  We propose an efficient basis expansion for electron orbitals to describe
real-time electron dynamics in crystalline solids. Although a conventional grid
representation in the three-dimensional Cartesian coordinates works robustly,
it requires a large amount of computational resources. To reduce computational
costs, we consider an expansion using basis functions with a truncation. A
simple choice employing eigenstates of the ground state Hamiltonian with a
truncation turned out to be useless. We have found that adding occupied
eigenstates of nearby $k$-points to the truncated basis functions composed of
eigenstates of the original $k$-point is crucially important. We demonstrate
the usefulness of the method for linear and nonlinear electron dynamics
calculations in crystalline SiO$_2$.
