Dimensional reduction of electromagnetic boundary value problems
1 Department of Mathematics, Tampere University of Technology, P.O. Box 553, Tampere FI-33101, Finland
2 Electromagnetics, Tampere University of Technology, P.O. Box 692, Tampere FI-33101, Finland
Boundary Value Problems 2011, 2011:9 doi:10.1186/1687-2770-2011-9Published: 29 July 2011
This paper develops a systematic and formal approach to dimensional reduction of electromagnetic boundary value problems. The approach is based on the concept of continuous symmetry, and the definitions and the mathematical structures used are conceptually distinct and completely coordinate-free and independent of dimensions. The approach leads to sufficient conditions for when a boundary value problem can be solved as a lower-dimensional one and it shows how to systematically formulate the lower-dimensional problems. The symmetries are described with Lie groups that are products of connected 1-D Lie groups.