Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
smoothed aggregation; parallel preconditioner; BPX preconditioner
smoothed aggregation; parallel preconditioner; BPX preconditioner
Summary:
We prove nearly uniform convergence bounds for the BPX preconditioner based on smoothed aggregation under the assumption that the mesh is regular. The analysis is based on the fact that under the assumption of regular geometry, the coarse-space basis functions form a system of macroelements. This property tends to be satisfied by the smoothed aggregation bases formed for unstructured meshes.
References:
[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] Bramble, J. H., Pasciak, J. E., Xu, J.: Parallel multilevel preconditioners. Math. Comput. 55 (1990), 1-22. DOI 10.1090/S0025-5718-1990-1023042-6 | MR 1023042 | Zbl 0725.65095
[3] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems. Studies in Mathematics and Its Applications 4 North-Holland Publishing Company, Amsterdam (1978). MR 0520174 | Zbl 0383.65058
[4] Vaněk, P.: Acceleration of convergence of a two-level algorithm by smoothing transfer operators. Appl. Math., Praha 37 (1992), 265-274. MR 1180605
[5] Vaněk, P.: Fast multigrid solver. Appl. Math., Praha 40 1-20 (1995). MR 1305645 | Zbl 0824.65016
[6] Vaněk, P., Brezina, M.: Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing. Appl. Math., Praha 58 369-388 (2013). 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 aggregation. Numer. Math. 88 559-579 (2001). DOI 10.1007/s211-001-8015-y | MR 1835471 | Zbl 0992.65139
[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, M.: Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 56 (1996), 179-196. DOI 10.1007/BF02238511 | MR 1393006
[10] Vaněk, P., Mandel, J., Brezina, M.: Algebraic multigrid on unstructured meshes. UCD/CCM Report 34, Center for Computational Mathematics, University of Colorado at Denver, http://www.math.cudenver.edu/ccmreports/rep34.ps.gz, 1994.
Search
Partner of
