Mathematical Physics within DIAM

Characterization by means of key words

Random walk particle methods, perturbation analysis, asymptotic expansions, wave analysis, shallow water equations, transport modeling in surface and subsurface flows, vibrations of mechanical structures, wave-structure interaction, multiple scale analysis, Kalman filter, parallel linear algebra, data assimilation for porous media, polymer physics.

General description

Mathematical Physics is concerned with mathematical modeling of physical phenomena. The models that we study consist of one or multiple differential equations, most often partial differential equations. In our group we study such equations from the constructive point of view, i.e. methods are investigated that enable the computation of approximations of members of the solution space. Both analytical and numerical methods are used for this.

In many cases, data from measurements are available besides a mathematical model. It is possible to use the measurements to set up an improved model (data assimilation). Data assimilation is in particular important in environmental studies. Such studies are characterized by uncertainty in the underlying physical description, leading to modeling errors that can only be corrected by including measurements. In the field of data assimilation, our specialism is Kalman filtering and its extensions.

Applications play a central role in our studies and the primary goal is to obtain results with practical significance. In this context, interaction with external partners often takes place against the background of their daily software. One of the issues put forward is that the interest in complex and detailed models is growing. Enlargement of scale is visible, among others because advanced computational facilities have become a common engineering tool. This leads to large scale numerical questions. We address such questions against the background of high-performance computing. Parallel computing aspects of the applied methods are important.