Optimizing the discrete-dipole approximation for sequences of scatterers with identical shapes but differing sizes or refractive indices

Abstract

We study scattering of light by small particles with identical shapes but either moderately differing sizes or refractive indices by utilizing the discrete-dipole approximation (DDA). Assuming that accurate DDA solutions are available for either a sequence of sizes or refractive indices, we initialize the iterative conjugate gradient solver for a new size or refractive index by making “educated guesses” of the electric field vectors using classical Lagrange, rational-function, and modified Adams–Bashforth–Moulton extrapolation schemes. In the present pilot study, we assess the initialization schemes for spherical and cubic particles. As compared to the common initialization using the incident electric field, we show that careful extrapolation can significantly reduce the number of iterations. At best, the computing time can decrease by an order of magnitude whereas, typically, the improvement is some tens of percent for sizes comparable to the wavelength. In solving large numbers of single-particle scattering problems, initialization via extrapolation can yield substantial savings in computing time. In particular, the present approach should prove useful when the precise scatterer sizes and refractive indices are unknown, e.g., when interpreting astronomical observations of atmosphereless solar-system objects and experimental measurements.