Abstract:
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.
Fulltext:
PDF file (573 kB)