  We investigate the high harmonic generation (HHG) from solids by simulating
the dynamics of a single active electron in periodic potentials. The
corresponding time-dependent Schr\"odinger equations (TDSE) are solved
numerically by using B-spline basis sets in coordinate space. The energy band
structure and wave vectors can be directly retrived from the eigenfunctions.
The harmonic spectra obtained agree well with the results simulated by TDSE in
$k$ space using Bloch states and show a two-plateau structure. Both of the
cutoff energies of the two plateaus in the harmonic spectrum scale linearly
with the field strength. We also study HHG driven by intense few-cycle laser
pulses and find that the cutoff energy of the harmonic spectrum is as sensitive
to the changes of the carrier envelope phase, as to HHG from gas samples, which
suggests recollision pictures in HHG as found by recent experiments (Nature
{\bf 522}, 462 (2015)).
