  The quasistatic approximation (QSA) is an efficient method of simulating
laser- and beam-driven plasma wakefield acceleration, but it becomes imprecise
if some plasma particles make long longitudinal excursions in a strongly
nonlinear wave, or if waves with non-zero group velocity are present in the
plasma, or the plasma density gradients are sharp, or the beam shape changes
rapidly. We present an extension to QSA that is free from its limitations and
retains its main advantages of speed and reduced dimensionality. The new
approach takes into account the exchange of information between adjacent plasma
layers. We introduce the physical model, describe its numerical implementation,
and compare the simulation results with available analytical solutions and
other codes.
