Accelerating adjoint variable method based photonic optimization with Schur complement domain decomposition.

Area of Science:

• Photonics and Nanotechnology
• Computational Electromagnetics
• Optimization Methods

Background:

• Adjoint variable method and gradient descent are standard for nanophotonic inverse design.
• Current methods often simulate the entire computational domain, even when the design region is small.

Purpose of the Study:

• To improve the computational efficiency of inverse design for nanophotonic structures.
• To integrate the adjoint variable method with domain decomposition techniques.

Main Methods:

• Combining the adjoint variable method with the Schur complement domain decomposition method.
• Restricting simulations to degrees of freedom within the specific design region during optimization steps.

Main Results:

• Demonstrated a novel combination of adjoint method and Schur complement domain decomposition.
• The simulation scope is confined to the design region, reducing computational load.

Conclusions:

• The proposed method significantly enhances the computational efficiency of inverse design for nanophotonic devices.
• This approach offers a more scalable and faster solution for optimizing complex photonic structures.