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Finite element and conjugate gradient methods for a nonlinear optimal heat transfer control problem
Author(s) -
Meric R. A.
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.1620141207
Subject(s) - conjugate gradient method , discretization , finite element method , optimal control , mathematics , nonlinear conjugate gradient method , boundary value problem , nonlinear system , dimension (graph theory) , slab , mathematical optimization , mixed finite element method , mathematical analysis , computer science , physics , gradient descent , quantum mechanics , machine learning , geophysics , artificial neural network , pure mathematics , thermodynamics
Abstract The boundary control problem of optimal heating of an infinitely long slab with tempertue‐dependent thermal conductivity, subjected to a convection and radiation boundary condition, is analysed by numerical methods. In order to reformulate the optimal control problem of distributed parameter systems as a mathematical programming problem of finite dimension, a space, co‐ordinate is discretized by use of the finite element method, while the Runge–Kutta method is utilized for time integrations. Finally, the performance index of the optimal control problem is minimized by the conjugate gradient method of optimization.