A Stable FDTD Method with Embedded Reduced-Order Models

TL;DR

This paper introduces a stable FDTD method that embeds reduced-order models to improve computational efficiency for complex geometries while ensuring stability up to the CFL limit.

Contribution

A systematic approach to generate and embed reduced models into FDTD simulations with guaranteed stability and extended CFL limits.

Findings

Method guarantees stability up to the CFL limit of the fine mesh.

Numerical tests confirm the stability and acceleration of multiscale FDTD.

Reduced models are applicable to inhomogeneous and lossy materials.

Abstract

The computational efficiency of the Finite-Difference Time-Domain (FDTD) method can be significantly reduced by the presence of complex objects with fine features. Small geometrical details impose a fine mesh and a reduced time step, significantly increasing computational cost. Model order reduction has been proposed as a systematic way to generate compact models for complex objects, that one can then instantiate into a main FDTD mesh. However, the stability of FDTD with embedded reduced models remains an open problem. We propose a systematic method to generate reduced models for FDTD domains, and embed them into a main FDTD mesh with guaranteed stability up to the Courant-Friedrichs-Lewy (CFL) limit of the fine mesh. With a simple perturbation technique, the CFL of the whole scheme can be further extended beyond the fine grid's CFL limit. Reduced models can be created for arbitrary domains containing inhomogeneous and lossy materials. Numerical tests confirm the stability of the proposed method, and its potential to accelerate multiscale FDTD simulations.