# Accelerating Adjoint Variable Method Based Photonic Optimization with Schur Complement Domain Decomposition

## TL;DR

This paper introduces a novel combination of the adjoint variable method with Schur complement domain decomposition to significantly improve computational efficiency in photonic device optimization by focusing calculations on the design region.

## Contribution

The paper presents a new approach that integrates Schur complement domain decomposition with the adjoint variable method for faster photonic device optimization.

## Key findings

- Reduces computational load by focusing on the design region
- Enables faster convergence in photonic optimization tasks
- Improves efficiency of inverse design processes in nanophotonics

## Abstract

Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total computational domain. Here we show that the adjoint variable method can be combined with the Schur complement domain decomposition method. With this combination, in each optimization step, the simulation only involves the degrees of freedom that are inside the design region. Our approach should significantly improve the computational efficiency of adjoint variable method based optimization of photonic structures.