DocumentCode :
796792
Title :
A failure of a numerical electromagnetics code to match a simple boundary condition
Author :
Ludwig, Art C.
Author_Institution :
Toyon Res. Corp., Santa Barbara, CA, USA
Volume :
43
Issue :
7
fYear :
1995
fDate :
7/1/1995 12:00:00 AM
Firstpage :
723
Lastpage :
727
Abstract :
It is shown that it is impossible to satisfy the boundary condition for a perfectly conducting hemisphere-capped dipole without creating a discontinuity in the first derivative of the scattered field on the boundary. Since solutions of Maxwell´s equations are analytic in a source-free region, all field derivatives must be continuous in the region where the source-free equations are satisfied. The basis functions used by the generalized multipole technique (GMT) are solutions of Maxwell´s source-free equations in a region which includes the scattering surface. Therefore, a GMT solution to the dipole problem can exist only in the sense that the boundary value error approaches zero as the number of basis functions approaches infinity. This in itself is not surprising, but the difficulty of matching the boundary condition at the discontinuity affects the convergence of the technique. For the method-of-moments (MOM) technique, where a source current exists on the scattering surface, it is not clear if a perfect boundary value solution to the dipole problem can be theoretically realized or not
Keywords :
Maxwell equations; boundary-value problems; conductors (electric); convergence of numerical methods; dipole antennas; electromagnetic wave scattering; method of moments; Maxwell´s source-free equations; basis functions; boundary condition; boundary value error; boundary value solution; convergence; field derivatives; first derivative discontinuity; generalized multipole technique; method-of-moments; numerical electromagnetics code; perfectly conducting hemisphere-capped dipole; scattered field; scattering surface; source current; source-free region; Art; Boundary conditions; Distributed Bragg reflectors; Electromagnetic radiation; Electromagnetic scattering; H infinity control; Maxwell equations; Message-oriented middleware; Moment methods; Region 2;
fLanguage :
English
Journal_Title :
Antennas and Propagation, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-926X
Type :
jour
DOI :
10.1109/8.391146
Filename :
391146
Link To Document :
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