Convergence of the discrete dipole approximation. I. Theoretical analysis

Abstract

We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the latter is in the range of DDA applicability. Moreover, the linear term is significantly smaller for cubically than for non-cubically shaped scatterers. Therefore, for small d errors for cubically shaped particles are much smaller than for non-cubically shaped. The relative importance of the linear term decreases with increasing size, hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive numerical simulations were carried out for a wide range of d. Finally we discuss a number of new developments in DDA and their consequences for convergence.

23 pages, 5 figures; added several corrections according to the published erratum except for Eq.(6) (it was correct in the original paper) and with additional correction in Eq.(96) [$\bar{\mathbf{G}}(...){\mathbf{P}}_i^s-{\bar{\mathbf{G}}}^s(...){\mathbf{P}}_i^p$ instead of $(\bar{\mathbf{G}}(...)-{\bar{\mathbf{G}}}^s(...)){\mathbf{P}}_i^s$]

References in corpus (3)

• Experimental and theoretical study of light scattering by individual mature red blood cells by use of scanning flow cytometry and discrete dipole approximation
• Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy
• Propagation of Electromagnetic Waves on a Rectangular Lattice of Polarizable Points

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• Convergence of a simple discretization of the finite Hilbert transformation