The research program of the Numerical Analysis group of TUD belongs to the field of computational science and engineering. We concentrate on the development and application of computing methods to the applied sciences.
The focus is on mathematical models relying heavily on partial differential equations, such as occur in fluid dynamics. But we also consider similar mathematical models arising in other fields, for instance materials science, electro-magnetic problems, mechanical models, financial engineering, and reservoir engineering, usually in cooperation with domain experts. A specialty is problems involving partial differential equations with moving internal boundaries, such as occur in bubbly flows and in phase transition problems.
To diminish computing time in large-scale applications, iterative methods for solving large systems of algebraic equations are developed further, using deflation, multi-block, preconditioning and multigrid techniques. Furthermore these methods are implemented on the newest computer architectures as there are:
Beowulf clusters, multi-core processors, grid computing and GPU's.

For our group the collaboration with the other group of the Delft Centre for Computational Science and Engineering (DCSE) is of primary importance

See also this link for a more elaborate description of Numerical Analysis.