Research Foci
- (Localized) Model Order Reduction and reduced basis methods
- Theory and numerics of Friedrichs' systems
- Optimally stable discretizations, Discontinuous Petrov-Galerkin (DPG) methods, First-order least-squares methods
- Loclaized training approaches for multiscale problems
Doctoral AbstractThesis
Numerical methods for Friedrichs’ systems: Approximation theory, localized training and inherently stable model order reduction
- Supervisors
- Doctoral Subject
- Mathematik
- Doctoral Degree
- Dr. rer. nat.
- Awarded by
- Department 10 – Mathematics and Computer Science
Academic Education
- PhD in Mathematics, University of Münster
- MSc. Mathematics with minor in computer science, Westfälische Wilhelms-Universität Münster
- BSc. Mathematics with minor in computer science, Westfälische Wilhelms-Universität Münster
Teaching
- Lecture: Scientific Computing [108417]
(in cooperation with Christian Engwer)
- Practical: Nichtlineare Modellierung in den Naturwissenschaften [106341]
(in cooperation with Julia Schleuß, André Schlichting, Svetlana Gurevich, Andreas Heuer, Christian Engwer and Mario Ohlberger)
- Practical: Nichtlineare Modellierung in den Naturwissenschaften [104493]
(in cooperation with Svetlana Gurevich, Julia Schleuß, André Schlichting, Andreas Heuer, Christian Engwer and Mario Ohlberger)
- Practical: Nichtlineare Modellierung in den Naturwissenschaften [102396]
(in cooperation with Svetlana Gurevich, Julia Schleuß, André Schlichting, Andreas Heuer, Christian Engwer and Mario Ohlberger)
- Practical: Einführung in die Numerik mit Python [100378]
(in cooperation with Hendrik Kleikamp and Mario Ohlberger) - Practical: Nichtlineare Modellierung in den Naturwissenschaften [100417]
(in cooperation with Svetlana Gurevich, André Schlichting, Andreas Heuer, Christian Engwer and Mario Ohlberger)
- Practical: Nichtlineare Modellierung in den Naturwissenschaften [108414]
(in cooperation with Svetlana Gurevich, André Schlichting, Andreas Heuer, Christian Engwer and Mario Ohlberger)
- Practical: Nichtlineare Modellierung in den Naturwissenschaften [106351]
(in cooperation with Julia Schleuß, André Schlichting, Hendrik Kleikamp, Svetlana Gurevich, Andreas Heuer, Christian Engwer and Mario Ohlberger)
- Practical: Nichtlineare Modellierung in den Naturwissenschaften [104437]
(in cooperation with Svetlana Gurevich, Julia Schleuß, Andreas Heuer, Christian Engwer and Mario Ohlberger)
Publications
- Kleikamp, Hendrik, and Renelt, Lukas. “Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems.” Journal of Scientific Computing (78), № 104 () doi: 10.1007/s10915-025-02988-w.
- Engwer, Christian, Ohlberger, Mario, and Renelt, Lukas. “Sectional Kolmogorov N-widths for parameter-dependent function spaces: A general framework with application to parametrized Friedrichs' systems.” Preprint, submitted in . doi: 10.48550/arXiv.2507.00678.
- Engwer, Christian, Ohlberger, Mario, and Renelt, Lukas. “Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems.” SIAM Journal on Scientific Computing (5), № 46 (): A3205–A3229. doi: 10.1137/23M1613402.
- Engwer, Christian, Ohlberger, Mario, and Renelt, Lukas. “Construction of local reduced spaces for Friedrichs' systems via randomized training.” contribution to the Central-European Conference on Scientific Computing, ALGORITMY, Podbanské ().
- Renelt, Lukas, Ohlberger, Mario, and Engwer, Christian. “An optimally stable approximation of reactive transport using discrete test and infinite trial spaces.” in Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, Springer Proceedings in Mathematics & Statistics, edited by Emmanuel Franck, Jürgen Fuhrmann, Michel-Dansac Victor and Laurent Navoret. (Cham: Springer, in Kürze). doi: 10.1007/978-3-031-40860-1_30.
Talks
Practical Talks
- Renelt, Lukas : “Local and global approximation strategies for (parametrized) Friedrichs' systems”. SIAM Conference on Computational Science and Engineering 2025, Fort Worth, .
- Renelt, Lukas : “Model order reduction and localization of Friedrichs’ systems”. Reduced-Order Modeling for Complex Engineering Problems, Chicago, .
- Renelt, Lukas : “Nonlinear discretization of instationary PDEs with EDNNs: An introduction to Neural Galerkin and JAX”. Oberseminar Numerik, Münster, .
- Renelt, Lukas : “Efficient linear Model Order Reduction for Friedrichs’ systems”. Model Reduction and Surrogate Modeling (MORe) 2024, La Jolla, .
- Renelt, Lukas : “Custom linear algebra backends: Using pyMOR with dune-istl”. pyMOR School and User meeting 2024, Münster, .
- Renelt, Lukas : “Model Order Reduction for Friedrichs' systems”. Minisymposium on 'New Trends in Model Order Reduction and Learning' at ALGORITMY 2024, Podbanske, .
