Paper Info
Title
Two-level local refinement preconditioners for nonsymmetric and indefinite elliptic problems
Abstract
Preconditioners of optimal order for nonselfadjoint and indefinite elliptic boundary value problems discretized on grids with local refinement are constructed. The proposed technique utilizes solution of a discrete problem on a uniform coarse grid; then, the reduced problem is handled by a generalized conjugate gradient (GCG) method. The reduced problem is coercive if the initial coarse mesh is sufficiently fine and is local, solving only for the unknowns on the subdomains where local refinement has been introduced. The reduced problem can be preconditioned by a preconditioner for the symmetric positive definite matrix arising from the symmetric and coercive principal part of the original bilinear form restricted to the subdomains containing local refinement. This problem also utilizes a uniform grid. In the numerical tests, the recent algebraic multilevel. (AMLI) preconditioners [Axelsson and Vassilevski, SIAM J. Numer. Anal., 27 (1990), pp. 1569-1590; Saad and Schultz, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869], which are of optimal order for selfadjoint and coercive elliptic problems, were used.
Year
DOI
Venue
1994
10.1137/0915010
SIAM J. Scientific Computing
Keywords
Field
DocType
INDEFINITE PROBLEMS,NONSYMMETRIC PROBLEMS,OPTIMAL ORDER PRECONDITIONER,LOCAL REFINEMENT,2-LEVEL METHOD,GENERALIZED CONJUGATE GRADIENTS,ELLIPTIC PROBLEMS
Conjugate gradient method,Discretization,Boundary value problem,Mathematical optimization,Bilinear form,Algebraic number,Preconditioner,Mathematical analysis,Positive-definite matrix,Mathematics,Principal part
Journal
Volume
Issue
ISSN
15
1
1064-8275
Citations 
PageRank 
References 
0
0.34
2
Authors
3
Name
Order
Citations
PageRank
Richard E. Ewing125245.87
Svetozara I. Petrova2168.87
Panayot S. Vassilevski3500118.98