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Analysis of Wave Propagation Eigenproblem in Periodic Structures
, Ph.D. Dissertation Sharif University of Technology ; Akbari, Mahmood (Supervisor)
Abstract
The Fourier modal method is one of the most important methods in the analysis of flat periodic structures (gratings). Using this method, the problem of wave propagation in the periodic medium leads to an eigenproblem, in which eigenvalues represent the propagation constants and eigenvector or eigenfunctions determine the filed distribution of the modes. On the other side, considering all the generalizations and modifications reported so far, the Fourier modal method still faces two fundamental problems. First, for problems involving large dielectric constants or high contrasts, the matrix form of the eigenproblem (the modal matrix) can be large, dense, and require a high computational cost....
Exclusive robustness of Gegenbauer method to truncated convolution errors
, Article Journal of Computational Physics ; Volume 452 , 2022 ; 00219991 (ISSN) ; Akbari, M ; Sharif University of Technology
Academic Press Inc
2022
Abstract
Spectral reconstructions provide rigorous means to remove the Gibbs phenomenon and accelerate the convergence of spectral solutions in non-smooth differential equations. In this paper, we show the concurrent emergence of truncated convolution errors could entirely disrupt the performance of most reconstruction techniques in the vicinity of discontinuities. These errors arise when the Fourier coefficients of the product of two discontinuous functions, namely f=gh, are approximated via truncated convolution of the corresponding Fourier series, i.e. fˆk≈∑|ℓ|⩽Ngˆℓhˆk−ℓ. Nonetheless, we numerically illustrate and rigorously prove that the classical Gegenbauer method remains exceptionally robust...