Abstract
We introduce a multilevel preconditioner based on an approximate Schur complement using sparse approximate inverses. We give a brief introduction to the algorithm followed by some results for two-dimensional and three-dimensional model problems.
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Benzi, M., Cullum, J., and Tama, M.: Robust approximate inverse preconditioning for the conjugate gradient method, Technical Report LA-UR-99–2899, Los Alamos National Laboratory, Los Alamos, NM, (1999)
Benzi, M., Marin, J., and Vilna, M.: Parallel Preconditioning with Factorized Sparse Approximate Inverses. In Proc. of the Ninth SIAM Conference on Parallel Processing for Scientific Computing (1999)
Benzi, M., Marin, J., and Tama, M.: A Two-Level Parallel Preconditioner Based on Sparse Approximate Inverses. In Iterative Methods in Scientific Computation II, (to appear)
Benzi, M. and Túma, M.: A sparse approximate inverse preconditioner for non-symmetric linear systems. SIAM J. Sci. Comput., 19(1998) 968–994
Benzi, M. and Túma, M.: A comparative study of sparse approximate inverse preconditioners. Appl. Numer. Math. 30(1999) 305–340
Benzi, M. and Tama, M.: Orderings for factorized sparse approximate inverse preconditioning, SIAM J. Sci. Compu., (to appear)
Brand, C. and Kraus, J.: Preconditioning by approximate Schur complements on hierarchical grids. In Proc. of the Ninth International GAMM Workshop on Parallel Multigrid Methods (1996)
Cormen, T., Leiserson, C., and Rivest, R.: Introduction to Algorithms. MIT Press, Cambridge, Massachusetts (1990)
de Zeeuw, P.: Matrix-dependent prolongations and restrictions in a blackbox multigrid solver. J. Comp. Appl. Math., 33(1990) 1–27
Elman, H.: Approximate Schur complement preconditioners on serial and parallel computers. SIAM J. Sci. Stat. Comput., 10(1989) 581–601
Fuhrmann, J.: A modular algebraic multilevel method. In Proc. of the Ninth International GAMM Workshop on Parallel Multigrid Methods (1996)
Knapek, S.: Matrix-dependent multigrid-homogenization for diffusion problems. In Proc. of the Fourth Copper Mountain Conf. on Iterative Methods (1996)
Reusken, A.: Multigrid with matrix-dependent transfer operators for a singular perturbation problem. Computing, 50(1993) 199–211
Reusken, A.: Multigrid with matrix-dependent transfer operators for convection-diffusion problems. In P. Hemker and P. Wesseling, editors, Multi-grid Methods IV: Proc. of the Fourth European Multigrid Conf., pages 269–280. Birkhäuser Verlag (1994)
Reusken, A.: A multigrid method based on incomplete Gaussian elimination. Num. Lin. Alg. Appl., 3 (1996) 369–390
Reusken, A.: On a robust multigrid solver. Computing, 56(1996) 303–322
Reusken, A.: On the approximate cyclic reduction preconditioner. Technical Report 144, Institut fir Geometrie and Praktische Mathematik, RWTH Aachen (1997)
Ruge, J., and Stu ben, K.: Algebraic Multigrid. In S. McCormick, editor, Multi-grid Methods, volume 3 of Frontiers in Applied Mathematics, pages 73–130. SIAM, Philadelphia, PA, (1987)
Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing Company, Boston, Massachusetts (1996)
Saad, Y., and Schultz, M.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7 (1986) 856–869
Stüben, K.: Algebraic Multigrid (AMG): An Introduction with Applications. GMD Report 53, GMD Forschungszentrum Informationstechnik GmBH, SchloßBirlinghoven, Germany (1999)
Wagner, C., Kinzelbach, W., and Wittum, G.: Schur-complement multigrid: A robust method for groundwater flow and transport problems. Numer. Math., 75 (1997) 523–545
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Benzi, M., DeLong, M. (2000). Approximate Schur Complement Multilevel Methods for General Sparse Systems. In: Dick, E., Riemslagh, K., Vierendeels, J. (eds) Multigrid Methods VI. Lecture Notes in Computational Science and Engineering, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58312-4_6
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DOI: https://doi.org/10.1007/978-3-642-58312-4_6
Publisher Name: Springer, Berlin, Heidelberg
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