Choice of the perfectly matched layer boundary condition for frequency-domain Maxwell’s equations solvers

• Published in: Journal of computational physics Vol. 231; no. 8; pp. 3406 - 3431
• Main Authors: Shin, Wonseok, Fan, Shanhui
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.04.2012; Elsevier
• Subjects: Boundary conditions; Computational techniques; Condition number; Convergence; Exact sciences and technology; Finite-difference frequency-domain method; Finite-element method; Iterative methods; Mathematical analysis; Mathematical methods in physics; Matrices; Maxwell's equations; Perfectly matched layer; Perfectly matched layers; Physics; Preconditioner; Preconditioning; Solvers; Finite-difference frequency-domain method; Perfectly matched layer; Preconditioner; Maxwell’s equations; Finite-element method; Condition number; Iterative methods; Frequency domain method; Maxwell's equations; Maxwell equations; Calculation methods; Convergence speed; Finite element method; Calculation; Performance; Preconditioning; Boundary layers
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2012.01.013

We show that the performance of frequency-domain solvers of Maxwell’s equations is greatly affected by the kind of the perfectly matched layer (PML) used. In particular, we demonstrate that using the stretched-coordinate PML (SC-PML) results in significantly faster convergence speed than using the uniaxial PML (UPML). Such a difference in convergence behavior is explained by an analysis of the condition number of the coefficient matrices. Additionally, we develop a diagonal preconditioning scheme that significantly improves solver performance when UPML is used.