A multigrid method for a heat equation with discontinuous coefficients with a special choice of grids
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A new multigrid method is proposed for the solution of systems of linear algebraic equations obtained as a result of the discretization of the initial boundary-value problems for a heat equation with a discontinuous heat conduction coefficient. In the method, a special construction of the next level grid is used, with special treatment of subregions near the discontinuity lines of the heat conduction coefficient. The numerical experiments with a 2D model problem discretized on orthogonal grids demonstrated a high convergence rate for the method and weak dependence of the convergence on the discontinuity jump of the coefficient.
Keywordsparabolic equations multigrid methods speed of convergence of an iterative method
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- 2.N. S. Bakhvalov, N. P. Zhidkov and G. M. Kobelkov, Numerical Methods (Nauka, Moscow, 1987) [in Russian]. http://phys.spb.ru/Stud/Books/index.phpGoogle Scholar
- 9.V. V. Shaidurov, Multigrid Methods for Finite Elements, Mathematics and its Applications, Vol. 318 (Nauka, Moscow, 1989; Springer, Netherlands, 1995).Google Scholar
- 10.Yu. V. Vasilevskii and M. A. Ol’shanskii, Short Course on Multi-Grid Methods and Methods of Domain Decomposition (Mosk. Gos. Univ. im. M. V. Lomonosova, Moscow, 2007) [in Russian].Google Scholar
- 11.A. Brandt, S. F. McCormick, and J. W. Ruge, “Algebraic multigrid (AMG) for sparce matrix equations,” in Sparsity and Its Applications, Ed. by D. J. Evans (Cambridge Univ. Press, Cambridge, UK, 1985), pp. 257–284.Google Scholar
- 12.K. Stüben, “An introduction to algebraic multigrid,” in Multigrid, Ed. by U. Trottenberg, C. Oosterlee, and A. Schüller (Academic, San Diego, CA, 2001), pp. 413–532.Google Scholar
- 17.O. Yu. Milyukova and V. F. Tishkin, “A numerical method for the solution of heat conduction equation on triangular grids using the multigrid techniquies,” Preprint IPM No. 29 (Inst. Prikl. Mat. im. M. V. Keldysha RAN, Moscow, 2011).Google Scholar
- 18.O. Yu. Milyukova and V. F. Tishkin, “Method for the numerical solution of heat transfer equation with discontinuous coefficient based on multigrid techniques,” Preprint IPM No. 64 (Inst. Prikl. Mat. im. M. V. Keldysha RAN, Moscow, 2011).Google Scholar
- 19.Y. Saad, Iterative Methods for Sparse Linear Systems (PWS, Int. Tompson, New York, 1995).Google Scholar