The piece-by-piece solution of elliptic boundary value problems

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Abstract
A method of solution of a particular class of two-dimensional elliptic boundary value problems is developed. The method relies on splitting the region of the field into a number of sub-regions in each of which a field solution may be obtained in terms of well-known functions. Integral equations are formed for postulated source distributions on the interfaces between the sub-regions which are solved using Galerkin's method. The technique is particularly suitable for those cases where a functional of the field rather than the field itself is the required end product. An example is given of the calculation of the modification to the magnetic flux crossing an air gap due to the presence of slots.

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