LAUSR

The numerical approach for computer simulation of femtosecond laser pulse interaction with a semiconductor is considered under the formation of 3D contrast time‐dependent spatiotemporal structures. The problem is governed by the set of nonlinear partial differential equations describing a semiconductor characteristic evolution and a laser pulse propagation. One of the equations is a Poisson equation concerning electric field potential with Neumann boundary conditions that requires fulfillment of the well‐known condition for Neumann problem solvability. The Poisson equation right part depends on free‐charged particle concentrations that are governed by nonlinear equations. Therefore, the charge conservation law plays a key role for a finite‐difference scheme construction as well as for solvability of the Neumann difference problem. In this connection, the iteration methods for the Poisson equation solution become preferable than using direct methods like the fast Fourier transform. We demonstrate the following: if the finite‐difference scheme does not possess the conservatism property, then the problem solvability could be broken, and the numerical solution does not correspond to the differential problem solution. It should be stressed that for providing the computation in a long‐time interval, it is crucial to use a numerical method that possessing asymptotic stability property. In this regard, we develop an effective numerical approach—the three‐stage iteration process. It has the same economic computing expenses as a widely used split‐step method, but, in contrast to the split‐step method, our method possesses conservatism and asymptotic stability properties. Computer simulation results are presented.