A Finite-Element—Boundary-Integral Method for Scattering and Radiation by Two- and Three-Dimensional Structures

This paper presents a review of a hybrid finite-element—boundary-integral formulation for scattering and radiation by two- and three-dimensional composite structures. In contrast to other hybrid techniques involving the finite-element method, the proposed one is in principle exact, and can be implemented using low, O(N), amounts of storage. This is of particular importance for large-scale applications, and is a characteristic of the boundary chosen to terminate the finite-element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals, which can be evaluated via the fast Fourier transform (FFT), without the need to generate a matrix, thus retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method’s accuracy, efficiency and capability.