Accelerated solution of the frequency-domain Maxwell's equations by engineering the eigenvalue distribution of the...

Area of Science:

• Electromagnetism
• Computational Physics
• Numerical Analysis

Background:

• Iterative solvers for frequency-domain Maxwell's equations struggle with convergence for deep-subwavelength structures due to operator eigenvalue properties.
• The presence of near-zero eigenvalues complicates numerical solutions in electromagnetic simulations.

Purpose of the Study:

• To introduce a simple and effective method for accelerating the convergence of iterative solvers for Maxwell's equations.
• To address the challenges posed by near-zero eigenvalues in deep-subwavelength electromagnetic simulations.

Main Methods:

• Utilizing the continuity equation to modify the operator.
• Eliminating the high multiplicity of near-zero eigenvalues.
• Ensuring the operator remains nearly positive-definite.

Main Results:

• Achieved accelerated convergence for iterative solvers.
• Demonstrated the elimination of problematic near-zero eigenvalues.
• Explained the mechanism of accelerated convergence through visualization of residual vectors and polynomials.

Conclusions:

• The proposed method offers a significant improvement in computational efficiency for simulating deep-subwavelength structures.
• The technique provides a robust way to handle challenging eigenvalue distributions in electromagnetic modeling.
• This approach enhances the practical applicability of numerical methods in advanced optics and photonics research.