Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems
| Autor: | Yuri A. Kuznetsov, Richard E. Ewing, Serguei Maliassov, Raytcho D. Lazarov, Zhangxin Chen |
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| Rok vydání: | 1996 |
| Předmět: |
Algebra and Number Theory
Applied Mathematics Linear system MathematicsofComputing_NUMERICALANALYSIS Triangulation (social science) Mixed finite element method Finite element method Mathematics::Numerical Analysis Algebra symbols.namesake Simple (abstract algebra) Lagrange multiplier ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION symbols Algebraic number Condition number Mathematics |
| Zdroj: | Numerical Linear Algebra with Applications. 3:427-453 |
| ISSN: | 1099-1506 1070-5325 |
| DOI: | 10.1002/(sici)1099-1506(199609/10)3:5<427::aid-nla92>3.0.co;2-i |
| Popis: | A new approach for constructing algebraic multilevel preconditioners for mixed finite element methods for second order elliptic problems with tensor coefficients on general geometry is proposed. The linear system arising from the mixed methods is first algebraically condensed to a symmetric, positive definite system for Lagrange multipliers, which corresponds to a linear system generated by standard nonconforming finite element methods. Algebraic multilevel preconditioners for this system are then constructed based on a triangulation of the domain into tetrahedral substructures. Explicit estimates of condition numbers and simple computational schemes are established for the constructed preconditioners. Finally, numerical results for the mixed finite element methods are presented to illustrate the present theory. |
| Databáze: | OpenAIRE |
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