Robust Maxwell Formulation

Description

A novel unified method for the stable numerical solution of the time-harmonic Maxwell's equations for any frequency is developed. The method is based on an extended variational formulation of the full linear Maxwell's equations [1]. This formulation avoids stability problems in the stationary limit, where it reduces to the equations of electrostatics and magnetostatics. Both capacitive and inductiv effects are taken into account in a robust fashion for all frequencies.

Since this project is funded by ABB, the goal is to develop a fast and reliable 3D FEM Solver (called HADAPT) that has to be integrated in the given environment. Currently it is already used by engineers in some business units. HADAPT is also used in other ABB research projects.

We have realised the "fast and reliable" of the solver description with an novel preconditioner [2] and a lot of tests. The novel preconditioner is based on the operator preconditioner technique [3]. We have utilized this preconditioner also for the eddy-current formulation [4], which is a approximation of Maxwell's equations.

In [2] and [4] we have also shown the applicability of hierarchical matrices as a preconditioner method for the robust maxwell formulation. This is the current focus of our research.

Publications / Preprints or SAM-Reports

[1] Hiptmair, R. and Krämer, F. and Ostrowski, J. A robust Maxwell formulation
for all frequencies, IEEE Transactions on Magnetics 44(2008), no. 6, pages 682-685.
[2] Ostrowski, J. and Bebendorf, M. and Hiptmair, R. and Krämer, F. H-Matrix-Based Operator Preconditioning for Full Maxwell at Low Frequencies, IEEE Transactions on Magnetics 46(2010), no. 8, pages 3193-3196.
[3] Hiptmair, R. Operator preconditioning, Computers and Mathematics with Applications 52(2006), no. 5, pages 699-706.
[4] Krämer, F. and Bebendorf, M. and Ostrowski, J. and Hiptmair, R. Hierarchical matrix preconditioners for eddy current problems, Electromagnetics in Advanced Applications, 2009. ICEAA'09, pages 724-727.

References

None

Funding

ABB corporate research in Baden Dättwil

Contacts

Prof. Ralf Hiptmair
Florian Krämer