Efficient inexact Newton-like methods with application to problems of the deformation theory of plasticity

Radim Blaheta; Roman Kohut

Applications of Mathematics (1993)

  • Volume: 38, Issue: 6, page 411-427
  • ISSN: 0862-7940

Abstract

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Newton-like methods are considered with inexact correction computed by some inner iterative method. Composite iterative methods of this type are applied to the solution of nonlinear systems arising from the solution of nonlinear elliptic boundary value problems. Two main quastions are studied in this paper: the convergence of the inexact Newton-like methods and the efficient control of accuracy in computation of the inexact correction. Numerical experiments show the efficiency of the suggested composite iterative techniques when problems of the deformation theory of plasticity are solved.

How to cite

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Blaheta, Radim, and Kohut, Roman. "Efficient inexact Newton-like methods with application to problems of the deformation theory of plasticity." Applications of Mathematics 38.6 (1993): 411-427. <http://eudml.org/doc/15762>.

@article{Blaheta1993,
abstract = {Newton-like methods are considered with inexact correction computed by some inner iterative method. Composite iterative methods of this type are applied to the solution of nonlinear systems arising from the solution of nonlinear elliptic boundary value problems. Two main quastions are studied in this paper: the convergence of the inexact Newton-like methods and the efficient control of accuracy in computation of the inexact correction. Numerical experiments show the efficiency of the suggested composite iterative techniques when problems of the deformation theory of plasticity are solved.},
author = {Blaheta, Radim, Kohut, Roman},
journal = {Applications of Mathematics},
keywords = {nonlinear systems; inexact Newton-like methods; composite iterations; deformation theory of plasticity; numerical experiments; nonlinear elliptic problems; generalized Picard method; secant modulus method; preconditioned conjugate gradients; convergence; numerical experiments; inexact Newton-like methods; nonlinear elliptic problems; generalized Picard method; secant modulus method; preconditioned conjugate gradients; convergence; deformation theory of plasticity},
language = {eng},
number = {6},
pages = {411-427},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Efficient inexact Newton-like methods with application to problems of the deformation theory of plasticity},
url = {http://eudml.org/doc/15762},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Blaheta, Radim
AU - Kohut, Roman
TI - Efficient inexact Newton-like methods with application to problems of the deformation theory of plasticity
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 6
SP - 411
EP - 427
AB - Newton-like methods are considered with inexact correction computed by some inner iterative method. Composite iterative methods of this type are applied to the solution of nonlinear systems arising from the solution of nonlinear elliptic boundary value problems. Two main quastions are studied in this paper: the convergence of the inexact Newton-like methods and the efficient control of accuracy in computation of the inexact correction. Numerical experiments show the efficiency of the suggested composite iterative techniques when problems of the deformation theory of plasticity are solved.
LA - eng
KW - nonlinear systems; inexact Newton-like methods; composite iterations; deformation theory of plasticity; numerical experiments; nonlinear elliptic problems; generalized Picard method; secant modulus method; preconditioned conjugate gradients; convergence; numerical experiments; inexact Newton-like methods; nonlinear elliptic problems; generalized Picard method; secant modulus method; preconditioned conjugate gradients; convergence; deformation theory of plasticity
UR - http://eudml.org/doc/15762
ER -

References

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  1. Blaheta R., Incomplete factorization preconditioning techniques for linear elasticity problems, Z. angew. Math. Mech. 71 (1991), T638-640. (1991) Zbl0751.73063
  2. Blaheta R., Displacement decomposition-incomplete factorization preconditioning for linear elasticity problems, to appear in J. Numer. Lin. Alg. Appl. 1992/1993. (1992) 
  3. Desai C.S., H. J. Siriwardane, Constitutive laws for engineering materials with emphasis on geologic materials, Prentice Hall, Englewood Cliffs, NJ, 1984. (1984) Zbl0543.73004
  4. Kohut R., R. Blaheta, Efficient iterative methods for numerical solution of plasticity problems, Proc. of the NUMEG'92 Conference, Prague 1992, vol. 1, pp. 129-134. (1992) 
  5. Nečas J., Introduction to the theory of nonlinear elliptic equations, Teubner Texte zur Mathematik, Band 52, Leipzig, 1983. (1983) MR0731261
  6. Nečas J., I. Hlaváček, Mathematical theory of elastic and elasto-plastic bodies: An introduction, Elsevier, Amsterdam, 1981. (1981) MR0600655
  7. Dembo R. S., Eisenstat S. C., T. Steingang, 10.1137/0719025, SIAM J. Numer. Anal. 19 (1982), 400-408. (1982) MR0650059DOI10.1137/0719025
  8. Deuflhard P., Global inexact Newton methods for very large scale nonlinear problems, Impact of Соmр. in Science and Engng. 3 (1991), 366-393. (1991) Zbl0745.65032MR1141306

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