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Least‐squares finite element method and preconditioned conjugate gradient solution
Author(s) -
Carey G. F.,
Jiang B. N.
Publication year - 1987
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.1620240705
Subject(s) - conjugate gradient method , mathematics , preconditioner , least squares function approximation , weighting , finite element method , convergence (economics) , conjugate residual method , gradient descent , nonlinear conjugate gradient method , rate of convergence , derivation of the conjugate gradient method , mathematical analysis , mathematical optimization , iterative method , computer science , statistics , physics , computer network , channel (broadcasting) , estimator , machine learning , artificial neural network , acoustics , economics , thermodynamics , economic growth
A least‐squares variational procedure for first‐order systems of differential equations and an approximate formulation based on finite elements are developed. Error estimates, a condition number bound and analysis of weighting factors are given. Steepest descent and conjugate gradient solution procedures are examined, and an appropriate preconditioner constructed which is demonstrated to yield rapid convergence and to be insensitive to problem size. Numerical studies of rates of convergence for a test problem are given.