Alternative sub-domain moment methods for analyzing thin-wire circular loops

Abstract

An alternative sub-domain formulation is presented, in two variants, for the analysis of thin-wire circular loops via moment methods. Curved piecewise sinusoids are used as basis functions, while both point matching and reaction matching (Galerkin's method) are examined as testing schemes. The present study is primarily focused on frill-driven loops, but some of the essential similarities and differences between them and gap-driven ones are also discussed in brief. Numerical results are presented to verify the two variants of the proposed formulation and demonstrate their capabilities for analyzing small and large loops. Special attention is drawn to the behavior of the solutions as the number of basis/testing functions grows. Finally, a complexity analysis is attempted and the potential savings in execution times that may be attained by taking advantage of certain features of the proposed numerical schemes are discussed.