Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

Area of Science:

• Computational Electromagnetics
• Applied Physics
• Materials Science

Background:

• Topology optimization is crucial for designing electromagnetic devices.
• Handling divergence-free conditions in 3D electromagnetic wave propagation presents unique challenges.
• Existing methods often struggle with the complexities of 3D wave behavior.

Purpose of the Study:

• To develop a robust topology optimization procedure for 3D electromagnetic waves.
• To effectively incorporate and satisfy divergence-free conditions for field variables.
• To enable the design of advanced electromagnetic devices through computational methods.

Main Methods:

• Utilized an edge element-based finite-element method (FEM) for discretizing wave equations.
• Implemented divergence-free conditions directly within the FEM framework.
• Employed Helmholtz filtering, threshold projection, and a continuous adjoint method for optimization.
• Developed a regularization technique for element-wise density variable projection.

Main Results:

• Successfully adapted topology optimization for 3D electromagnetic waves.
• Developed distinct nodal and element-wise optimization algorithms based on field formulation (magnetic vs. electric).
• Demonstrated a method to regularize nodal densities into element-wise physical densities for improved filter applicability.

Conclusions:

• The proposed edge element-based FEM approach effectively handles 3D electromagnetic wave topology optimization.
• The method provides a versatile framework adaptable to different field formulations and material properties.
• This work advances the design capabilities for complex electromagnetic devices.