Nearly all areas in natural scientific and engineering applications – from Plasma- to Hydrodynamics technologies -- are based on transport-, reaction- and flow-problems. Often such problems are numerically stiff, means we obtain highly variations of time- and spatial scales. Standard simulation methods have biggest difficulties and alternative methods are important to overcome the problems. In the lecture, we discuss the derivation of Maxwell- and transport-reaction equations, which are used as modelling problems in the engineering applications. After the derivation of the modelling equation, we discuss efficient and robust methods for each equation type. We present Finite Difference and FDTD-Methoden (Finite-Difference Time-Domain) for the spatial discretization. Next, we discuss modern numerical solver methods, so called Multiscale methods. We discuss efficient combinations of microscopic and macroscopic solvers, which allow to overcome the multiple time- and spatial-scales. For solving such large scale problems, we discuss Multigrid and iterative solver methods. In the lecture, we present the theoretical principles of the algorithms and their mathematical background. Further, we apply the theoretical knowledge to practical engineering examples, e.g., heat-flux and particle transport. For the participants, we present additional opensource programs (commercial and academics). The Program-packages can be tested in an Hands-On-part as Matlab programs in the CIP pool.
- Kursleiter/in: Jürgen Geiser