Spectral methods for the computation of discontinuous solutions

Gruberger, Nira

doi:10.1007/bf01061267

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…Apart from mollifiers, there are other methods in the literature to mitigate the effects of Gibbs phenomenon and improve the accuracy of the spectral methods. Nira Gruberger [14] introduced new post‐processing filters for Fourier and Chebyshev spectral methods by considering corresponding approximations of the Dirac delta function. With a marginal modification of the filter at the point of discontinuity, the results have improved significantly for Burgers' equation but disappointing in the case of astrophysical problem.…”

Section: Introductionmentioning

confidence: 99%

Mollification of Fourier spectral methods with polynomial kernels

Puthukkudi,

Godavarma Raja

2024

Math Methods in App Sciences

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Many attempts have been made in the past to regain the spectral accuracy of the spectral methods, which is lost drastically due to the presence of discontinuity. In this article, an attempt has been made to show that mollification using Legendre and Chebyshev polynomial based kernels improves the convergence rate of the Fourier spectral method. Numerical illustrations are provided with examples involving one or more discontinuities and compared with the existing Dirichlet kernel mollifier. Dependence of the efficiency of the polynomial mollifiers on the parameter is analogous to that in the Dirichlet mollifier, which is detailed by analyzing the numerical solution. Further, they are extended to linear scalar conservation law problems.

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Section: Introductionmentioning

confidence: 99%

Mollification of Fourier spectral methods with polynomial kernels

Puthukkudi,

Godavarma Raja

2024

Math Methods in App Sciences

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show abstract

“…Apart from mollifiers, there are other methods in the literature to mitigate the effects of Gibbs phenomenon and improve the accuracy of the spectral methods. Nira Gruberger 6 introduced new post-processing filters for Fourier and Chebyshev spectral methods by considering corresponding approximations of the Dirac delta function. With a marginal modification of the filter at the point of discontinuity, the results have improved significantly for Burgers' equation but disappointing in the case of astrophysical problem.…”

Section: Introductionmentioning

confidence: 99%

Mollification of Fourier Spectral Methods with Polynomial Kernels

Chandhini

Megha

2023

Preprint

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Many attempts have been made in the past to regain the spectral accuracy of the spectral methods, which is lost drastically due to the presence of discontinuity. In this article, an attempt has been made to show that mollification using Legendre and Chebyshev polynomial based kernels improves the convergence rate of the Fourier spectral method. Numerical illustrations are provided with examples involving one or more discontinuities and compared with the existing Dirichlet kernel mollifier. Dependence of the efficiency of the polynomial mollifiers on the parameter P is analogous to that in the Dirichlet mollifier, which is detailed by analysing the numerical solution. Further, they are extended to linear scalar conservation law problems.

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Two algorithms for periodic extension on uniform grids

Gruberger

Levin

2020

Numer Algor

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Spectral methods for the computation of discontinuous solutions

Cited by 3 publications

References 10 publications

Mollification of Fourier spectral methods with polynomial kernels

Mollification of Fourier spectral methods with polynomial kernels

Mollification of Fourier Spectral Methods with Polynomial Kernels

Two algorithms for periodic extension on uniform grids

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