High-frequency approximation of the green's function for the Helmholtz equation in an axial nonhomogeneous medium
Tóm tắt
A method is proposed for constructing the field of a point source in an axial two-dimensionally nonhomogeneous medium. The problem is reduced to an integral equation of the 2nd kind. If the frequency ω of the point source is sufficiently high, the equation can be solved by the method of successive approximations. The Neumann series converges in the usual sense for ω>>1 and it is an asymptotic series for ω→∞. The Neumann series also converges in the case of weak dependence of the medium on the coordinate φ.
Tài liệu tham khảo
A. Sommerfeld, Partielle Differentialgleichungen der Physik, Geest & Portig, Leipzig (1996), pp. 194–197.
N. Dunford and J. T. Schwartz, Linear Operators. Spectral Theory [Russian translation], Mir, Moscow (1966).
V. I. Dmitriev and E. G. Saltykov, “Proof of uniform high-frequency asymptotic expansion of the Green's function of the Helmholtz equation,” UMN,46 No. 6(282), 176 (1991).
V. I. Dmitriev and E. G. Saltykov, “Proof of uniform high-frequency asymptotic expansion of the Green's function of the Helmholtz equation,” in: Mathematical Modeling and Solution of Inverse Problems of Mathematical Physics [in Russian], Izd. MGU, Moscow (1994), pp. 125–129.