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A study of the various methods for computing electromagnetic field utilizing thin wire integral equations
Author(s) -
Sarkar Tapan K.
Publication year - 1983
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs018i001p00029
Subject(s) - integral equation , galerkin method , operator (biology) , sequence (biology) , iterative method , mathematics , monotonic function , range (aeronautics) , series (stratigraphy) , electromagnetic field , field (mathematics) , basis function , inverse problem , mathematical analysis , algorithm , finite element method , physics , quantum mechanics , pure mathematics , paleontology , biochemistry , chemistry , genetics , materials science , repressor , biology , gene , transcription factor , composite material , thermodynamics
In this paper we analyze the numerical aspects of the various methods that have been utilized to analyze thin wire antennas. First, we derive the properties of the operators for Pocklington's and Hallen's integral equation. On the basis of these properties, we discuss the various iterative methods used to find current distribution on thin wire structures. An attempt has been made to resolve the question of numerical stability associated with various entire domain and subdomain expansion functions in Galerkin's method. It has been shown that the sequence of solutions generated by the iterative methods monotonically approaches the exact solution provided the excitations chosen for these problems are in the range of the operator. Such a statement may not hold for Galerkin's methods if the inverse operator is unbounded. Moreover, if the excitation function is not in the range of the operator, then the sequence of solutions forms an asymptotic series. Examples have been presented to illustrate this point.