Projects

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Publications

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Theses

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• Julian Roth. 2024. Space-time goal-oriented error control and adaptivity for discretizations and reduced order modeling of multiphysics problems.
  Dissertation, Leibniz University Hannover, Germany, June 2024.   Link
• Julian Roth. 2021. Proper Orthogonal Decomposition for Fluid Mechanics Problems.
  Master's thesis, Leibniz University Hannover, Germany, August 2021.   PDF
• Julian Roth. 2020. Geometric Multigrid Methods for Maxwell’s Equations.
  Bachelor's thesis, Leibniz University Hannover, Germany, July 2020.   PDF

Papers

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• Denis Khimin, Julian Roth, Alexander Henkes, Thomas Wick. 2024. Optimal control of partial differential equations in PyTorch using automatic differentiation and neural network surrogates. arXiv: https://doi.org/10.48550/arXiv.2408.12404 . Code: https://github.com/Denis-Khimin/OptimalControlPDEAutoDiff
• Robin Schmöcker, Alexander Henkes, Julian Roth, Thomas Wick. 2024. Generalization capabilities of MeshGraphNets to unseen geometries for fluid dynamics. arXiv: https://doi.org/10.48550/arXiv.2408.06101 . Code: https://github.com/codebro634/modulus
• Hendrik Fischer, Julian Roth, Ludovic Chamoin, Amelie Fau, Mary F. Wheeler, Thomas Wick. 2024. Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity. Advanced Modeling and Simulation in Engineering Sciences (AMOS), Vol. 11, 2024, article number 9. Journal: https://doi.org/10.1186/s40323-024-00262-6 . arXiv: https://arxiv.org/abs/2311.08907
• Julian Roth, Martyna Soszyńska, Thomas Richter, Thomas Wick. 2024. A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems. Journal of Computational and Applied Mathematics (JCAM), Vol. 446, 2024, No. 115831. Journal: https://doi.org/10.1016/j.cam.2024.115831 . arXiv: https://arxiv.org/abs/2307.12455 . Code: https://github.com/mathmerizing/TemporalMultirateFEM
• Hendrik Fischer, Julian Roth, Thomas Wick, Ludovic Chamoin, and Amelie Fau. 2024. MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals. Journal of Computational Physics (JCP), Vol. 504, 2024, 112863. Journal: https://doi.org/10.1016/j.jcp.2024.112863 . arXiv: https://arxiv.org/abs/2304.01140
• Julian Roth, Jan Philipp Thiele, Uwe Köcher, and Thomas Wick. 2024. Tensor-product space-time goal-oriented error control and adaptivity with partition-of-unity dual-weighted residuals for nonstationary flow problems. Computational Methods in Applied Mathematics (CMAM), vol. 24, no. 1, 2024, pp. 185-214.. Journal: https://doi.org/10.1515/cmam-2022-0200 . arXiv: https://arxiv.org/abs/2210.02965 . Code: https://github.com/mathmerizing/dwr-instatfluid
• Denis Khimin, Julian Roth, and Thomas Wick. 2022. Space-time fluid-structure interaction: formulation and dG(0) time discretization. In: Proceedings of ECCOMAS 2022, Dec 2022. URL: http://dx.doi.org/10.23967/eccomas.2022.257
• Julian Roth, Max Schröder, and Thomas Wick. 2022. Neural network guided adjoint computations in dual weighted residual error estimation. SN Applied Sciences 4, 62 (2022). DOI: https://doi.org/10.1007/s42452-022-04938-9
• Sebastian Kinnewig, Julian Roth, and Thomas Wick. 2021. Geometric multigrid with multiplicative Schwarz smoothers for eddy-current and Maxwell’s equations in deal.II. Examples and Counterexamples (EXCO), Vol. 1, 2021, 100027. DOI: https://doi.org/10.1016/j.exco.2021.100027
• Michael Nolting, Julian Roth, and Ulf Wittke. 2020. Towards Autonomous Digital Health Coaching for Scalable Chronic Disease Prevention. In Proceedings of the 14th EAI International Conference on Pervasive Computing Technologies for Healthcare (PervasiveHealth '20). Association for Computing Machinery, New York, NY, USA, 259–262. DOI: https://doi.org/10.1145/3421937.3421966

Lecture Notes

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• Sebastian Kinnewig, Leon Kolditz, Julian Roth, and Thomas Wick. 2022. Numerical Methods for Algorithmic Systems and Neural Networks. Lecture Notes. Institut für Angewandte Mathematik, Leibniz Universität Hannover, 2022, 441 pages. DOI: https://doi.org/10.15488/11897

CV

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