论文信息 - The contraction number of a multigrid method for solving the Poisson equation

The contraction number of a multigrid method for solving the Poisson equation

SummaryThe treatment of a multigrid method in the framework of numerical analysis elucidates that regularity of the solution is not necessary for the convergence of the multigrid algorithm but only for fast convergence. For the linear equations which arise from the discretization of the Poisson equation, a convergence factor 0,5 is established independent of the shape of the domain and of the regularity of the solution.

D. Braess

[1] Lothar Collatz,et al. Numerische Behandlung von Differentialgleichungen , 1948 .

[2] J. Gillis,et al. Matrix Iterative Analysis , 1961 .

[3] James E. Gunn. THE SOLUTION OF ELLIPTIC DIFFERENCE EQUATIONS BY SEMI-EXPLICIT ITERATIVE TECHNIQUES* , 1965 .

[4] I. Babuška,et al. Mathematical problems of computational decisions in the finite element method. Technical report TR-426 , 1975 .

[5] R. Nicolaides. On the ² convergence of an algorithm for solving finite element equations , 1977 .

[6] T. Meis,et al. Numerische Behandlung partieller Differentialgleichungen , 1978 .

[7] R. A. Nicolaides,et al. On some theoretical and practical aspects of multigrid methods , 1979 .

[8] P. Wesseling,et al. The rate of convergence of a multiple grid method , 1980 .

[9] Meis, Th./Marcowitz, U., Numerische Behandlung partieller Differentialgleichungen. Hochschultext. Berlin-Heidelberg-New York, Springer-Verlag 1978. VIII, 452 S., 31 Abb., DM 38,–. US $ 20.90 , 1980 .

[10] Randolph E. Bank,et al. An optimal order process for solving finite element equations , 1981 .