March 2014
Intermediate
876 pages
28h 17m
English
Content preview from The Finite Element Method in Electromagnetics, 3rd Edition
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CHAPTER 11FINITE ELEMENT–EIGENFUNCTION EXPANSION METHODS
In Chapter 10 we presented a hybrid finite element–boundary integral (FE–BI) method for treating unbounded field problems. In the FE–BI method, the unbounded region was first divided into an interior and an exterior region. The field in the interior region was formulated using the finite element method, and the field in the exterior region was formulated via the boundary integral equation method. The interior and exterior fields were subsequently coupled by the continuity conditions at the boundary separating the two regions. The method has been shown to be accurate and powerful, and can be applied to a variety of open-region problems. However, the boundary integral equation method is not the only method that can be used to formulate the exterior field. In this chapter we consider an alternative method for unbounded field problems. In this method the unbounded region is also divided into an interior and an exterior region, and the finite element method is again employed to formulate the field in the interior region. The method differs from the FE–BI method, however, in the formulation of the exterior field, which is now represented by an expansion of eigenfunctions instead of a boundary integral equation.
The eigenfunctions are a set of homogeneous solutions of a partial differential equation satisfying certain boundary conditions. Their expansion can be used to represent a solution (in the source-free region) of the corresponding ...
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