Algebraic properties of BEMFEM coupling with Whitney elements

• Published in: Compel Vol. 24; no. 2; pp. 480 - 494
• Main Authors: Auchmann, B., Kurz, S., Rain, O., Russenschuck, S.
• Format: Journal Article
• Language: English
• Published: Emerald Group Publishing Limited 01.06.2005
• Subjects: Boundaryelements methods; Electromagnetism; Finite element analysis
• ISSN: 0332-1649
• DOI: 10.1108/03321640510586114

Purpose To introduce a Whitneyelement 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. Designmethodologyapproach The FEM is interpreted in the framework of the theory of discrete electromagnetism DEM. The BEM formulation is given in a DEMcompatible notation. This allows for a physical interpretation of the algebraic properties of the resulting BEMFEM system matrix. To these ends we give a concise introduction to the mathematical concepts of DEM. Findings Although the BEMFEM 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 limitationsimplications 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 BEMFEM coupling. Originalityvalue 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 righthand side that is not in the image of the matrix. The issue of a gridtransfer matrix is briefly mentioned.