Solving coupled 3-D paraxial wave and thermal diffusion equations with mixed-mode parallel computations

The application of parallel computational methods to the modeling of laser light interactions with a thermally self-induced inhomogeneous medium is described. In these processes, laser light dynamically changes the local refractive index through heat absorption, which in-turn alters the beam profile. The mathematical model couples the 3-D heat diffusion and paraxial wave equations resulting in a system of non-linear equations. An explicit, finite-difference method (FDM) for solving the heat diffusion equation is coupled with an implicit FDM solution of the paraxial wave equation. The reasons for choosing these schemes are presented, along with a mixed-mode parallelization method in which OpenMP is used for the explicit solver, and MPI for the implicit solver. Finally, convergence, stability, accuracy and code performance is presented.