The chair of Applied Mathematics and Numerics (LS3) at the Department of Mathematics of the TU Dortmund is held by Prof. Dr. Stefan Turek. Our main focus are numerical techniques for partial differential equations (PDEs), high performance computing and scientific computing with respect to engineering sciences (fluid and structural mechanics). Also part of this chair is the Junior Professorship "Hardware-oriented numerics for large systems" of Jun.-Prof. Dr. Dominik Göddeke.
Main research topics include finite element discretizations, enhanced and adapted to the special characteristics of convection-diffusion equations and saddle point problems like the Navier-Stokes equations. We are also interested in the design and implementation of fast multigrid and domain decomposition solvers which our own solver variant ScaRC (Scalable Recursive Clustering) aims to combine and supersede.
Exceeding these mathematical aspects we focus on (numerically and implementationally) efficient FEM software, in particular by pursuing hardware-oriented approaches. While maintaining and steadily improving our legacy FEM software packages FEAT2D/3D and FEATFLOW, we are currently working on the successor packages as a part of the FEAST project which will yield a high performance FEM toolbox.
Our international team employs the software to solve complex problems in the field of fluid mechanics that have an industrial background. Models are usually based on variants of incompressible Navier-Stokes equations with extensions like non-linear viscosity (granular flow, non-Newtonian flow, viscoelasticity), fluid-structure-interaction, multiphase flows with chemical reactions, and free boundary value problems emerging in solidification processes. Typically, some of them are put to use in industrial projects as well.