JProf. Dr. Roland Maier
 by appointment
 Kollegiengebäude Mathematik (20.30)
 3.009
 +49 721 608 46954
 +49 721 608 43767
 roland.maier@kit.edu

Karlsruhe Institute of Technology (KIT)
Institute for Applied and Numerical Mathematics
Englerstr. 2
76131 Karlsruhe
Germany
Welcome on my webpage. Since July 2023, I am junior professor at the Institute for Applied and Numerical Mathematics and leader of the junior research group Numerics of PDEs. I mainly work on numerical homogenization methods for multiscale problems and on specifically designed time stepping techniques for coupled PDEs. Moreover, I am very interested in the combination of machine learning techniques and classical numerical methods.
In the summer term 2024, I will give a lecture on Numerical Analysis of Neural Networks. The lecture is an introduction to the mathematical foundation of neural networks using tools from Numerical Analysis. It will cover, e.g., approximation results, efficient training algorithms, and applications such as PhysicsInformed Neural Networks.
If you are interested in writing a Bachelor or Master thesis in the area of Numerical Mathematics, feel free to talk to me or write me an informal email.
Semester  Titel  Typ 

Summer Semester 2024  Numerical Analysis of Neural Networks  Lecture 
Winter Semester 2023/24  Analytical and Numerical Homogenization  Lecture 
Ringvorlesung Wavephenomena  Lecture 
Upcoming Events
 SciCADE in Singapore (Minisymposium), July 2024
 CMAM in Bonn (Minisymposium), June 2024
 JAM Workshop on Computational PDEs in Jena, May 2024
Research Interests
 Multiscale Methods
 Numerical Homogenization
 Semiexplicit methods for coupled PDEs
 Discretization of (timedependent) PDEs
Short CV
 since JUL 2023: Junior Professor for Numerics of Partial Differential Equations, Karlsruhe Institute of Technology
 OCT 2021  JUN 2023: Junior Professor for Numerical Analysis, Friedrich Schiller University Jena, Germany
 SEP 2020  SEP 2021: PostDoc, Chalmers University of Technology and University of Gothenburg, Sweden
 APR 2020  AUG 2020: PostDoc, University of Augsburg, Germany
 APR 2017  MAR 2020: Doctoral student, University of Augsburg, Germany
 SEP 2012  MAR 2017: Bachelor and Master studies, University of Bonn, Germany
Awards and Prizes
 Winner of the ECCOMAS PhD Olympiad 2021
 Dr.KlausKörper prize of the GAMM 2021
 Kulturpreis Bayern 2020, dissertation prize
 Appointed member of the GAMM Juniors (20202022)
Publications
Submitted Articles
 F. Krumbiegel and R. Maier. A higherorder multiscale method for the wave equation. ArXiv Preprint, 2023.
 M. Hauck, R. Maier, and A. Målqvist. An algebraic multiscale method for spatial network models. ArXiv Preprint, 2023.
 P. Lu, R. Maier, and A. Rupp. A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods. ArXiv Preprint, 2023.
Refereed Articles
 D. Gallistl and R. Maier. Localized implicit time stepping for the wave equation. Accepted for publication in SIAM J. Numer. Anal., 2024.
 R. Altmann, R. Maier, and B. Unger. Semiexplicit integration of second order for weakly coupled poroelasticity. BIT Numer. Math., 64, Article No. 20, 2024.
 F. Kröpfl, R. Maier, and D. Peterseim. Neural network approximation of coarsescale surrogates in numerical homogenization. Multiscale Model. Simul., 21(4):14571485, 2023.
 Z. Dong, M. Hauck, and R. Maier. An improved highorder method for elliptic multiscale problems. SIAM J. Numer. Anal., 61(4):19181937, 2023.
 S. Geevers and R. Maier. Fast mass lumped multiscale wave propagation modelling. IMA J. Numer. Anal., 43(1):4472, 2023.
 R. Maier, P. Morgenstern, and T. Takacs. Adaptive refinement for unstructured Tsplines with linear complexity. Comput. Aided Geom. Design, 96:102117, 2022.
