WG Numerics of PDEs

Administration: Prof. Dr. Alfred Schmidt

The group on Numerical Methods for Partial differential Equations (NumPDE) works in the development, analysis and application of efficient computational methods for stationary and non-stationary problems. Additionally, the methods are used to solve diverse applied problems in cooperation with our partners from the natural sciences and engineering. Our teaching includes the main lecture on Numerical Methods for PDEs as well as some special advanced lectures and seminars in which contents of our current research projects are presented.

We mainly work in development and application of Finite Element Methods and Adaptive Finite Element Methods. The latter ones consist on an automatic mesh modification for the numerical simulations, achieving in some cases a strong reduction of the computational cost. This is done with the support of mathematical techniques for error estimations ensuring a good approximation level in the obtained solutions. In this area, we cooperate with the groups of Prof. Siebert (Universität Duisburg), Prof. Bänsch (Universität Erlangen) and Prof. Veeser (Università di Milano).

Our applied projects in Material Science are joint works with diverse engineering research groups. The group participates in the two Collaborative Research Centers 570 “Distortion Engineering” and 747 “Micro Cold Forming” and has currently research projects with:

• Bremer Institut für Angewandte Strahltechnik (BIAS)
• Faculty of Production Engineering, Universität Bremen
• Institut für Mathematik, Universität Augsburg
• Institut für Statistik (IfS), Universität Bremen
• Institut für Werkstofftechnik (IWT)
• Weierstrass Institut (WIAS)
• Institut für Fertigungstechnik und Werkzeugmaschinen (IFW)
• Alfred-Wegener Institut (AWI)

Here you can access a more detailed description of our projects.

Methods for the numerical simulation of non-homogeneous materials in which the microscale has significant effects in the macroscale are developed and analyzed together with the group on Modeling and PDEs. Some examples of these materials are concrete, steel, nacre, and sand.

We also carry out the implementation of our scientific computing solutions. For this, some of our project simulations are performed in the academic software toolbox ALBERTA, while some other projects include other FORTRAN or C implementations of finite element methods. Furthermore, some parallelization methods are being implemented and tested in the Linux-Cluster at our Research Center.

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