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HALF-SPACE ANALYSIS OF THE DEFECT-CORRECTION METHOD FOR FROMM DISCRETIZATION OF CONVECTION.

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Title: HALF-SPACE ANALYSIS OF THE DEFECT-CORRECTION METHOD FOR FROMM DISCRETIZATION OF CONVECTION.
Authors: Diskin, Boris1 bdiskin@icase.edu, Thomas, James I.1 j.l.thomas@larc.nasa.gov
Source: SIAM Journal on Scientific Computing. 2000, Vol. 22 Issue 2, p633-655. 23p.
Subjects: Defect correction methods (Numerical analysis), Numerical analysis, Approximation theory, Iterative methods (Mathematics), Stochastic convergence, Mathematical functions, Asymptotic expansions
Abstract: A novel, comprehensive, discrete, half-space analysis for the defect-correction method has been developed. This analysis plays the same role for nonelliptic-problem solvers as the full-space Fourier mode analysis plays for elliptic-problem solvers. Numerical simulations confirm the accuracy of the half-space analysis. The following important findings about the defect-correction method applied to the Fromm discretization of the two-dimensional convection equation are reported: 1. The initial convergence rate of the defect-correction method is principally a function of the relative accuracy of the operators involved in the defect-correction iterations. 2. The asymptotic convergence rate is about 0.5 per defect-correction iteration. 3. If the driver operator is first-order accurate, then the initial convergence rates may be slow. The number of iterations required to get into the asymptotic convergence regime or/and to converge the algebraic error below the discretization-error level can be proportional to h- 1/3. This h-dependent delay is a multidimensional phenomenon—it cannot be observed in one-dimensional problems, and it disappears in the case of close alignment between the grid and the convection equation characteristic. 4. If the driver operator is second-order accurate, the defect-correction solver demonstrates the asymptotic convergence rate from the very beginning. Only one defect-correction iteration is required to converge algebraic error substantially below the discretization-error level. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: HALF-SPACE ANALYSIS OF THE DEFECT-CORRECTION METHOD FOR FROMM DISCRETIZATION OF CONVECTION.
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  Data: A novel, comprehensive, discrete, half-space analysis for the defect-correction method has been developed. This analysis plays the same role for nonelliptic-problem solvers as the full-space Fourier mode analysis plays for elliptic-problem solvers. Numerical simulations confirm the accuracy of the half-space analysis. The following important findings about the defect-correction method applied to the Fromm discretization of the two-dimensional convection equation are reported: 1. The initial convergence rate of the defect-correction method is principally a function of the relative accuracy of the operators involved in the defect-correction iterations. 2. The asymptotic convergence rate is about 0.5 per defect-correction iteration. 3. If the driver operator is first-order accurate, then the initial convergence rates may be slow. The number of iterations required to get into the asymptotic convergence regime or/and to converge the algebraic error below the discretization-error level can be proportional to h- 1/3. This h-dependent delay is a multidimensional phenomenon—it cannot be observed in one-dimensional problems, and it disappears in the case of close alignment between the grid and the convection equation characteristic. 4. If the driver operator is second-order accurate, the defect-correction solver demonstrates the asymptotic convergence rate from the very beginning. Only one defect-correction iteration is required to converge algebraic error substantially below the discretization-error level. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1137/S1064827599358637
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      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Approximation theory
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      – SubjectFull: Iterative methods (Mathematics)
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      – SubjectFull: Stochastic convergence
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      – SubjectFull: Mathematical functions
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      – TitleFull: HALF-SPACE ANALYSIS OF THE DEFECT-CORRECTION METHOD FOR FROMM DISCRETIZATION OF CONVECTION.
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              Text: 2000
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