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Reflection/diffraction ray methods
Geometrical optics (GO), the geometrical
theory of diffraction (GTD) and its improved derivatives GTD/UTD (Uniform
theory of diffraction), GTD/UAT (uniform asymptotic theory of diffraction)
are capable in principle of handling 3D-problems if all the canonical contributions
are treated correctly, i.e. single and multiple reflections from surfaces,
diffractions from wedges etc. Approximate formulas for the canonical 3D-problem
of general wedges with different non-metallic materials and of tips exist
meanwhile. The objects are described (mostly) by locally plane patches
which must be large compared to the wavelength. This method is a so-called
asymptotic method where the amount of effort does not depend on the size
of the problem, if the size is large compared to the wavelength. However,
in real cases not all of the possible rays can be taken into account and
discontinuities occur which yield locally increased errors.
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Current integration methods
Physical optics (PO), Kirchhoff
integration and its improvements assume the required current on a metallic
surface by deriving that from the incoming magnetic field. The objects
have to be in the farfield from each other and from the antenna. The objects
have to be large compared to the wavelength and rim currents need a special
(difficult and approximate) treatment, (i.e. the Physical theory of diffraction
PTD). The field in the shadow region of a real object cannot be calculated
in a general sense because no diffraction around the rim is taken into
account. Interactions between objects and 3D-ground and non-metallic objects
are almost impossible to be handled. Due to the integration technique the
resulting curves are always smooth and without discontinuities. However,
that does not mean by itself that the results are accurate.
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Integral equation method
The method of moments (MoM) is a
candidate under this heading . It is well suited and a rigorous method
for all arbitrary shaped wire type objects and those objects which can
be described by wire modeling. Extensions allow the treatment of two-dimensional
currents on patches which can be composed to closed surfaces. The numerical
procedure transfers the electromagnetic problem (i.e. an integral equation)
by the segmentation into an algebraic equation matrix which can be inverted
yielding the unknown currents. The method requires a drastically increasing
storage compared to the above mentioned methods. Hence, due to practical
aspects, the integral equation method is restricted to small to medium
problems or, in special cases, as part of a hybrid method. A particular
case for this method is the analysis of the effects of cranes and aircraft
on airports on the ILS. Extensions of this method exist which can handle
to some extent wires and dielectric materials.
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Spatial grid discretisation methods
Finite element (FE), Finite difference
(FD) and Finite integration (FI) are methods whereby the spatial currents
are calculated in small spatial volumes which are interacting on the base
of field and material parameters. This method is the most general but requires
a spatial discretisation depending on the wavelength and on the geometry
(material, shape). A matrix inversion takes place in principle. However,
the inversion can be performed very efficiently due to the nature of the
matrix elements. As a conclusion this class of methods is not suitable
for navaids except for solving details as part of the hybrid method.
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Parabolic equation method
The Parabolic Equation (PE) is a
very modern special numerical method and is specially suited for wave propagation
over ground and buildings. It is presently restricted to 2D problems and
appplied, e.g., to the fieldstrength calculation of humped runways. It
is not yet a generally applicable method since most problems involve 3D-geometries.
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Hybrid methods, which
combine two or more of the aforementioned methods.
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Special methods for the
analysis of details, e.g. of snow effects on the image type glideslope
treated as a multilayer problem.
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