The general solution of the 2D electromagnetic scattering problem may be expressed in terms of the so called Cylindrical Waves . In the presence of a plane discontinuity, the solution of the electromagnetic problem may be found by means of the plane-wave expansion of the Cylindrical Waves and by characterizing the discontinuity by means of the reflection coefficient. In this way a numerical solution implies the quadrature of 2D radiation integrals with a highly oscillating kernel, to be solved by means of special quadrature algorithms. In particular, to achieve accurate and fast computation, a special adaptive Gauss-Kronrod quadrature algorithm has been developed. Numerical stability and accuracy tests are presented.
Borghi, R., Frezza, F., Santarsiero, M., Santini, C., Schettini, G. (2000). A quadrature algorithm for the evaluation of a 2D radiation integral with a highly oscillating kernel RID B-3453-2010. JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS, 14(10), 1353-1370 [10.1163/156939300X00121].