Development of Vector Parabolic Equation Technique for Propagation in Urban and Tunnel Environments
Final rept. 1 Jun 2004-30 Nov 2008
MASSACHUSETTS UNIV AMHERST MA OFFICE OF GRANT AND CONTRACT ADMIN
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A vector version of parabolic equation PE was used to study the 3D propagation of electromagnetic waves in enclosed structures such as tunnels. The tunnels walls could be lossy, rough, gently curved, or branched. The PE was solved numerically by adopting the Alternate Direction Implicit finite difference technique. Extensive comparisons with experimental results conducted by other researchers were carried out to elaborate on the accuracy and limitations of the technique. The angular correlation of received fields in 2D multipath environments was studied through full-wave Monte Carlo simulations. The results showed that the uncorrelated scattering assumption remains valid for the discrete finite spectra when the scattering objects are distributed randomly and that the correlation among wave components from different angles increases only when the randomness of the scatterer distribution is reduced. Separately, expressions for the transitional probabilities for a four-state random walk FRW that is used to solve the PE in free-space and with material boundaries were derived by using transform techniques. An absorbing boundary condition for use with the FRW was also derived using transform techniques. Appropriateness of the random walk technique for wave propagation problems was demonstrated.
- Numerical Mathematics
- Theoretical Mathematics