Implementation of High-Order On-Surface Radiation Boundary Conditions

Electromagnetic scattering problems that involve far-field radiation patterns and the calculation of total currents induced in a perfect conductor can be solved using local radiation boundary conditions. These local conditions are often imposed on a domain enclosing the scatterer, and the typical finite-element methods are incorporated so that the well-posedness of the modified problems encompassing the local radiation boundary conditions is preserved. Much effort in recent years has been devoted to attempts to construct higher order far-field conditions, so that the solution accuracy can be improved. In this article, we avoid extensive computations and bring the radiation boundary on the scatter's surface itself. This procedure is known as the on-surface radiation boundary condition (OSRBC). The limitations in the past have been the implementable order of the OSRBC. Nevertheless, the key feature of the OSRBC to calculate the relevant quantities for engineers is the normal derivative of the solution on the OSRBC. This article introduces a new method for calculating the normal derivative of the electric field on the surface of a scatterer of the known shape. The method is based on a formulation of the boundary conditions through a recursive sequence of differential operators. The numerical implementation of this formulation allows one to extract a relation which is then used to solve for the quantity of interest, such as radar cross section.