Performance analysis of multi-core CPUs and GPU computing on SF- FDTD scheme for third order nonlinear materials and periodic media

Abstract

The Split-Field Finite-Difference Time-Domain (SF-FDTD) scheme is an optimal formulation for modeling periodic optical media by means of a single unit period. The split-field components and the Periodic Boundary Condition (BPC) in the periodic boundaries allow to obtain successful results even with oblique angle of incidence. Under this situation the standard FDTD scheme requires multiple periods and smaller spatial and time resolutions in order to provide accurate results, thus degrading the computational performance of this method. However, considering nonlinear materials in SF-FDTD requires an iterative fixed-point procedure for solving the nonlinear system of equations. Furthermore, complex notation is needed for the split-field components and for correctly apply PBC. Although SF-FDTD is more appropriate for modeling periodic media than the standard FDTD scheme, the addition of nonlinear media degrades the overall performance of this method. In this work, the SF-FDTD formulation for third-order nonlinear materials is implemented taking into consideration parallel hardware architectures. The influence of the fixed-point procedure has been analyzed in both multi-core Central Processing Units (CPUs) and Graphic Processing Units (GPUs).The results show that highly optimized CPU version is competitive amongst GPU computing. Both optimized versions are not dramatically affected by the iterative process due to massive usage of their inner cache memories.