A semi-analytical approach for radiation and scattering problems with circular boundaries
In this paper, the radiation and scattering problems with circular boundaries are studied by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. In implementation, the null-field point can be located on the real boundary owing to the introduction of degenerate kernels for fundamental solution. An adaptive observer system of polar coordinate is considered to fully employ the property of degenerate kernels. For the hypersingular equation, vector decomposition for the radial and tangential gradient is carefully considered. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. Neither hypersingularity in Burton and Miller approach nor the CHIEF concepts were required to deal with the problem of irregular frequencies. Four gains, well-posed model, singularity free, boundary-layer effect free and exponential convergence are achieved by using the present approach. A fast convergence rate in exponential order than algebraic one in BEM stems from the series expansions. Three examples were demonstrated to see the validity of the present formulation and show the better accuracy than BEM.
radiation scattering null-field integral equation degenerate kernel fourier series helmholtz