Computational Methods for PDEs

Group Langer

The "Computational Mathematics Group" (CMG) will mainly focus on the development, analysis and implementation of novel computational methods for complicated multiple field problems (e.g., but not exclusively, modelled by systems of partial differential equations) arising in classical and novel application fields like computational fluid mechanics, structural mechanics, electro-magnetics, computational physics and chemistry, computational finance and, in the future, computational life sciences. Methods currently studied include domain decomposition and multigrid methods with special emphasis on adaptivity. Multi-level approximation techniques are among the most powerful tools for constructing fast and efficient (mostly parallel) methods for solving discretised field problems of high complexity. The development of the numerical methods is usually driven by hard applications. The numerical handling of hard applications requires some kind of Scientific Problem Solver Environment (PSE) that contains a set of interacting scientific computing tools such as:

  • Geometry and problem editor
  • Mesh generator and mesh handler
  • Parallelisation tools
  • Solver tools (adaptive discretisation and solution techniques)
  • Optimisation tools
  • Visualisation