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A class of preconditioned conjugate gradient methods for the solution of a mixed finite element discretization of the biharmonic operator
Author(s) -
Axelsson Owe,
Munksgaard Niels
Publication year - 1979
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.1620140705
Subject(s) - biharmonic equation , mathematics , conjugate gradient method , discretization , finite element method , coefficient matrix , mathematical analysis , matrix (chemical analysis) , derivation of the conjugate gradient method , dirichlet problem , conjugate residual method , linear system , mathematical optimization , gradient descent , computer science , boundary value problem , physics , eigenvalues and eigenvectors , materials science , quantum mechanics , machine learning , artificial neural network , composite material , thermodynamics
The homogeneous Dirichlet problem for the biharmonic operator is solved as the variational formulation of two coupled second‐order equations. The discretization by a mixed finite element model results in a set of linear equations whose coefficient matrix is sparse, symmetric but indefinite. We describe a class of preconditioned conjugate gradient methods for the numerical solution of this linear system. The precondition matrices correspond to incomplete factorizations of the coefficient matrix. The numerical results show a low computational complexity in both number of computer operations and demand of storage.