Coupled Field Problems: Advanced Numerical Methods and Applications to Nonlinear Magnetomechanical Systems (project of the SFB "Numerical and Symbolic Scientific Computing")

The subject of this project is the development, analysis, implementation and application of advanced numerical methods for the solution of 3D non-linear, stationary and instationary (dynamic) coupled magnetomechanical field problems described by Maxwell's and Navier's systems of Partial Differential Equations (PDEs) as well as the development of an advanced user surface including the handling of parallel processing. In recent years, advanced numerical methods have been developed for 3D Maxwell's as well as for Lame-Navier's equations separately, whereas the development and, especially, the analysis of similar methods for the coupled problems are at the very beginning. The usual approach to the solution of such problems consists in decoupling the field problems by an alternate iteration scheme. However, this decoupling can lead to a loss in efficiency of the corresponding numerical schemes, especially, in the presence of non-linearities and strong coupling terms. Therefore, new numerical schemes should avoid these losses in efficiency and should be based on hierarchical adaptive approximation and solver techniques including algebraic and hybrid multilevel solvers. The numerical solver together with appropriate pre- and postprocessing tools including automatic 3D mesh generators should enable us to simulate more and more complicated problems in advanced electromechanical applications.