GPU-based optimizations of the boundary integral equation method to solve direct and inverse diffraction grating problems

A numerical solution of the inverse conical diffraction grating problem is considered. The boundary integral equation method is used to solve the direct problem, and a genetic algorithm is applied to solve the grating optimization problem. In this work, the acceleration techniques to the boundary integral equation method are proposed, i.e., computations of linear algebraic systems and Green's functions utilizing the modern graphical processor unit (GPU) devices. This approach reduces the computation time of the algorithm up to four times in our experiments. The dependency of the convergence of a solution from the intrinsic parameters of the genetic algorithm is shown.