- Renelt, Lukas : “Model Order Reduction for Friedrichs' systems”. YMMOR - Young Mathematicians in Model Order Reduction, Stuttgart, .
- Renelt, Lukas : “Model order reduction for inf-sup-stable problems using optimally stable discretization schemes”. Posterpresentation at MORTech 2023, Paris-Saclay, .
- Renelt, Lukas : “Friedrichs' systems and their use in model order reduction”. Oberseminar Numerik, Münster, .
- Renelt, Lukas : “An optimally stable numerical scheme for reactive transport”. Posterpresentation at Finite Volumes for Complex Applications 10 (FVCA10), Strasbourg, .
- Renelt, Lukas : “Representation of parametric PDEs in Dune-PDELab and application to model order reduction”. 7th DUNE user meeting, Dresden, .
- Renelt, Lukas : “Model order reduction for reaction-advection problems”. Minisymposium on 'Reducing the irreducible: model reduction for transport-dominated problems' at ENUMATH 2023, Lisbon, .
- Renelt, Lukas : “An optimally stable discretization scheme for parametrized convection-dominated problems”. Minisymposium on 'Numerical methods for differential equations' at GAMM 93rd annual meeting, Dresden, .
- Renelt, Lukas : “Localized Model Order Reduction for convection-dominated problems using an optimally stable discretization”. YMMOR - Young Mathematicians in Model Order Reduction, Ulm, .
- Renelt, Lukas : “Localized MOR for advection-dominated convection-diffusion problems”. YMMOR - Young Mathematicians in Model Order Reduction, Münster, .
- Keil, Tim; Renelt, Lukas : “Introduction to the Reduced Basis Method”. YMMOR - Young Mathematicians in Model Order Reduction, Münster, .
Scientific Talks
- Renelt, Lukas : “Local and global approximation strategies for (parametrized) Friedrichs' systems”. SIAM Conference on Computational Science and Engineering 2025, Fort Worth, .
- Renelt, Lukas : “Model order reduction and localization of Friedrichs’ systems”. Reduced-Order Modeling for Complex Engineering Problems, Chicago, .
- Renelt, Lukas : “Nonlinear discretization of instationary PDEs with EDNNs: An introduction to Neural Galerkin and JAX”. Oberseminar Numerik, Münster, .
- Renelt, Lukas : “Efficient linear Model Order Reduction for Friedrichs’ systems”. Model Reduction and Surrogate Modeling (MORe) 2024, La Jolla, .
- Renelt, Lukas : “Custom linear algebra backends: Using pyMOR with dune-istl”. pyMOR School and User meeting 2024, Münster, .
- Renelt, Lukas : “Model Order Reduction for Friedrichs' systems”. Minisymposium on 'New Trends in Model Order Reduction and Learning' at ALGORITMY 2024, Podbanske, .
- Renelt, Lukas : “Model Order Reduction for Friedrichs' systems”. YMMOR - Young Mathematicians in Model Order Reduction, Stuttgart, .
- Renelt, Lukas : “Model order reduction for inf-sup-stable problems using optimally stable discretization schemes”. Posterpresentation at MORTech 2023, Paris-Saclay, .
- Renelt, Lukas : “Friedrichs' systems and their use in model order reduction”. Oberseminar Numerik, Münster, .
- Renelt, Lukas : “An optimally stable numerical scheme for reactive transport”. Posterpresentation at Finite Volumes for Complex Applications 10 (FVCA10), Strasbourg, .
- Renelt, Lukas : “Representation of parametric PDEs in Dune-PDELab and application to model order reduction”. 7th DUNE user meeting, Dresden, .
- Renelt, Lukas : “Model order reduction for reaction-advection problems”. Minisymposium on 'Reducing the irreducible: model reduction for transport-dominated problems' at ENUMATH 2023, Lisbon, .
- Renelt, Lukas : “An optimally stable discretization scheme for parametrized convection-dominated problems”. Minisymposium on 'Numerical methods for differential equations' at GAMM 93rd annual meeting, Dresden, .
- Renelt, Lukas : “Localized Model Order Reduction for convection-dominated problems using an optimally stable discretization”. YMMOR - Young Mathematicians in Model Order Reduction, Ulm, .
- Renelt, Lukas : “Localized MOR for advection-dominated convection-diffusion problems”. YMMOR - Young Mathematicians in Model Order Reduction, Münster, .
- Keil, Tim; Renelt, Lukas : “Introduction to the Reduced Basis Method”. YMMOR - Young Mathematicians in Model Order Reduction, Münster, .
The YMMOR conference format
The YMMOR (Young Mathematicians in Model Order Reduction) is a conference format aimed at PhD students and early Postdocs working in the field of Model Order Reduction (website). More experienced researchers such as professors are explicitly not a part of both organisation and realisation of the conference in order to foster the informal atmosphere. The conference editions in Münster (2022), Ulm (2023) and Stuttgart (2024) were all well received by the approximately 40 international participants. The next iteration will take place in spring 2025 in Trieste, Italy.
The sustainability of the conference format is ensured by the YMMOR committee which also serves for connecting young researchers from different workgroups. I am a member of the committee and currently also responsible for the acquisition of new members. If you are interested you are very welcome to contact me!