Optimizing GPU Performance in Cylindrical FDTD Simulations

Abstract

Simulating large-area metasurfaces presents a major computational challenge due to their fine structural features and large physical dimensions. Traditional full-wave methods, such as finite-difference time-domain (FDTD), become infeasible for such problems due to excessive memory and runtime requirements. To address this, several approximate techniques have been developed, including the localized perturbation approximation (LPA), overlapping-domain approximation (ODA), and zoned discrete axisymmetry (ZDA), each balancing accuracy and efficiency for different metasurface geometries.

In this thesis, we focus on ZDA, a method tailored for metasurfaces with rotational symmetry. By expressing electromagnetic fields as a sum of angular modes and discretizing the radial domain into concentric zones, ZDA reduces a 3D problem to a series of much smaller and fewer simulations. This dimensionality reduction enables accurate modeling of freeform optical devices with fine resolution using modest computational resources. We implement this approach via a GPU-accelerated FDTD solver in cylindrical coordinates, enabling scalable and efficient simulation of broadband, high-performance metasurfaces. Our results demonstrate that symmetry-aligned simulation strategies such as ZDA can unlock practical design workflows for metasurfaces previously beyond reach. My personal work though was mostly on accelerating our FDTD code using the power given by the GPUs.