Method of Continued Boundary Conditions

Application of the method of continued boundary conditions to the solution of the problems of wave diffraction on various types of scatterers with complex structure

“…where observation points 𝑀 (r ± ) belong to contours 𝑆 ± 𝛿 and point 𝑀 (r) ∈ 𝑆 and it is denoted that 𝑈 = 𝑈 − . Note that the contours that are separated from 𝑆 by a fairly small distance 𝛿 are most often chosen as 𝑆 ± 𝛿 ; i.e., equidistant contours are considered [1,10]. Further, to solve system of equations ( 3), ( 4), the Krylov-Bogolyubov method is used.…”

“…where cos 𝛾 0 (𝜃, 𝜑) = sin 𝜃 sin 𝜃 0 cos 𝜑 + cos 𝜃 cos 𝜃 0 . According to the standard scheme of the MCBC, we then substitute formula (9) into boundary condition (6) imposed on the auxiliary surface 𝑆 𝛿 shifted by a small distance 𝛿 from the surface 𝑆 [1,10,14]. As a result, the problem will be reduced to solving a two-dimensional Fredholm integral equation of the first kind, which has the following form in spherical coordinates: 17) was solved using a piecewise-constant approximation of an unknown function with subsequent application of the Krylov-Bogolyubov method.…”

“…In this paper, the method of continued boundary conditions (MCBC) [1] is considered. In MCBC, the surface on which the observation point is chosen, denoted by 𝑆 𝛿 , is located outside the scatterer at some sufficiently small distance 𝛿 from its boundary 𝑆, which is the carrier of the (auxiliary) current and over which integration is carried out.…”