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

##### 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
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