(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

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) Type of Publication: 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 Type of Publication: Research article in digital collection (conference)
Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems Kleikamp, Hendrik; Renelt, Lukas (2024) In: arXiv:2408.15900. Type of Publication: Research article in digital collection
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. Type of Publication: Research article in edited proceedings (conference)

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
Model Order Reduction for Friedrichs' systems Renelt, Lukas (19/03/2024) Minisymposium on 'New Trends in Model Order Reduction and Learning' at ALGORITMY 2024, Podbanske Type of talk: scientific 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