 F. Kröpfl, R. Maier, and D. Peterseim. Operator compression with deep neural networks. Adv. Cont. Discr. Mod., 2022, Paper No. 29, 2022.
 P. Ljung, R. Maier, and A. Målqvist. A spacetime multiscale method for parabolic problems. Multiscale Model. Simul., 20(2):714740, 2022.
 R. Maier and B. Verfürth. Multiscale scattering in nonlinear Kerrtype media. Math. Comp., 91(336):16551685, 2022.
 R. Altmann and R. Maier. A decoupling and linearizing discretization for weakly coupled poroelasticity with nonlinear permeability. SIAM J. Sci. Comput., 44(3):B457B478, 2022.
 R. Maier. A highorder approach to elliptic multiscale problems with general unstructured coefficients. SIAM J. Numer. Anal., 59(2):10671089, 2021.
 R. Altmann, R. Maier, and B. Unger. Semiexplicit discretization schemes for weaklycoupled ellipticparabolic problems. Math. Comp., 90(329):10891118, 2021.
 A. Caiazzo, R. Maier, and D. Peterseim. Reconstruction of quasilocal numerical effective models from lowresolution measurements. J. Sci. Comput., 85(1), Article No. 10, 2020.
 R. Altmann, E. Chung, R. Maier, D. Peterseim, and S.M. Pun. Computational multiscale methods for linear heterogeneous poroelasticity. J. Comput. Math., 38(1):4157, 2020.
 P. Hennig, R. Maier, D. Peterseim, D. Schillinger, B. Verfürth, and M. Kästner. A diffuse modeling approach for embedded interfaces in linear elasticity. GAMMMitteilungen, 43(1):e202000001, 2020.
 S. Fu, R. Altmann, E. Chung, R. Maier, D. Peterseim, and S.M. Pun. Computational multiscale methods for linear poroelasticity with high contrast. J. Comput. Phys., 395:286297, 2019.
 R. Maier and D. Peterseim. Explicit computational wave propagation in microheterogeneous media. BIT Numer. Math., 59(2):443462, 2019.
 C. Paulus, R. Maier, D. Peterseim, and S. Cotin. An immersed boundary method for detailpreserving soft tissue simulation from medical images. In: P. Nielsen, A. Wittek, K. Miller, B. Doyle, G. Joldes, and M. Nash, editors, Computational Biomechanics for Medicine, MICCAI 2017, pp. 5567. Springer, Cham, 2019.
Articles in Collections
 P. Hennig, M. Kästner, R. Maier, P. Morgenstern, and D. Peterseim. Adaptive isogeometric phasefield modeling of weak and strong discontinuities. In: J. Schröder and P. Wriggers, editors, Nonstandard Discretisation Methods in Solid Mechanics, volume 98 of Lecture Notes in Applied and Computational Mechanics, pp. 243282. Springer, Cham, 2022.
Articles in Proceedings
 R. Altmann, R. Maier, and B. Unger. A semiexplicit integration scheme for weaklycoupled poroelasticity with nonlinear permeability. Proc. Appl. Math. Mech., 20(1):e202000061, 2021.
 A. Caiazzo, R. Maier, and D. Peterseim. Reconstruction of quasilocal numerical effective models from lowresolution measurements. Oberwolfach Reports, 16(3):21492152, 2019.
 R. Maier and D. Peterseim. Fast timeexplicit microheterogeneous wave propagation. Proc. Appl. Math. Mech., 18(1):e201800294, 2018.
Theses
 R. Maier. Computational Multiscale Methods in Unstructured Heterogeneous Media. Doctoral Thesis, University of Augsburg, 2020.
 R. Maier. Simulation of Elastic Deformation by the Immersed Boundary Method. Master Thesis, University of Bonn, 2017.
 R. Maier. Die SpaceTimeDGMethode: Theorie und Numerik für parabolische Gleichungen in einer Dimension. Bachelor Thesis, University of Bonn, 2015. In German.