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- . . ‘Localized Model Reduction in PDE Constrained Optimization.’ Contributed to the DFG-AIMS Workshop on Shape optimization, homogenization and control, AIMS Sénégal, Mbour, Sénégal. [Submitted]
- . . ‘Extending DUNE: The dune-xt modules.’ Archive of Numerical Software 5, No. 1: 193-216. doi: 10.11588/ans.2017.1.27720.
- . . ‘Non-Conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE constrained Optimization.’ In Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, edited by , 357-365. Cham: Springer International Publishing. doi: 10.1007/978-3-319-57394-6_38.
- . . ‘True Error Control for the Localized Reduced Basis Method for Parabolic Problems.’ In Model Reduction of Parametrized Systems, edited by , 169-182. Cham: Springer International Publishing. doi: 10.1007/978-3-319-58786-8_11.
- . . Model reduction for parametric multi-scale problems Doctoral Thesis, Westfälische Wilhelms-Universität Münster.
- . . ‘Adaptive Localized Model Reduction.’ Oberwolfach Reports 13, No. 3: 2406-2409. doi: 10.4171/OWR/2016/42.
- . . ‘pyMOR - Generic algorithms and interfaces for model order reduction.’ SIAM Journal on Scientific Computing 38, No. 5: 194-216. doi: 10.1137/15M1026614.
- . . ‘Model Reduction for Multiscale Lithium-Ion Battery Simulation.’ In Numerical Mathematics and Advanced Applications ENUMATH 2015, edited by , 317-331.: Springer. doi: 10.1007/978-3-319-39929-4_31.
- . . ‘Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment.’ SIAM J. Sci. Comput. 37, No. 6: A2865-A2895. doi: 10.1137/151003660.
- . . ‘A-Posteriori Error Estimates for the Localized Reduced Basis Multi-Scale Method.’ In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, edited by , 421-429.: Springer International Publishing. doi: 10.1007/978-3-319-05684-5_41.
- . . ‘Model reduction for multiscale problems.’ Oberwolfach Reports 39: 2228-2230. doi: 10.4171/OWR/2013/39.
- . . ‘The localized reduced basis multi-scale method with online enrichment.’ Oberwolfach Reports 7: 406-409. doi: 10.4171/OWR/2013/07.
- . . ‘The Localized Reduced Basis Multiscale Method.’ Contributed to the Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, Vysoke Tatry, Podbanske.
Selected research, projects, ...
The following is an extremely incomplete list of my activities. I just started collecting them and they should grow over time ...
- I recently started looking into discontinuous Galerkin (DG) and Finite Volume (FV) methods for hyperbolic equations, such as approximating the solution \(u\) of: $$\partial_t u + \nabla_x \cdot f(u) = 0$$ I was particularly interested in how to support the implementation of both FV and DG methods in our software library. Preliminary findings are documented here.
dune-gdt is a DUNE module which provides a generic discretization toolbox for grid-based numerical methods. It contains building blocks - like local operators, local integrands, local assemblers - for discretization methods as well as generic interfaces for objects like discrete function spaces and basefunction sets. Implementations are provided using the main DUNE discretization modules, like dune-fem, dune-functions and dune-pdelab. For more information visit the official homepage.
pyMOR - Model Order Reduction with Python - is a software library for building model order reduction applications with the Python programming language. Its main focus lies on the application of reduced basis methods to parameterized partial differential equations. All algorithms in pyMOR are formulated in terms of abstract interfaces for seamless integration with external high-dimensional PDE solvers. Moreover, pure Python implementations of finite element and finite volume discretizations using the NumPy/SciPy scientific computing stack are provided for getting started quickly. For more information visit the official homepage.
- . . ‘pyMOR - Generic algorithms and interfaces for model order reduction.’ SIAM Journal on Scientific Computing 38, Nr. 5: 194-216. doi: 10.1137/15M1026614.
- Ohlberger M, Rave S, Schindler F (): "Fully certified and adaptive localized model reduction for elliptic and parabolic problems". Recent developments in numerical methods for model reduction, Institute Henri Poincaré, Paris, France, .
The list of talks is not yet complete.