Problem of diffraction by wavy surface: Comparison of numerical methods of solution
Abstract
The problem of diffraction of a wave whose field satisfies the equation (D squared phi/D x squared) + (D squared phi/D y squared) + K squared by a periodically wavy surface is solved by reduction to an integral equation of the first kind for the simplest (Dirichlet) boundary condition squared = 0. The numerical integration is performed independently by three methods. The integralequation method is based on series expansion of the two functions in the integral equation. In the Rayleigh method the reflected field is resolved into diffraction waves all the way to the surface, where the boundary condition is an equallyreflected field and incident field. In the MaselMerrilMiller method the Rayleigh hypothesis and the Dirichlet condition are extended by analytic continuation. Numerical solutions obtained for a sinusoidally wavy surface on an M10 calculator, with the aid of fast Fourier transformation, indicate that highcapacity highspeed computers should make it feasible to advance from approximate methods such as perturbations and physical optics to more rigorous exact mathematical ones.
 Publication:

USSR Rept Electron Elec Eng JPRS UEE
 Pub Date:
 January 1985
 Bibcode:
 1985RpEEE....R...6V
 Keywords:

 Electromagnetic Fields;
 Mathematical Models;
 Numerical Integration;
 Surface Properties;
 Wave Diffraction;
 Computation;
 Differential Equations;
 Dirichlet Problem;
 Integral Equations;
 Series Expansion;
 Communications and Radar