Review and accuracy comparison of various permittivity-averaging schemes for material discontinuities in the...

Area of Science:

• Computational electromagnetics
• Numerical methods for wave propagation
• Electromagnetic scattering

Background:

• The finite-difference frequency-domain (FDFD) method is crucial for solving electromagnetic problems.
• Material discontinuities pose accuracy challenges for standard FDFD.
• Averaging techniques are employed to mitigate these challenges.

Purpose of the Study:

• To review, test, and compare the accuracy of various averaging techniques for the FDFD method.
• To implement these techniques using Supercover Digital Differential Analyzer and modified Liang-Barsky algorithms.
• To evaluate performance for both transverse electric (TE) and transverse magnetic (TM) polarizations.

Main Methods:

• Numerical testing of FDFD with Gaussian blurring, volume-polarized effective permittivity, and anisotropic smoothing (AS).
• Implementation using Supercover Digital Differential Analyzer and modified Liang-Barsky algorithms.
• Comparison of accuracy for scattering by homogeneous cylinders (dielectric and metallic) against analytical solutions.

Main Results:

• FDFD with anisotropic smoothing (AS) demonstrates superior accuracy, particularly in satisfying boundary conditions.
• For high-index dielectrics and metals, standard FDFD performs well for parallel field components.
• FDFD (AS) consistently provides higher accuracy for in-plane field components.

Conclusions:

• FDFD (AS) is the most accurate averaging technique for FDFD, especially for complex material interfaces.
• The choice of averaging technique impacts accuracy depending on material properties and polarization.
• Efficient implementation using computer graphics algorithms enhances the applicability of these methods.