Finite-difference schemes and iterative methods for multidimensional elliptic equations with mixed derivatives
https://doi.org/10.29235/1561-2430-2018-54-4-454-459
Abstract
Finite difference schemes and iterative methods of solving anisotropic diffusion problems governing multidimensional elliptic PDE with mixed derivatives are considered. By the example of the test problem with discontinuous coefficients, it is shown that the spectral characteristics of the finite difference problem and the efficiency of their preconditioning depend on the mixed derivatives approximation method. On the basis of the comparative numerical analysis, the most adequate approximation formulas for the mixed derivatives providing a maximum convergence rate of the bi-conjugate gradients method with the incomplete LU factorization and the Fourier – Jacobi preconditioners are discovered. It is shown that the monotonicity of the finite difference scheme does not guarantee advantages at their iterative implementation. Moreover, the grid maximum principle is not provided under the conditions of essential anisotropy.
About the Authors
V. M. Volkov
Belarusian State University
Belarus
D. Sc. (Physics and Mathematics), Professor
Belarus
D. Sc. (Physics and Mathematics), Professor
A. U. Prakonina
Belarusian State University
Belarus
Senior Lecturer
Belarus
Senior Lecturer
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