Convergence of algebraic multigrid based on smoothed aggregation. (English) Zbl 0992.65139

Vaněk, Petr; Brezina, Marian; Mandel, Jan

Numer. Math. 88, No. 3, 559-579 (2001).

The authors prove an abstract convergence estimate for algebraic multigrid with a prolongation defined by disaggregation followed by a smoothing. The construction is described for the case of a general elliptic system. The condition number has polynomial growth in the number of levels.

Reviewer: J.D.P.Donnelly (Oxford)

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
65F35	Numerical computation of matrix norms, conditioning, scaling
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

algebraic multigrid; smoothed aggregation; convergence; elliptic system; condition number