Matthias' main research interests are finite element methods and isogeometric analysis for computational fluid dynamic problems with particular emphasis on high-resolution adaptive schemes for compressible flows and transport problems as well as fast solvers. Since recently he is working in the field of hybrid mesh-particle methods with special emphasis on the material point method, which could be extended towards higher-order approximations by using ideas from isogeometric analysis. Beside the development and analysis of numerical schemes Matthias is also interested in their efficient implementation on heterogeneous multi- and manycore systems and accelerators. His interest in future computing technologies led him to start research on quantum computing and, in particular, on quantum-accelerated numerical linear algebra with the focus on developing quantum solutions for practical applications.