Premium
Optimal algebraic multilevel preconditioning for local refinement along a line
Author(s) -
Margenov S.,
Maubach J.
Publication year - 1995
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680020404
Subject(s) - preconditioner , polygon mesh , mathematics , algebraic number , finite element method , vertex (graph theory) , line (geometry) , algorithm , mathematical optimization , iterative method , geometry , discrete mathematics , mathematical analysis , graph , physics , thermodynamics
The application of some recently proposed algebraic multilevel methods for the solution of two‐dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.