Algebraic properties of BEM-FEM coupling with Whitney elements B. Auchmann CERN-AT-MEL, Geneva, Switzerland S. Kurz Helmut-Schmidt-Universita ¨ t Hamburg, Hamburg, Germany O. Rain Robert Bosch GmbH, Stuttgart, Germany, and S. Russenschuck CERN-AT-MEL, Geneva, Switzerland Abstract Purpose – To introduce a Whitney-element based coupling of the Finite Element Method (FEM) and the Boundary Element Method (BEM); to discuss the algebraic properties of the resulting system and propose solver strategies. Design/methodology/approach – The FEM is interpreted in the framework of the theory of discrete electromagnetism (DEM). The BEM formulation is given in a DEM-compatible notation. This allows for a physical interpretation of the algebraic properties of the resulting BEM-FEM system matrix. To these ends we give a concise introduction to the mathematical concepts of DEM. Findings – Although the BEM-FEM system matrix is not symmetric, its kernel is equivalent to the kernel of its transpose. This surprising finding allows for the use of two solution techniques: regularization or an adapted GMRES solver. Research limitations/implications – The programming of the proposed techniques is a work in progress. The numerical results to support the presented theory are limited to a small number of test cases. Practical implications – The paper will help to improve the understanding of the topological and geometrical implications in the algebraic structure of the BEM-FEM coupling. Originality/value – Several original concepts are presented: a new interpretation of the FEM boundary term leads to an intuitive understanding of the coupling of BEM and FEM. The adapted GMRES solver allows for an accurate solution of a singular, unsymetric system with a right-hand side that is not in the image of the matrix. The issue of a grid-transfer matrix is briefly mentioned. Keywords Electromagnetism, Finite element analysis, Boundary-elements methods Paper type Conceptual paper 1. Introduction The simulation of electromagnetic fields in the aperture of accelerator magnets poses a challenge to numerical tools. The requirement for an accurate modelling of the superconducting coils has been met by a finite element method (FEM) with a reduced vector potential formulation (Biro et al., 1998), and with a coupling method between the boundary element method (BEM) and FEM, both with node-based element shape functions (Kurz and Russenschuck, 1999). The necessity to use Whitney-forms as The Emerald Research Register for this journal is available at The current issue and full text archive of this journal is available at www.emeraldinsight.com/researchregister www.emeraldinsight.com/0332-1649.htm COMPEL 24,2 480 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Vol. 24 No. 2, 2005 pp. 480-494 q Emerald Group Publishing Limited 0332-1649 DOI 10.1108/03321640510586114