A natural boundary element reduced-dimension model for uniform high-voltage transmission line problem in an unbounded outer domain

The radiation generated around a uniform high-voltage transmission line can be regarded as an external problem in the two dimensional unbounded region. The natural boundary element (NBE) method is one of the most effective approaches to solve the external problem. But the NBE model for the external problem includes a lot of unknowns. Hence, in this paper, we employ a proper orthogonal decomposition to reduce the dimension of finite element space in the NBE model for the external problem. We first develop an NBE reduced-dimension recurrence (NBERDR) model for the external problem. We then use the Hahn–Banach theorem in functional analysis to link the NBE method with the NBERDR method to establish the theory of the existence and stability as well as convergence for the NBERDR solutions. We finally employ some numerical experiments to verify the correctness of theoretical results. As far as we know, there have been no similar reports. Therefore, this paper can facilitate the theoretical study and applications of NBERDR method for the uniform high-voltage transmission line.