The f(A)bulous Network for Matrix Functions and Exponential Integrators

• Applicant: Privatdozent Dr. Marcel Schweitzer
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 566049107

Matrix functions are increasingly vital in many areas of science and engineering, particularly as the backbone of exponential integration schemes for numerically solving stiff differential equations. Our network brings together experts in the theory and algorithms of matrix functions with those developing exponential integrators to foster collaboration and better coordinate parallel research efforts. We also include specialists in matrix equations and model order reduction, since the algorithms used in these areas closely resemble those for matrix functions. This interdisciplinary exchange is expected to benefit both communities and accelerate algorithm development. In addition to establishing a dynamic research environment with long-term discovery potential, the network has several concrete, short-term objectives: One barrier to the wider adoption of exponential integration schemes and matrix function methods is that expertise is largely confined to a small community, while the broader field often relies on “tried and true” methods supported by more accessible resources (for example, methods based on solving linear systems, such as implicit time stepping schemes). To address this, we plan to write two survey papers—one on the computation of matrix functions and one on exponential integration schemes—to make these techniques more accessible to the research community. Proposals for both surveys have already been accepted by SIAM Review. Another challenge is the lack of robust and efficient publicly available implementations, as well as standardized benchmarking frameworks that facilitate the comparison of different algorithms, variants, and hyperparameter choices to identify the best method for a given application. We therefore aim to develop a prototype for a comprehensive software toolbox that incorporates today’s most important matrix function algorithms and is built in a modular fashion to accommodate future developments. In addition, we intend to establish a repository of standardized benchmark problems. More broadly, we also hope to further promote adherence to the FAIR principles within our community.

• DFG Programme: Scientific Networks