Expansion of Integral Equations Arising in Scattering Theory
PENNSYLVANIA STATE UNIV UNIVERSITY PARK APPLIED RESEARCH LAB
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The key to solving a general scattering problem is first to obtain a solution for the relevant field parameter evaluated on the scattering surface. For all but very simple cases, which can be treated numerically, this entails an approximation which thence limits the region of applicability of the result obtained. This article has considered three different formulations of the boundary integral equation for plane wave incidence on a periodic pressure release surface. In the low-frequency limit, the three equations yield different results. Only Uretskys integral equation yields physically acceptable reflection coefficients and these are identical to those obtained using the Rayleigh or small wave height approximation. Whereas the Rayleigh approximation is in good agreement with exact solutions for scattering at low frequencies and grazing angles, when the frequency or grazing angle is significantly increased, this approximation yields scattering strength predictions considerably higher than those experimentally observed. It appears that Uretskys integral equation is the only viable starting point for developing a general scattering theory applicable over a greater range of parameters.
- Numerical Mathematics