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On the convergence properties of the method of auxiliary sources in 3D problems with open boundaries
Author(s) -
Papakanellos P. J.,
Heretakis I. I.,
Capsalis C. N.
Publication year - 2004
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.562
Subject(s) - convergence (economics) , planar , boundary (topology) , dissipative system , dipole , simple (philosophy) , plane (geometry) , ground plane , field (mathematics) , boundary value problem , computer science , mathematics , mathematical optimization , mathematical analysis , geometry , physics , pure mathematics , telecommunications , philosophy , antenna (radio) , economics , economic growth , computer graphics (images) , epistemology , quantum mechanics
In this paper, the convergence behaviour of the method of auxiliary sources (MAS) is studied in cases of simple three‐dimensional (3D) problems with open regions. For the assessment of the convergence behaviour in such cases in a general manner, the cases considered herein consist in elemental electric dipoles radiating in the close proximity to a planar dissipative ground. Both vertically and horizontally oriented dipoles with respect to the ground plane are examined. The aim of the study is to investigate the interrelation between the auxiliary sources locations and the resultant field continuity errors. For this, the dependence of the boundary conditions errors on the number and spacing of the auxiliary sources is exhibited and general rules regarding their behaviour are extracted. Moreover, the influence of these errors on quantities of interest is examined. Finally, a few concluding remarks are outlined and their possible utilization in cases of more composite 3D problems is discussed. Copyright © 2004 John Wiley & Sons, Ltd.