  We introduce a new approach to the numerical simulation of Scanning
Transmission Electron Microscopy images. The Lattice Multislice Algorithm (LMA)
takes advantage of the fact that electron waves passing through the specimen
have limited bandwidth and therefore can be approximated very well by a
low-dimensional linear space spanned by translations of a well-localized
function $u$. Just like in the PRISM algorithm recently published by C. Ophus,
we utilize the linearity of the Schr\"odinger equation, but perform the
approximations with functions that are well localized in real space instead of
Fourier space. This way, we achieve a similar computational speedup as PRISM,
but at a much lower memory consumption and reduced numerical error due to
avoiding virtual copies of the probe waves interfering with the result. Our
approach also facilitates faster recomputations if local changes are made to
the specimen such as changing a single atomic column.
