Re: NEC-LIST: Basis functions in NEC.

>Good day,
>
>I have been reading the theory sections of both the NEC2
>and NEC4 manual, concerning the basis functions. I am
>beginning to think that I understand the system, so I'm
>asking the NEC experts if I'm right.
>
>In NEC2, the fundamental basis functions are a constant, a
>sine, and a cosine function. Each of these components have
>a domain of definition which extends over just their related
>segment. Now associated with segment k is a main set of
>these functions, say f_k, and a set of tail functions
>defined over each connecting segment. Each of these tail
>functions and its derivative go to zero at the end of its
>domain segment farthest from segment k. f_k and the tail
>functions have to meet current and charge continuity
>conditons at each end of segment k.
>
>For example, let's consider a 3-segment wire. On segment 1,
>there is the main function f_1, and it has a tail function
>defined over segment 2. On segment 2 there is f_2 and it
>has tail functions defined over both segments 1 and 3. On
>segment 3 the main function is f_3, and it has a tail
>function defined over segment 2. Associated with segment 1
>are six unknown coefficients and five continuity and
>boundary conditions, if the charge at the open end is left
>free. Associated with segment 2 are nine unknowns and 8
>boundary and continuity conditions.
>
>Is this right?
>
>Doug Miron
>
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>NEC-List_at_robomod.net
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Doug,

I guess there may be some differences in the definition of a basis
function. I consider the basis functions to be the set of functions
for which you determine the amplitudes by solving the linear system
from MoM. The NEC-2 and 4 basis functions are constructed from
constant, sin(k*s) and cos(k*s) functions over each segment in their
support, the center segment and the tails. Your description looks
correct for those components. After enforcing the current and charge
continuity conditions there remains one degree of freedom which is
the amplitude of the basis function, and that is determined from the
linear system solution. That basis function is the spidery looking
thing illustrated on page 13 of the NEC-2 Theory manual. After the
amplitudes have been determined by the linear system solution, NEC
calls subroutine CABC that determines the total constant, sine and
cosine components on each segment (AIR, AII, BIR, BII, CIR, CII
coefficients). You can use those to plot the smooth current. The
total current at the center of the segment is (A+C), since
sin(k*(s-s0)) is zero there.

NEC-4 is the same, but it uses cos(k*s)-1 in place of cos(k*s) since
that allows better numerical treatment when the segments are
electrically small.

Jerry Burke
LLNL

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