Publisher DOI: 10.1002/nla.599
Title: ℋ-matrix preconditioners for symmetric saddle-point systems from meshfree discretization
Language: English
Authors: Le Borne, Sabine  
Oliveira, Suely 
Yang, Fang 
Keywords: Algebraic multigrid; Hierarchical matrices; Meshfree method; Multilevel methods; Saddle-point systems
Issue Date: 28-Apr-2008
Publisher: Wiley
Source: Numerical Linear Algebra with Applications 15 (10): 911-924 (2008-12-01)
Abstract (english): 
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. Copyright © 2008 John Wiley & Sons, Ltd.
ISSN: 1099-1506
Journal: Numerical linear algebra with applications 
Document Type: Article
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