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(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

Academic Education
02/2021 - 01/2025	PhD in Mathematics, University of Münster
10/2018 - 09/2020	MSc. Mathematics with minor in computer science, Westfälische Wilhelms-Universität Münster
10/2016 - 09/2018	BSc. Mathematics with minor in computer science, Westfälische Wilhelms-Universität Münster
Work Experience
since 01/2021	Research assistant, workgroup Ohlberger, Universität Münster
09/2017 - 03/2020	Student assistant, Workgroup of Prof. Dr. Engwer, Westfälische Wilhelms-Universität Münster

Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems Kleikamp, Hendrik; Renelt, Lukas (2025) In: Journal of Scientific Computing, 104(78). Research article (journal)
Sectional Kolmogorov N-widths for parameter-dependent function spaces: A general framework with application to parametrized Friedrichs' systems Engwer, Christian; Ohlberger, Mario; Rebelt, Lukas (2025) In: arXiv:2507.00678. Research article in digital collection
Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems Engwer, Christian; Ohlberger, Mario; Renelt, Lukas (2024) In: SIAM Journal on Scientific Computing, 46(5). Research article (journal)
Construction of local reduced spaces for Friedrichs' systems via randomized training Engwer,Christian; Ohlberger, Mario; Renelt, Lukas (2024) In: Central-European Conference on Scientific Computing, ALGORITMY, Podbanské, Slovakia. Proceedings of the Conference Algoritmy 2024. Research article in digital collection (conference)
An optimally stable approximation of reactive transport using discrete test and infinite trial spaces Renelt, Lukas; Ohlberger, Mario; Engwer, Christian (2023) In: Franck, Emmanuel; Fuhrmann, Jürgen;, Michel-Dansac, Victor; Navoret, Laurent (eds.), Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems. Cham: Springer. Research article in edited proceedings (conference)

Local and global approximation strategies for (parametrized) Friedrichs' systems Renelt, Lukas (05/03/2025) SIAM Conference on Computational Science and Engineering 2025, Fort Worth Type of talk: scientific talk
Model order reduction and localization of Friedrichs’ systems Renelt, Lukas (07/02/2025) Reduced-Order Modeling for Complex Engineering Problems, Chicago Type of talk: scientific talk
Nonlinear discretization of instationary PDEs with EDNNs: An introduction to Neural Galerkin and JAX Renelt, Lukas (15/01/2025) Oberseminar Numerik, Münster Type of talk: scientific talk
Efficient linear Model Order Reduction for Friedrichs’ systems Renelt, Lukas (12/09/2024) Model Reduction and Surrogate Modeling (MORe) 2024, La Jolla Type of talk: scientific talk
Custom linear algebra backends: Using pyMOR with dune-istl Renelt, Lukas (29/08/2024) pyMOR School and User meeting 2024, Münster Type of talk: practical talk

Numerical methods for Friedrichs’ systems: Approximation theory, localized training and inherently stable model order reduction
Candidate: Renelt, Lukas | Supervisors: Ohlberger, Mario; Engwer, Christian | Reviewers: Ohlberger, Mario; Engwer, Christian; Vohralík; Martin
Period of time: 01/02/2021 - 10/01/2025
Doctoral examination procedure finished at: Doctoral examination procedure at University of Münster