Data-sparse Boundary and Finite Element Domain Decomposition Methods in Electromagnetics

Funding agency Austrian Science Fund (FWF)
Project number P 19255
Principal investigator Urlich Langer
International Research Partner
and Co-Investigator
Olaf Steinbach
Members and basic staff Sven Beuchler
Dylan Copeland
Sarah Engleder
Peter Gruber
Michael Kolmbauer
Günther Of
Clemens Pechstein
Markus Windisch
Monika Wolfmayr (née Kowalska)
Sabine Zaglmayr
Walter Zulehner
Duration 2007-05-01 – 2012-04-30

This website documents the work in the project Data-sparse Boundary and Finite Element Domain Decomposition Methods in Electromagnetics, which is supported by the Austrian Science Fund (FWF) under grant P19255-N18. This is a joint project of the Institute of Computational Mathematics at the Johannes Kepler University in Linz and the Institute of Computational Mathematics at the University of Technology in Graz.


Domain Decomposition (DD) methods are nowadays not only used for constructing parallel solvers for Partial Differential Equations (PDE), but also for coupling different physical fields and different discretization techniques. Since Finite Element Methods (FEM) and Boundary Element Methods (BEM) exhibit certain complementary properties, it is sometimes very useful to couple these discretization techniques and thus benefit from the advantages of both worlds. This concerns not only the treatment of unbounded domains (BEM), but also the right handling of singularities (BEM), moving parts (BEM), air regions in electromagnetics (BEM), source terms (FEM), non-linearities (FEM), etc. Therefore, it is not astonishing that the coupling of FEM and BEM within a DD framework is successfully used in many practical applications. Among the DD methods, the so-called Finite Element Tearing and Interconnecting (FETI) methods are probably the most successful, at least for large-scale parallel computations. Recently, the proposers have introduced data-sparse Boundary Element Tearing and Interconnecting (BETI) methods as boundary element counterparts of the well-established FETI methods, as well as coupled BETI-FETI methods for some model problems such as the potential equation and the linear elasticity system. The advantage of these tearing and interconnecting methods is not only the nearly optimal asymptotical behavior of the iteration numbers with respect to the discretization parameter h and the subdomain scaling parameter H, but also the robustness with respect to large coefficient jumps and the excellent scalability on massively parallel computers.

In this project, we propose to construct and analyze new DD solvers, including DD solvers based on the tearing and interconnecting technique, for large-scale finite element (FE), boundary element (BE), and coupled FE-BE DD equations derived from linear and non-linear magnetostatic problems as well as from linear and non-linear eddy current problems in both the time and frequency domains. The numerical treatment of non-linear eddy current problems in the frequency domain is not at all straightforward. A multiharmonic approach that is based on Fourier series is one possible technique to treat such problems. The construction of fast solvers, in particular, efficient DD solvers for the resulting large-scale system of non-linear equations, is quite challenging. The new DD algorithms to be developed in this project will essentially contribute to a new generation software in Computational Electromagnetics.


Recent Preprints

2012 - Refereed Journal Papers

2012 - Refereed Proceedings Papers

2011 - Refereed Journal Papers

2011 - Refereed Proceedings Papers

2010 - Refereed Journal Papers

2010 - Refereed Proceedings Papers

2009 - Refereed Journal Papers

2009 - Refereed Proceedings Papers

2008 - Refereed Journal Papers

2008 - Refereed Proceedings Papers

Among the following publications are also some earlier relevant works by members and associate members of this FWF project.

2007 and Before - Refereed Journal Papers

2007 and Before - Refereed Proceedings Papers

Books, Chapters in Books


PhD Theses

Master Theses

Technical reports



We have been successively developing a code framework for simplifying and unifying the software connected with our research. The framework is in C++ using high standard template and object-oriented techniques. A great consultant is Joachim Schöberl, the founder of NGSolve.


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Former developers:




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