Laser-atom interactions: a multiresolution approach

Isolated, attosecond laser pulses have allowed real-time measurement and control of electrons on atomic time scales. We present an explicit time-evolution scheme solving the time dependent Schro ̈dinger equation, which employs an adaptive, discontinuous, spectral-element basis that automatically refines to accommodate the requested precision providing efficient computation across many length scales in multiple dimensions. This method is illustrated through time evolution studies of single electron atoms and molecular ions in three and four dimensions under the influence of intense, few-cycle laser pulses.