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2004 | 14 | 1 | 13-18
Tytuł artykułu

Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each step.
Rocznik
Tom
14
Numer
1
Strony
13-18
Opis fizyczny
Daty
wydano
2004
otrzymano
2003-05-15
poprawiono
2003-12-29
Twórcy
autor
  • LIMOS, Université Blaise Pascal, CNRS UMR 6158 ISIMA, Campus des Cézeaux - BP 10125, F-63173 Aubière cedex, France
Bibliografia
  • Dennis J.E. and Schnabel R.B. (1996): Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Philadelphia: SIAM.
  • Golub G.H. and Van Loan C.F. (1989): Matrix Computations, Baltimore: The John Hopkins University Press.
  • Luenberger D. (1989): Linear and Nonlinear Programming - Reading, MA: Addison Wesley.
  • Meurant G. (1999): Computer Solution of Large Systems - Amsterdam: Elsevier.
  • Ortega J.M. and Rhainboldt W.C. (1970): Iterative Solution of Nonlinear Equations in Several Variables - New York: Academic Press.
  • Polak E. (1971): Computational Methods in Optimization. - New York: Academic Press.
  • Abbasian R.O. and Carey G.F. (1998): Hybrid MPE-iterative schemes for linear and nonlinear systems. - Appl. Math. Comput., Vol. 26, pp.277-291.
  • Golub G.H., Murray W. and Saunders M.A. (1974): Methods for modifying matrix factorizations - Math. Comp., Vol.28, No.126, pp.505-535.
  • Hughes J.T., Ferency R.M. and Halquist J.O. (1987): Large-scale vectorized implicit calculations in solid mechanics on a Cray X-MP/48 utilizing EBE preconditioned conjugate gradient. - Comput. Meth. Appl. Mech. Eng., Vol.61, pp.215-248.
  • Saad Y. (1990): SPARSKIT: A basic tool kit for sparse matrix computation. - Tech. Rep. CSRD TR 1029, University of Illinois, Urbana, IL.
  • Sonnenveld P., Wesseling P. and De Zeeuw P.M. (1985): Multigrid and conjugate gradient methods as convergence acceleration technique, In: Multigrid Meth. Integr. Diff. pp.117-167, Clarendon Press.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv14i1p13bwm
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