Fast finite element time domain - Floquet modal absorbing boundary condition modelling of periodic structures using recursive convolution

Finite element time domain (FETD) codes using a Floquet modal absorbing boundary condition to model scattering from periodic structures require the computation of time consuming convolution integrals. In this paper, we propose, for the first time, to reduce this computational burden using recursive convolution. Recursive convolution is based on the ability to accurately approximate functions, over the entire computation time, using a summation of exponential functions. A novel approach, based on the exponential curve fitting facility of the commercially available software MATLAB, is employed. The time efficiency of the developed FETD code based on recursive convolution is demonstrated by comparing its computational speed with that of an FETD code employing standard convolution when modelling plane wave scattering from two-dimensional singly-periodic structures