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Two‐level domain decomposition preconditioning for the p ‐version finite element method in three dimensions
Author(s) -
Mandel Jan
Publication year - 1990
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620290513
Subject(s) - preconditioner , domain decomposition methods , parallelizable manifold , finite element method , convergence (economics) , mathematics , bounded function , stiffness matrix , mixed finite element method , computation , stiffness , mortar methods , extended finite element method , mathematical optimization , mathematical analysis , algorithm , iterative method , structural engineering , engineering , economics , economic growth
This paper presents a flexible approach to domain decomposition preconditioning for problems expressed in terms of local stiffness matrices of subdomains. Evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain. Convergence factors can be bounded using properties of the local stiffness matrices only. The method is applied to the p ‐version finite element method for three‐dimensional elasticity. We treat each element as a subdomain and compute explicit convergence bounds.