# Efficient Computation of High-Order Electromagnetic Field Derivatives for Multiple Design Parameters in FDTD

## TL;DR

This paper presents a highly efficient and accurate computational framework for deriving electromagnetic field derivatives of any order with respect to multiple design parameters using FDTD, requiring minimal simulations.

## Contribution

The authors develop a novel FDTD-based method that computes high-order derivatives with respect to multiple parameters using only a few simulations, ensuring guaranteed accuracy.

## Key findings

- Requires only one or two FDTD simulations for derivatives of any order.
- Provides subtractive cancellation error-free derivatives.
- Enables precise sensitivity analysis and uncertainty quantification.

## Abstract

This paper introduces a new computational framework to derive electromagnetic field derivatives with respect to multiple design parameters up to any order with the Finite-Difference Time-Domain (FDTD) technique. Specifically, only one FDTD simulation is needed to compute the first-order field derivatives with respect to N parameters, while two FDTD simulations are needed to compute the field derivatives with respect to one parameter up to any order. The field derivatives with respect to N parameters up to any order are computed with (N+1) FDTD runs. In addition to its efficiency, this framework is based on a subtractive cancellation error-free approach, providing guaranteed accuracy toward the computation of field derivatives up to any order. With high-order field derivatives available, sensitivity analysis, parametric modelling and uncertainty quantification can be accurately performed.