Efficient Parallel Solution of a Semiconductor Laser Array Dynamics Model

this paper, the Lax-Wendroff scheme for the hyperbolic operator, which inserts a small dissipation term accounting for numerical diffusion is used, while the Hopscotch method is employed for the overall scheme. This hybrid method is a combination of explicit and implicit approximations which reduce the computations, is easy to implement and parallelize, and is also quite fast and stable [5]. In this work, we apply the Hopscotch method and propose an efficient implementation on a MIMD multiprocessor. The algorithm reduces by two the number of messages per cycle and enables the overlapping of these messages with the computations. We benchmark the algorithm for systems of pdes and show that it is considerably faster and more scalable, achieving a near-to-perfect speed-up than its usual implementation on parallel environments. The computer used for the simulation was the PARAMID multiprocessor (16 nodes). Each node is a multiprocessor system in itself consisting of an Intel i860XP processor for the computations and a Transputer T-805 processor as a message passing interface. The paper is organized as follows. In Section 2, the equations which describe the semiconductor laser array and the discretization of the equations using the Hopscotch method are presented. The parallel implementation of the discretized equations and the proposed optimization are shown in Section 3. In Section 4 some results are presented. Finally, some conclusions are summarized in Section 5