Junction Basis Functions

I am working on a moment method code. I cannot use NEC because I
have to account for different dielectrics. Anyway, I am having some
difficulty with the junctions which I hoped someone on this list
might be able to help me with.

                            x

                            ^
                            |

                            d
                   <---------------->
                   __________________
                            | / \
                            | |
                            | L
                            | |
                            |
             y < - - - | \|/

There are three wires with one junction. As I understand Chao and Strait
in AFCRL 79-0374, I can look at this problem as three wires with no
junction, but with overlapping basis function as follows.

Wire 1: (no overlap)
                            x

                            ^
                            |

                            d
                   <---------------->
                   __________
                                           / \
                                        |
                                         L
                                        |
                            
             y < - - - \|/
                            

Wire 2:
                            x

                            ^
                            |

                            d
                   <---------------->
                            _________
                            | / \
               overlap -> | |
                                         L
                                        |
                            
             y < - - - | \|/

Wire 3:
                            x

                            ^
                            |

                            d
                   <---------------->
                         ____
                overlap ^ | / \
                            | |
                            | L
                            | |
                            |
             y < - - - | \|/

There are two ways of interpreting this. First, one must integrate
in two dimensions for the inner product to account for the "corner"
basis function. (One basis function straddles each corner on wires
2 and 3). Second, one could just consider wires 2 and 3 to be
slightly longer than they really are by half a basis function. I
had hoped that the second case was correct and tried it since it is
simple enough. Unfortunately, the basis function which straddles
the junction on wire 2 turns up with a zero voltage coefficient. This
leads me to think that the first case must be correct. I had hoped
otherwise, particularly because I am doing this in the Fourier
Domain to account for different dielectric's above and below the
antenna plane. The inner product involves an infinite integral
which does not converge as rapidly for a "corner" basis function
(piecewise sinusiod).

Can someone confirm that I have must do it this way before I undertake
it? Thank you.

Brad

---------------------------------------------------------------
Brad Porter Research Assistant - Microwave and Millimeter
                        Wave Communications Laboratory
                University of Wisconsin - Madison, ECE Dept.
email: porterb_at_cae.wisc.edu
WWW URL: http://www.engr.wisc.edu/~porterb/homepage.html
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Received on Wed Oct 04 1995 - 15:05:00 EDT