Dynamic load balancing computation of pulses propagating in a nonlinear medium

The aim of this work is to present an efficient parallel approach for the numerical computation of pulse propagation in nonlinear dispersive optical media. We consider the nonlinear Maxwell's equations associated with the modelization of the residual susceptibilities. The numerical approach is based on the finite difference time domain (FDTD) method, developed in a system of coordinates moving with the group velocity of the main pulse. In order to improve the computational delay, the size of the window is defined dynamically. However, for high frequency pulses propagating in a large domain, the computational delay is still penalizing, particularly for 2D and 3D computations. Therefore the parallel technique is a way to develop an efficient approach. We present two parallel strategies, developed in the message passing framework. The first approach is based on a static load distribution and the associated communication structures are very simple. However, in this case the equivalent global load has been increased, compared to the optimal sequential computations. The second parallel approach preserves the global load of the optimal sequential computations. In this case, we have developed a load re-balancing strategy using specific communication structures. The parallel strategies are developed in the one dimensional case and their extension to specific multidimensional cases are straightforward. The efficiency of the parallel approaches is investigated with the computation of the second harmonic generation in a KDP type crystal. In a sequential context, we have investigated the self-focusing process in a nonlinear Kerr medium.