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On convergence and performance of iterative methods with fourth-order compact schemes

โœ Scribed by Jun Zhang

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
508 KB
Volume
14
Category
Article
ISSN
0749-159X

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โœฆ Synopsis

We study the convergence and performance of iterative methods with the fourth-order compact discretization schemes for the one-and two-dimensional convection-diffusion equations. For the one-dimensional problem, we investigate the symmetrizability of the coefficient matrix and derive an analytical formula for the spectral radius of the point Jacobi iteration matrix. For the two-dimensional problem, we conduct Fourier analysis to determine the error reduction factors of several basic iterative methods and comment on their potential use as the smoothers for the multilevel methods. Finally, we perform numerical experiments to verify our Fourier analysis results.

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