Analysis of aggregation-based multigrid. (English) Zbl 1163.65092

Muresan, Adrian C.; Notay, Yvan

SIAM J. Sci. Comput. 30, No. 2, 1082-1103 (2008).

The authors investigate an aggregation-based multigrid method with standard piecewise constant like prolongation. They also provide a Fourier analysis for a model two-dimensional anisotropic problem. Near grid-independent convergence is obtained for the \(W\)-cycle scheme accelerated by a recursive use of the conjugate gradient algorithm.

Reviewer: Constantin Popa (Constanţa)

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
65F50	Computational methods for sparse matrices
35J25	Boundary value problems for second-order elliptic equations
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65F35	Numerical computation of matrix norms, conditioning, scaling

Keywords:

multigrid; aggregation; Fourier analysis; Krylov subspace method; conjugate gradient; preconditioning; stability; convergence; \(W\)-cycle scheme