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ℋ-matrix preconditioners for symmetric saddle-point systems from meshfree discretization
Publikationstyp
Journal Article
Date Issued
2008-04-28
Sprache
English
Author(s)
Volume
15
Issue
10
Start Page
911
End Page
924
Citation
Numerical Linear Algebra with Applications 15 (10): 911-924 (2008-12-01)
Publisher DOI
Scopus ID
Publisher
Wiley
Meshfree methods are suitable for solving problems on irregular domains, avoiding the use of a mesh. To deal with the boundary conditions, we can use Lagrange multipliers and obtain a sparse, symmetric and indefinite system of saddle-point type. Many methods have been developed to solve the indefinite system. Previously, we presented an algebraic method to construct an LU-based preconditioner for the saddle-point system obtained by meshfree methods, which combines the multilevel clustering method with the ℋ-matrix arithmetic. The corresponding preconditioner has both ℋ-matrix and sparse matrix subblocks. In this paper we refine the above method and propose a way to construct a pure ℋ-matrix preconditioner. We compare the new method with the old method, JOR and smoothed algebraic multigrid methods. The numerical results show that the new preconditioner outperforms the preconditioners based on the other methods.
Subjects
Algebraic multigrid
Hierarchical matrices
Meshfree method
Multilevel methods
Saddle-point systems
DDC Class
510: Mathematik