Analytical Regularization Method for Rigorous Diffraction Analysis of Knife Edges for TM Waves

Hüseyin Yiğit,Fatih Dikmen

doi:10.3390/mca16030738

Hüseyin Yiğit, Fatih Dikmen

Open Access

https://doi.org/10.3390/mca16030738

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Abstract

A direct full-wave solution via the Analytical Regularization Method (ARM) is proposed for the diffraction problem concerning knife edges under TM wave excitation. This problem is reduced to solving an infinite linear algebraic equation system of the second kind which, in principle, can be solved with arbitrary predetermined accuracy via a truncation procedure.

Highlights

Multi-strip models are helpful for analyzing radio wave propagation over hills or over buildings, where they are widely known as “knife edges” [1]
We start with a rather classical solution scheme for the considered problem which arrives at an SLAE1 in space l2 and use Analytical Regularization Method (ARM) for its regularization, i.e., for the mathematically rigorous construction of an SLAE2 that is equivalent to the original boundary value problem (BVP) in space l2. (The space l2 corresponds best to the space of numbers and operations in a finite precision computational environment, i.e., the computer.) the ARM approach we propose builds on the Orthogonal Polynomials Method (OPM) invented in [14], one and a half decades prior to [17], and on the ARM ideas presented in [12] through [16]
This section includes the results of the numerical experiments done in order to (i) verify the physical relevance of the ARM approach to knife edge diffraction, and (ii) expand on the well-conditioned feature of the resulting SLAE2 obtained by said ARM approach

Summary

Introduction

Multi-strip models are helpful for analyzing radio wave propagation over hills (in rural areas) or over buildings (in urban areas), where they are widely known as “knife edges” [1]. An analytical solution for single-strip diffraction is numerically impractical to implement [2, 3], especially when the model requires multi-strip systems. For this reason and because of the enormous range of the problem’s domain, either physically corrected Fresnel or Kirchhoff diffraction models [4, 5] or high frequency approximations [1, 6] and marching methods applied to the parabolic approximate of the wave equation [7] are used to accurately investigate the related physics.

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