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This article is cited in 3 scientific papers (total in 3 papers)
Computational Mathematics
Iterative realization of finite difference schemes in the fictitious domain method for elliptic problems with mixed derivatives
V. M. Volkov, A. V. Prokonina Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
Abstract:
Development of efficient finite difference schemes and iterative methods for solving anisotropic diffusion problems in an arbitrary geometry domain is considered. To simplify the formulation of the Neumann boundary conditions, the method of fictitious domains is used. On the example of a two-dimensional model problem of potential distribution in an isolated anisotropic ring conductor a comparative efficiency analysis of some promising finite-difference schemes and iterative methods in terms of their compatibility with the fictitious domain method is carried out. On the basis of numerical experiments empirical estimates of the asymptotic dependence of the convergence rate of the bi-conjugate gradient method with Fourier – Jacobi and incomplete LU factorization preconditioners on the step size and the value of the small parameter determining the continuation of the conductivity coefficient in the fictitious domain method are obtained. It is shown, that for one of the considered schemes the Fourier – Jacobi preconditioner is spectrally optimal and allows to eliminate the asymptotical dependence of the iterations number to achieve a given accuracy both on the value of the step size and the value of the small parameter in the fictitious domain method.
Keywords:
finite-difference schemes; elliptic equations; mixed derivatives; iterative methods; fictitious domain method.
Received: 14.10.2018
Citation:
V. M. Volkov, A. V. Prokonina, “Iterative realization of finite difference schemes in the fictitious domain method for elliptic problems with mixed derivatives”, Journal of the Belarusian State University. Mathematics and Informatics, 1 (2019), 69–76
Linking options:
https://www.mathnet.ru/eng/bgumi14 https://www.mathnet.ru/eng/bgumi/v1/p69
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