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Coarse/fine mesh preconditioners for the iterative solution of finite element problems
Author(s) -
Dracopoulos M. C.,
Crisfield M. A.
Publication year - 1995
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.1620381908
Subject(s) - domain decomposition methods , finite element method , discretization , multigrid method , degrees of freedom (physics and chemistry) , mathematics , factorization , lu decomposition , computer science , algorithm , mathematical optimization , matrix decomposition , partial differential equation , mathematical analysis , structural engineering , eigenvalues and eigenvectors , physics , quantum mechanics , engineering
A class of preconditioners built around a coarse/fine mesh framework is presented. The proposed method involves the reconstruction of the stiffness equations using a coarse/fine mesh idealization with relative degrees‐of‐freedom derived from the element shape functions. This approach leads naturally to effective preconditioners for iterative solvers which only require a factorization involving coarse mesh variables. A further extension is the application of the proposed method to super‐elements in conjunction with substructuring (domain decomposition) techniques. The derivation of the coarse/fine mesh discretization via the use of transformation matrices, allows a straightforward implementation of the proposed techniques (as well as multigrid type procedures) within an existing finite element system.