EM modelling of arbitrary shaped anisotropic dielectric objects using an efficient 3D leapfrog scheme on unstructured...

Area of Science:

• Computational Electromagnetics
• Numerical Methods
• Materials Science

Background:

• The standard Yee algorithm is a cornerstone of computational electromagnetics due to its simplicity and divergence-free properties.
• However, its application to unstructured meshes and curved interfaces often leads to accuracy losses.
• Modeling anisotropic lossy materials presents a significant challenge for existing schemes.

Purpose of the Study:

• To generalize the Yee algorithm for 3D unstructured meshes, enhancing accuracy for complex geometries.
• To develop a robust numerical scheme capable of modeling electric and magnetic anisotropic lossy materials.
• To address the limitations of the standard Yee scheme in representing curved material interfaces.

Main Methods:

• Adoption of a generalized Yee scheme utilizing a Delaunay primal mesh and its high-quality Voronoi dual.
• Implementation of a 3D dual mesh leapfrog scheme.
• Development of a method to circumvent accuracy losses associated with staircased interface representations.

Main Results:

• The proposed method successfully overcomes accuracy degradation on unstructured meshes.
• The 3D dual mesh leapfrog scheme effectively models both electric and magnetic anisotropic lossy materials.
• Accurate representation of curved material interfaces is achieved, surpassing the standard Yee scheme.

Conclusions:

• The generalized Yee algorithm on 3D unstructured meshes offers a significant improvement in accuracy and capability.
• This approach provides a powerful tool for simulating advanced materials like composites and metamaterials.
• The developed scheme is well-suited for addressing current practical problems in computational electromagnetics.