The time-dependent Maxwell’s equations are solved for mobile device applications using a multilevel-multigrid finite-difference time-domain (FDTD) method. For three-dimensional models that simulate system level details of mobile devices, the smallest features are in the nanometre (10
− − 9
m) range, leading to a time-step size in the attosecond (10
− − 18
s) range. The feature sizes of mobile devices are in the centimetre (10
− − 2
m) range, while for health and safety studies that include human models features are in the metre range.