RWG 基函数 1982 文献
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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION,
VOL.
AP-30, NO.
3,
h4AY
1982
Electromagnetic Scattering by Surfaces
of
Arbitrary Shape
SADASIVA
M.
RAO, DONALD
R.
WILTON,
SENIOR
MEtmER,
IEEE,
AND
ALLEN
w.
GLISSON,
MEMBER, IEEE
409
Abstract-The electric field integral equation (EFIE) is used with
the moment method to develop a simple and efficient numerical
procedure for treating problems
of
scattering by arbitrarily shaped
objects. For numerical purposes,
the
objects are modeled using planar
triangular surfaces patches. Because the EFIE formulation
is
used,
the procedure is applicable to both open and closed surfaces. Crucial
to the numerical formulation is the development of a set of special
subdomain-type basis functions which are defined on pairs of adjacent
triangular patches and yield a current representation free of line
or
point charges at subdomain boundaries. The method
is
applied
to
the
scattering problems of a plane wave illuminated flat square plate, bent
square plate, circular disk, and sphere. Excellent correspondence
between the surface current computed via the present method and
that obtained via earlier approaches
or
exact formulations is
demonstrated in each case.
E
I.
INTRODUCTION
NGINEERS AND researchers in electromagnetics have been
quick to take advantage of the expanding capabilities of
digital computers over the past two decades by developing ef-
fective numerical techniques applicable to a wide variety of
practical electromagnetic radiation and scattering problems.
As new computer developments dramatically increase com-
putational capabilities, however, it becomes less cost effective
to develop highly efficient but specialized codes for treating
certain classes of geometries than to use less efficient but
existing general purpose codes that can handle a wide variety
of problems. For these reasons there has been a growing
in-
terest
in
the use and development of computer codes for
treating scattering by arbitrarily shaped conducting bodies.
To date, the most notable approaches for treating such
problems have used integral equation formulations in con-
junction with the method of moments. The body surface in
these approaches is generally modeled either as a wire mesh-
the so-called wire-grid model-or as a surface partitioned into
smooth or piecewise-smooth patches-the so-called surface
patch model.
The wire-grid modeling approach has been remarkably suc-
cessful in treating many problems, particularly in those re-
quiring the prediction
of
far-field quantities such as radiation
patterns and radar cross sections
[
1
1.
Not only is the con-
nectivity of a wire-grid model easily specified for computer in-
put, but the approach also has the advantage that all numerically
computed integrals in the moment matrix are one dimensional.
Manuscript received May 28, 1980; revised August 6, 1981. This
work was supported by the Rome Air Development Center, Griffiss
AFB, NY, under Contract
No.
F30602-78-C-0148.
S.
hi.
Rao was with Syracuse University, Syracuse, NY, on leave
from the Department of Electrical Engineering, University
of
Mississippi,
University,
MS
38677. He is
now
with the Department of Electrical
Engineering, Rochester Institute of Technology, Rochester, NY 14623.
D. R. Wilton was with Syracuse University, Syracuse, NY, on leave
from the Department
of
Electrical Engineering, University of Mississippi,
University:
MS
38677.
A.
W.
Glisson is with the Department of Electrical Engineering, Uni-
versity of Mississippi, .University, MS 38677.
However, the approach is
not
well suited for calculating near-.
field and surface quantities such as surface current and input
impedance. Some of the problems encountered include the
presence
of
fictitious loop currents in the solution, ill-condi-
tioned moment matrices and incorrect currents at the cavity
resonant frequencies of the scatterer
[2],
and difficulties in in-
terpreting computed wire currents and relating them to equiv-
alent surface currents. The accuracy of wire-grid modeling has
also been questioned
on
theoretical grounds
[
31.
Most of these
difficulties can be either wholly or partially overcome by sur-
face patch approaches, however, which account for much
of
the recent activity in this area.
Several approaches to surface patch modeling have been re-
ported
in
the literature. Knepp and Goldhirsh
[4]
partitioned
a conducting surface into nonplanar quadrilateral patches and
,
employed the magnetic field integral equation (MFIE) to solve
the electromagnetic scattering problem. Albertsen
et
al.
[5]
solved for the current and computed radiation patterns for
satellite structures with attached wire antennas, booms, and
solar panels. They employed a hybrid formulation in which
the MFIE, with planar quadrilateral surface patches, was used
to model the satellite, and the electric field integral equation
(EFIE) was used to treat the wire antennas. Their approach
also forms the basis for the arbitrary surface treatment of the
widely used numerical electromagnetic code (NEC) developed
at the Lawrence Livermore Laboratory
[
61.
Wang
et
a/.
[
71
used an EFIE formulation and modeled relatively complex
surfaces by means of planar rectangular patches. Newman and
Pozar
[8]
extended the use of the well-known piecewise-
sinusoidal basis functions
of
thin-wire theory to the treatment
of surfaces in their EFIE formulation for surfaces with at-
tached wires. Sankar and Tong
[
91
employed planar triangular
patches to model a square plate and pointed out the possibility
of extending their approach to arbitrary bodies. Their formu-
lation, based
on
a variational formula for the current made
stationary with respect to a set of trial functions, is equivalent
to a Galerkin solution
of
the EFIE. Wang
[lo],
[
11
]
em-
ployed planar triangular patches in conjunction with the MFIE,
but used basis functions containing the phase variation of the
incident field in each patch, which unfortunately yield a
mo-
ment matrix dependent
on
the incident field. Jeng and Wexler
[
121 suggested using the MFIE and nonplanar triangles to
model arbitrary surfaces, while Singh and Adams
[
131
pro-
posed the use
of
planar quadrilateral patches and sinusoidal
basis functions in conjunction with the EFIE for the same pur-
pose.
In
arbitrary surface modeling the EFIE has the advantage of
being applicable to both open and closed bodies, whereas the
MFIE applies only to closed surfaces.
On
the other hand, for
arbitrarily shaped objects the EFIE is considerably more diffi-
cult to apply than the MFIE. In fact, of the above authors,
only Wang
et
al.
and Newman and Pozar have actually applied
the EFIE to nonplanar structures-and the use of rectangular
patches limits their approaches to structures with curvature
in
one dimension only.
001
8-926X/82/0500-O409$00.75
O
1982 IEEE
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