Speaker :  Jürgen Geiser (Ruhr University of Bochum, Department of Electrical Engineering and Information Technology, Germany)

Title : Recent advanced in Iterative Splitting Methods for Multicomponent and Multiscale: Theory and Applications

Abstract :

Since recent years, decomposition methods for multicomponent and multiscale problems have become an increasingly important role in the numerical solution for spatial- and time-dependent partial differential equations.
Decomposition strategies are important to reduce computational time of large scale and
multicomponent and multiscale problems and are nowadays applied to physical and engineering problems.

Based on the ideas of the physical conservations of the problems, the methods have taken into account the numerical and physical errors of the problems.

The talk will present the latest research results in iterative splitting methods of high accuracy, efficiency and effectiveness in the field of multiscale and multicomponent problems.
Iterative Splitting schemes use relaxation and linearization methods to overcome nonlinear problems in space and time of the partial differential equations.

We investigate the following topics for important engineering and physics applications and discuss:

– Theory of iterative splitting and multi-splitting methods,

– Iterative Splitting methods as Multiscale solvers,

– Stability and convergence of iterative splitting methods,

– Engineering applications in computational fluid-dynamics (CFD) problems
based on deterministic and stochastic differential equations.

At the end of the talk, we summarize our results.