. Dr.-Ing. Wolfgang Peukert (Erlangen), Opens external link in new windowProf. Dr. Ulf Peschel (Jena), Opens external link in new windowProf. Dr. Robin N. Klupp Taylor (Erlangen), Dr. Lukas Pflug (Erlangen)


  • (2018) ISIAM 14th Conference of Indian Society of Industrial and Applied Mathematics (Amritsar, India) "Nonlocal balance laws, modeling, simulation and optimization"
  • (2018) Indo-German Workshop on "Optimal control, Inverse problems and their applications" (IIT Dehli, India) "Nonlocal balance laws, modeling, simulation and optimization"
  • (2017) International Congress Engineering of Advanced Materials ICEAM2017 (Erlangen, Germany) "Particle synthesis modeled by nonlocal balance laws – process simulation and optimization"
  • (2017) SPP 1679 Summer School 2017 (Hamburg, Germany) "Optimal control in particle synthesis"
  • (2016) UMN-FAU Workshop, University of Minnesota (Minnesota, USA) "Optimized Nanoparticles: From Process to Design"
  • (2016) Advanced Seminar, Chair of applied Mathematics (Bayreuth, Germany) "Numerical Shape Optimization of Nanostructures in Electromagnetic Applications"
  • (2016) ECCOMAS (Crete Island, Greece) "Material optimization of nanoparticles with respect to their optical properties"
  • (2016) SPP 1679 Statusseminar 2016 (Hamburg, Germany) "Optimal control in particle synthesis"
  • (2015) 27th IFIP TC7 Conference 2015 (Sophia Antipolis, France) "Shape optimization in electromagnetic applications"
  • (2013) ERC Workshop „New Trends in Shape Optimization“ (Erlangen, Germany) "Shape optimization for electrodynamics"
  • (2013) 9th Workshop on Numerical Methods for Optical Nano Structures (Zürich, Swiss) "Shape optimization for electrodynamics"
  • (2013) EAM WinterSchool (Kirchberg, Austria)


  • J. Semmler, L. Pflug, and, M. Stingl, “Material optimization in transverse electromagnetic scattering applications”, SIAM Journal on Scientific Computing 40, B85–B109 (2018)
  • A. Keimer, L. Pflug, and M. Spinola, “Existence, uniqueness and regularity of multi-dimensional nonlocal balance laws with damping”, Journal of Mathematical Analysis and Applications, 466, 18–55 (2018).
  • T. Meincke, H. Bao, L. Pflug, M. Stingl, and R. Klupp Taylor, “Heterogeneous nucleation and surface conformal growth of silver nanocoatings on colloidal silica in a continuous flow static T-mixer”, Chemical Engineering Journal 308, 89–100 (2017)
  • A. Keimer and L. Pflug, “Existence, uniqueness and regularity results on nonlocal balance laws”, Journal of Differential Equations, 263, 4023–4069 (2017)
  • M. Distaso, O. Zhuromskyy, B. Seemann, L. Pflug, M. Mackovic, E. Encina, R. Klupp Taylor, R. Müller, G. Leugering, E. Spiecker, U. Peschel, and W. Peukert, “Interaction of light with hematite hierarchical structures: experiments and simulations”, Journal of Quantitative Spectroscopy and Radiative Transfer, 189, 369–382 (2017)
  • G. Leugering, L. Pflug, and M. Spinola, “Adjungierten-basierte prozessoptimierung der nanopartikel-synthese”, Chemie Ingenieur Technik, 88, 1366–1367 (2016)
  • J. Semmler, L. Pflug, M. Stingl, and G. Leugering, Shape Optimization in Electromagnetic Applications, edited by G. L. Aldo Pratelli, Vol. 166, International Series of Numerical Mathematics (Springer), pp. 251–269 (2015)
  • W. Peukert, D. Segets, L. Pflug, and G. Leugering, Unified design strategies for particulate products, Vol. 46, Advances in Chemical Engineering (2015)
  • M. Haderlein, D. Segets, M. Gröschel, L. Pflug, G. Leugering, and W. Peukert, "FIMOR: an efficient simulation for zno quantum dot ripening applied to the optimization of nanoparticle synthesis”, Chemical Engineering Journal, 260, 706–715 (2015)


  • PhD thesis, "One-Dimensional Nonlocal Balance Laws - Modeling and Simulation", urn:nbn:de:bvb:29-opus4-97431 (2018)
  • Masterthesis, "Volume preserving Shape Optimization for Linear Elasticity and Navier-Stokes Equation" (2012)