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It is interesting
to define basis functions on the parametric
space that conform to the curvature of the physical surface. The basis function
proposed by Wilkes and Cha [2] is illustrated in
Figure 2.3. The domain of
the basis function is a pair of adjacent triangles,
and
. The basis function is defined by


where
are local vertices in the parametric u-v space.
is
the area of the triangle
.
This basis function has the following desirable properties:
- There are no line charges along the boundary (including the common
edge of the conjoined triangle pair
and
)
- the component normal to the shared edge is continuous, and thus,
does not generate a line charge accumulation.
- The surface divergence of the basis function, which is proportional
to the surface charge density associated with the basis element is


- When the patch dimensions become small compared to the radius of
curvature, this basis function approaches linearly the RWG (Rao,
Wilton, and Glisson [14]) basis function for a flat triangle.
- This basis function is defined in terms of a general surface
parameterization, and it is not tied to any specific surface
parameterization. This feature has allowed for simple modular
inclusion of several different parameterizations in the method of moment
procedure.
After reviewing the above properties of the function defined in (
), we will
select this function as a basis function to approximate the electric currents induced
on the surface of scatterers. This basis function will be used throughout
this thesis.