Solution of wave diffraction problem with integral equations - method

In design and implementation of complex antenna systems the necessity of mathematical modeling of wave diffraction-s process appears. The topical problem is to discount contagion of the surrounding objects. This by-turn generates the necessity of solving wave diffraction problems in areas with complex shapes.

This paper shows the solution of the boundary-value problem of Neumann for the Helmholtz equation on the open screen, which describes the monochromatic wave diffraction. The numerical method is based on expressing the unknown solution as a potential of the double layer. And the three-dimensional problem reduces to two-dimensional boundary integral equation with hypersingular integrals. While quantization this integral equations the system of linear equations appears.

This approach was showed in other works, and the coefficients of the system of linear equations were expressed as a sum of contour and surface integrals, which were counted numerically. In this paper is shown the numerical scheme in which the coefficients of the system of linear equations can be counted analytically. This considerably improves computing potential.