nonstationary wave fields
method of discrete sources
The two-dimensional problem of diffraction of electromagnetic impulse propagating in planar waveguide on an obstacle inside the waveguide is considered. The solution is based on the presentation of the field in terms of Fourier integral. Thus the initial nonstationary problem is reduced to the stationary one. The latter problem is solved by the modified method of discrete sources. The system of integral equation relative to unknown currents on the auxiliary contour inside the contour of the body cross-section is derived. The kernels of this system are defined with the Green’s function of the waveguide. The Green’s function is calculated by integration in the complex plane. The developed method of calculation of the Green’s function permits to evaluate it with high accuracy over a wide range of variation of its arguments.
The wave field in time domain is calculated with technique based on the discrete Fourier transform. The method permits to estimate the field directly for many moments. This fact is very useful for calculations. Computing the field in far zone we faced with the problem of evaluation of the Fourier transform for the fast oscillating function. In order to overcome this difficulty the fast oscillating multiplier has been isolated from the integrand.
To test the method the residual of boundary condition at the contour of the body cross-section is calculated. We have considered the scatterer with circular and elliptic cross-section. It has been shown that the residual does not exceed 10-3. Energy conservation law fulfillment check is also made. The law of energy conservation is fulfilled with an error about 10-5. The time dependences of the field in several points near the body are obtained. It has been shown that the backward signal is composed from the impulses reflected from the front and back walls of the scatterer. The time dependences of the field in far zone have been also calculated.