DocumentCode :
1287610
Title :
Transparent boundary conditions for parabolic equation solutions of radiowave propagation problems
Author :
Levy, Mireille F.
Author_Institution :
Radio Commun. Res. Unit, Rutherford Appleton Lab., Chilton, UK
Volume :
45
Issue :
1
fYear :
1997
fDate :
1/1/1997 12:00:00 AM
Firstpage :
66
Lastpage :
72
Abstract :
Perfectly transparent boundary conditions are derived for truncating the integration domain when solving radiowave propagation problems with a parabolic equation (PE) method. The boundary conditions are nonlocal: they are expressed as a convolution integral involving the field at all previous ranges. The convolution kernel is matched to the refractive index vertical gradient at the boundary. The boundary conditions include an incoming energy term which can model an arbitrary incident field. In particular, they may be used with plane-wave incidence, or with a point-source located below or above the domain boundary. If required, the solution can be extended to heights above the boundary with a generalized horizontal PE method. Closed-form solutions for the incoming energy term are given for plane-wave incidence and for Gaussian sources when the refractive index above the boundary is constant or linear. The resulting finite-difference algorithms provide efficient solutions to problems involving airborne sources. Numerical examples are given, showing excellent agreement with a pure split-step/Fourier PE algorithm
Keywords :
Gaussian processes; boundary-value problems; finite difference methods; integration; parabolic equations; radiowave propagation; refractive index; Gaussian sources; airborne sources; arbitrary incident field; boundary conditions; closed-form solutions; convolution integral; convolution kernel; finite-difference algorithm; generalized horizontal PE method; incoming energy term; integration domain; parabolic equation solutions; plane-wave incidence; point-source; radiowave propagation problems; refractive index vertical gradient; transparent boundary conditions; Boundary conditions; Boundary value problems; Closed-form solution; Convolution; Finite difference methods; Integral equations; Kernel; Radio propagation; Radiowave propagation; Refractive index;
fLanguage :
English
Journal_Title :
Antennas and Propagation, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-926X
Type :
jour
DOI :
10.1109/8.554242
Filename :
554242
Link To Document :
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