A memory-reduction scheme for the FFT T-matrix method

A method is presented that reduces the storage requirement of the FFT T-matrix method. It is based on the configuration- and Fourier-domain symmetry relations of the translation coefficients of the transverse spherical multipole fields. Only a minimum set of these matrices needs to be computed and stored. Elements of the full matrices for a given modal combination are rapidly generated using appropriate symmetry relations as the convolution is carried out. The cost of generating the full matrices from the minimum set scales as O(N), while the cost of performing a convolution grows as O(N logN). Thus, the presented memory-reduction scheme increases the CPU time only negligibly. In addition, the method can readily be adapted to an exiting FFT T-matrix code, enabling it to handle larger problems.