Pseudo-spectral methods for atoms in strong magnetic fields

We present a new pseudo-spectral 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 1 per cent 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 × 10⁶ 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 10²-10⁵ times faster than finite-element methods to achieve similar accuracy).