A unified framework for the construction of various algebraic multilevel preconditioning methods |
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| Authors: | Bai Zhongzhi Owe Axelsson |
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| Affiliation: | (1) Institute of Computational Mathematics and Scientific/Engineering Computing, the Chinese Academy of Sciences, 100080 Beijing, China;(2) Faculty of Mathematics and Informatics, the University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, Netherlands |
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| Abstract: | A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of second order elliptic boundary value problems by the finite elementmethod. This framework covers not only all known algebraic multilevel preconditioning methods,but yields also new ones. It is shown that all preconditioners within this framework have optimalorders of complexities for problems in two-dimensional (2-D) and three-dimensional(3-D) problemdomains, and their relative condition numbers are bounded uniformly with respect to the numbersof both the levels and the nodes. |
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| Keywords: | Multilevel method polynomial acceleration finite element method optimal-order preconditioner |
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