| Title:
|
Efficient inexact Newton-like methods with application to problems of the deformation theory of plasticity (English) |
| Author:
|
Blaheta, Radim |
| Author:
|
Kohut, Roman |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
6 |
| Year:
|
1993 |
| Pages:
|
411-427 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
nonlinear systems |
| Keyword:
|
inexact Newton-like methods |
| Keyword:
|
composite iterations |
| Keyword:
|
deformation theory of plasticity |
| Keyword:
|
numerical experiments |
| Keyword:
|
nonlinear elliptic problems |
| Keyword:
|
generalized Picard method |
| Keyword:
|
secant modulus method |
| Keyword:
|
preconditioned conjugate gradients |
| Keyword:
|
convergence |
| MSC:
|
35J65 |
| MSC:
|
65H10 |
| MSC:
|
65N22 |
| MSC:
|
73E99 |
| MSC:
|
73V20 |
| MSC:
|
74B99 |
| MSC:
|
74C99 |
| MSC:
|
74D99 |
| idZBL:
|
Zbl 0805.65048 |
| idMR:
|
MR1241445 |
| DOI:
|
10.21136/AM.1993.104564 |
| . |
| Date available:
|
2008-05-20T18:46:20Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104564 |
| . |
| Reference:
|
[1] Blaheta R.: Incomplete factorization preconditioning techniques for linear elasticity problems.Z. angew. Math. Mech. 71 (1991), T638-640. Zbl 0751.73063 |
| Reference:
|
[2] Blaheta R.: Displacement decomposition-incomplete factorization preconditioning for linear elasticity problems.to appear in J. Numer. Lin. Alg. Appl. 1992/1993. |
| Reference:
|
[3] Desai C.S., H. J. Siriwardane: Constitutive laws for engineering materials with emphasis on geologic materials.Prentice Hall, Englewood Cliffs, NJ, 1984. Zbl 0543.73004 |
| Reference:
|
[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. |
| Reference:
|
[5] Nečas J.: Introduction to the theory of nonlinear elliptic equations.Teubner Texte zur Mathematik, Band 52, Leipzig, 1983. MR 0731261 |
| Reference:
|
[6] Nečas J., I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies: An introduction.Elsevier, Amsterdam, 1981. MR 0600655 |
| Reference:
|
[7] Dembo R. S., Eisenstat S. C., T. Steingang: Inexact Newton methods.SIAM J. Numer. Anal. 19 (1982), 400-408. MR 0650059, 10.1137/0719025 |
| Reference:
|
[8] Deuflhard P.: Global inexact Newton methods for very large scale nonlinear problems.Impact of Соmр. in Science and Engng. 3 (1991), 366-393. Zbl 0745.65032, MR 1141306 |
| . |
