Mathematics of Computational Science

Research The Mathematics of Computational Science (MACS) group focuses on the mathematical aspects of advanced scientific computing. The research in MACS concentrates on three main topics:

- The development, analysis and application of numerical algorithms for the (adaptive) solution of partial differential equations, in particular (discontinuous Galerkin) finite element methods.
- Mathematical modeling of multi-scale problems making these accessible for computation, in particular for multi-phase flows and geophysical problems.
- Efficient (parallel) solution algorithms, such as multigrid and Krylov subspace methods, for large algebraic systems of equations resulting from numerical discretizations.

In order to support these activities a significant research effort is directed towards the design of hpGEM, an object oriented toolkit for finite element discretizations, written in C++, and suitable for high performance parallel computers. Since 2012 MACS is a member of the MESA+ Institute for Nanotechnology. This has resulted in the past year in a significant reorientation of the research direction. In particular, a close collaboration with the MESA+ Complex Photonic Systems group was established. This has resulted already in two externally funded PhD positions working on photonic crystals that started in the fall of 2013. We plan to further extend the research in nanophotonics, which is a very fruitful area for our mathematical expertise in developing advanced finite element discretizations for the Maxwell equations.

A new research area is wave phenomena in heterogeneous elastic media, for which recently research funding was obtained. Another focal point is inkjet printing, where we have a close collaboration with the MESA+ group Physics of Fluids and Océ technologies, which have a great need for advanced simulation tools in the development of large industrial inkjet printers. This research has a close relation with our research on other free surface problems, such as water waves.

Other research areas are phase transition, granular problems and multigrid techniques. Continuous efforts are being made to attract new research funding and PhD students to develop our research program. Recently, funding for four new PhD students and one PostDoc was obtained in projects funded by FOM and STW. Currently, nine PhD students are active within MACS.

We participate in the Dutch researchschool for fluid mechanics: