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Abstract <p>The paper considers various types of Chebyshev’s iterative methods for the solution of difference approximations of elliptic equations on voxel meshes. A general description of Chebyshev’s methods is given. The error structure of the methods and the method for eliminating the numerical error are presented. As part of the study, the effectiveness of using methods for solving systems of linear equations obtained by discretizing the Laplace equation with constant and nonconstant coefficients on voxel grids is compared. This study proposes a number of modifications of the Chebyshev method. Among them, a variant of the Chebyshev method is proposed for solving systems of linear equations with a clustered spectrum. Modifications of methods in cases where the boundaries of the spectrum are precisely known and in the opposite case are compared.</p>

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Application of Chebyshev’s Methods for Solving Elliptic Equations on Voxel Meshes

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • B. V. Kritskiy

摘要

Abstract

The paper considers various types of Chebyshev’s iterative methods for the solution of difference approximations of elliptic equations on voxel meshes. A general description of Chebyshev’s methods is given. The error structure of the methods and the method for eliminating the numerical error are presented. As part of the study, the effectiveness of using methods for solving systems of linear equations obtained by discretizing the Laplace equation with constant and nonconstant coefficients on voxel grids is compared. This study proposes a number of modifications of the Chebyshev method. Among them, a variant of the Chebyshev method is proposed for solving systems of linear equations with a clustered spectrum. Modifications of methods in cases where the boundaries of the spectrum are precisely known and in the opposite case are compared.