  We present a new pseudospectral algorithm for the calculation of the
structure of atoms in strong magnetic fields. We have verified this technique
for one, two and three-electron atoms in zero magnetic fields against
laboratory results and find typically better than one-percent accuracy. We
further verify this technique against the state-of-the-art calculations of
hydrogen, helium and lithium in strong magnetic fields (up to about $2\times
10^{6}$ T) and find a similar level of agreement. The key enabling advantages
of the algorithm are its simplicity (about 130 lines of commented code) and its
speed (about $10^2-10^5$ times faster than finite-element methods to achieve
similar accuracy).
