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Strong multiple scattering of the probe in scanning transmission electronmicroscopy (STEM) means image simulations are usually required for quantitativeinterpretation and analysis of elemental maps produced by electron energy-lossspectroscopy (EELS). These simulations require a full quantum-mechanicaltreatment of multiple scattering of the electron beam, both before and after acore-level inelastic transition. Current algorithms scale quadratically and cantake up to a week to calculate on desktop machines even for simple crystal unitcells and do not scale well to the nano-scale heterogeneous systems that areoften of interest to materials science researchers. We introduce an algorithmwith linear scaling that typically results in an order of magnitude reductionin compute time for these calculations without introducing additional error anddiscuss approximations that further improve computational scaling for largerscale objects with modest penalties in calculation error. We demonstrate thesespeed-ups by calculating the atomic resolution STEM-EELS map using the L-edgetransition of Fe, for of a nanoparticle 80 \AA\ in diameter in 16 hours, acalculation that would have taken at least 80 days using a conventionalmultislice approach.

A linear-scaling algorithm for rapid computation of inelastic transitions in the presence of multiple electron scattering