Previous |  Up |  Next


smoothed aggregation; improved convergence bound
The smoothed aggregation method has became a widely used tool for solving the linear systems arising by the discretization of elliptic partial differential equations and their singular perturbations. The smoothed aggregation method is an algebraic multigrid technique where the prolongators are constructed in two steps. First, the tentative prolongator is constructed by the aggregation (or, the generalized aggregation) method. Then, the range of the tentative prolongator is smoothed by a sparse linear prolongator smoother. The tentative prolongator is responsible for the approximation, while the prolongator smoother enforces the smoothness of the coarse-level basis functions.
[1] Bramble, J. H., Pasciak, J. E., Wang, J., Xu, J.: Convergence estimates for multigrid algorithms without regularity assumptions. Math. Comput. 57 (1991), 23-45. DOI 10.1090/S0025-5718-1991-1079008-4 | MR 1079008 | Zbl 0727.65101
[2] Brezina, M., Vaněk, P., Vassilevski, P. S.: An improved convergence analysis of smoothed aggregation algebraic multigrid. Numer. Linear Algebra Appl. 19 (2012), 441-469. DOI 10.1002/nla.775 | MR 2911383 | Zbl 1274.65315
[3] Fraňková, P., Mandel, J., Vaněk, P.: Model analysis of BPX preconditioner based on smoothed aggregations. Appl. Math., Praha 60 (2015), 219-250. DOI 10.1007/s10492-015-0093-7 | MR 3419960
[4] Vaněk, P.: Fast multigrid solver. Appl. Math., Praha 40 (1995), 1-20. MR 1305645 | Zbl 0824.65016
[5] Vaněk, P.: Acceleration of convergence of a two-level algorithm by smoothing transfer operator. Appl. Math., Praha 37 (1992), 265-274. MR 1180605
[6] Vaněk, P., Brezina, M.: Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing. Appl. Math., Praha 58 (2013), 369-388. DOI 10.1007/s10492-013-0018-2 | MR 3083519 | Zbl 1289.65064
[7] Vaněk, P., Brezina, M., Mandel, J.: Convergence of algebraic multigrid based on smoothed aggregations. Numer. Math. 88 (2001), 559-579. DOI 10.1007/s211-001-8015-y | MR 1835471
[8] Vaněk, P., Brezina, M., Tezaur, R.: Two-grid method for linear elasticity on unstructured meshes. SIAM J. Sci Comput. 21 (1999), 900-923. DOI 10.1137/S1064827596297112 | MR 1755171
[9] Vaněk, P., Mandel, J., Brezina, R.: Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 56 (1996), 179-196. DOI 10.1007/BF02238511 | MR 1393006
Partner of
EuDML logo