Time domain adjoint sensitivity analysis of electromagnetic problems with nonlinear media

Area of Science:

• Electromagnetics
• Computational Physics

Background:

• Sensitivity analysis is crucial for optimizing designs in electromagnetics.
• Analyzing nonlinear media presents unique computational challenges.
• Existing methods for linear problems are insufficient for nonlinear systems.

Purpose of the Study:

• To develop a novel theory for wideband adjoint sensitivity analysis in problems involving nonlinear media.
• To demonstrate an efficient method for calculating sensitivities to shape and material parameters.
• To provide a framework applicable to general time-domain objective functions.

Main Methods:

• Proposing a new theory for wideband adjoint sensitivity analysis.
• Utilizing time-domain transmission line modeling (TLM).
• Performing a single, time-varying adjoint simulation to obtain all sensitivities.

Main Results:

• Sensitivities to all shape and material parameters are derived from one adjoint simulation.
• The system matrices for the adjoint simulation are time-varying and determined by the original simulation.
• The proposed method offers an efficient approach for sensitivity analysis.

Conclusions:

• The developed theory provides an efficient and comprehensive method for sensitivity analysis in nonlinear media.
• The approach leverages time-domain TLM for practical implementation.
• The theory is validated through illustrative examples.