Application of Chebyshev methods for solving elliptic equations on voxel meshes

The paper considers various types of Chebyshev iterative methods for 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 work, a comparison of the effectiveness of using methods for solving systems of linear equations obtained by discretizing the Laplace equation with constant and non-constant coefficients on voxel grids was made. The work 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. A comparison of modifications of methods in cases where the boundaries of the spectrum are precisely known and in the opposite case was made.