Solving problem on faithful transfer of Sommerfeld radiation condition to a boundary of a bounded in 3D space

Abstract

New statement of the boundary conditions possessing property to suppress a wave, reflected from the boundary is offered to solve non-homogeneous Helmholtz equation in a threedimensional domain with a smooth boundary. And it’s described the boundary condition for the volume potential Helmholtz equation. The idea of construction of boundary value problems for partial differential equations by transfer boundary conditions goes back to [1,Vladimirov’55] where the study boundary value problems for ordinary differential secondorder equation. Also the method of demolition of the boundary conditions was used in [2,Bellman’58] and the review of applications of this method dimensional problems can be found in [3, Bellman and Vasudevan ’86]. Works devoted to the further development of technology transfer boundary conditions in problems for ordinary differential equations are presented in [4, Abramov’81] and [5, Abramov and Konyuhova’85].