ATML Numerical and Statistical Methods

The ATML "Numerical and Statistical Methods" develops, implements, and tests new procedures/methods in the area of stochastic ordinary and partial differential equations that arise, for example, in image processing, acoustic, electromagnetic, and elastic scattering problems, and reaction-diffusion-advection equations. In this context, the group also deals with algorithms for the solution of ill-posed inverse problems and the computation of eigenvalue problems.

Furthermore, the group provides software support for supercomputers and collaborates with domain scientists to help them integrate and use new numerical methods in their applications.

Additionally, group members teach bachelor and master courses in Applied Mathematics and Informatics at the Fachhochschule Aachen Campus Jülich.

Contact: Prof. Dr. Andreas Kleefeld

Special Methods for PDEs

Partial differential equations (PDEs) in unbounded domains can be solved efficiently with boundary integral equations.

Parallel FEM Simulations for Large Infrastructures

Another activity concerning PDEs is the analysis of complex infrastructures, like a long-span suspension bridge crossing the Bosphorus.

Parallel Preconditioning via Reinforcement Learning

Machine learning can be used to improve existing mathematical algorithms which approximate a PDE solution.