Dr Georg Maierhofer
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
G-Adaptive mesh refinement - leveraging graph neural networks and differentiable finite element solvers. Rowbottom, J., Maierhofer, G., Deveney, T., Schratz, K., Lio, P., Schönlieb, C.-B., Budd, C., preprint, https://arxiv.org/pdf/2407.04516
A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics. Jin, T., Maierhofer, G., Schratz, K., Xiang, Y., preprint, https://arxiv.org/pdf/2407.03945
Numerical integration of Schrödinger maps via the Hasimoto transform. Banica, V., Maierhofer, G., Schratz, K., SIAM J. Numer. Anal. (2024), https://doi.org/10.1137/22M1531555
Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations. Feng, Y., Maierhofer, G., Schratz, K., Mathematics of Computation (2023), https://doi.org/10.1090/mcom/3922
Recursive moment computation in Filon methods and application to high-frequency wave scattering in two dimensions. Maierhofer, G., Iserles, A., Peake, N., IMA J. Numer. Anal. (2023), https://doi.org/10.1093/imanum/drac067
Convergence analysis of oversampled collocation boundary element methods in 2D. Maierhofer, G., Huybrechs, D., Adv. Comput. Math. (2022), https://doi.org/10.1007/s10444-022-09924-8
My main research interests focus on problems in computational mathematics for partial differential equations (PDEs) and the study of waves. In more detail I have worked on the following topics:
- Numerical methods for dispersive nonlinear PDEs
- Geometric numerical integration
- Machine learning methods for PDEs
- Approximation theory and frames
- Wiener-Hopf method and applications
- Henslow Research Fellowship, Clare Hall, University of Cambridge (2023-present)
- Marie Skłodowska-Curie Fellowship, Laboratoire Jacques-Louis Lions, Sorbonne Université (2022-23)
- Smith-Knight & Rayleigh-Knight Prize, Faculty of Mathematics, University of Cambridge (2019)