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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 8, Pages 1450–1465 (Mi zvmmf614)  

This article is cited in 2 scientific papers (total in 2 papers)

On the convergence of a gradient method for the minimization of functionals in finite deformation elasticity theory and for the minimization of barrier grid functionals

V. A. Garanzha, I. E. Kaporin

Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: Gradient descent methods are examined for the minimization of barrier-type polyconvex functionals arising in finite-deformation elasticity theory and grid optimization. The minimum of a functional is sought in the class of continuous piecewise affine deformations that preserve orientation. Sufficient conditions are found for a sequence of iterative approximations to belong to the feasible set and for the norm of the gradient of the functional to converge to zero on this set. As the functional, one can use a measure of the deformation of a grid, for instance, a grid formed of triangles or tetrahedra.

Key words: nonlinear optimization, gradient method, finite deformation elasticity theory, polyconvex functionals, grid optimization.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:8, 1400–1415

Bibliographic databases:
UDC: 519.626.2
Received: 29.01.2005

Citation: V. A. Garanzha, I. E. Kaporin, “On the convergence of a gradient method for the minimization of functionals in finite deformation elasticity theory and for the minimization of barrier grid functionals”, Zh. Vychisl. Mat. Mat. Fiz., 45:8 (2005), 1450–1465; Comput. Math. Math. Phys., 45:8 (2005), 1400–1415

Citation in format AMSBIB
\Bibitem{GarKap05}
\by V.~A.~Garanzha, I.~E.~Kaporin
\paper On the convergence of a gradient method for the minimization of functionals in finite deformation elasticity theory and for the minimization of barrier grid functionals
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 8
\pages 1450--1465
\mathnet{http://mi.mathnet.ru/zvmmf614}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2191856}
\zmath{https://zbmath.org/?q=an:1091.74019}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 8
\pages 1400--1415


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pedregal P., “Some remarks on quasiconvexity, inner variations, and optimal meshes”, Journal of Convex Analysis, 15:2 (2008), 381–393  mathscinet  zmath  isi
    2. Garanzha V.A. Kudryavtseva L.N. Utyuzhnikov S.V., “Variational Method For Untangling and Optimization of Spatial Meshes”, J. Comput. Appl. Math., 269 (2014), 24–41  crossref  mathscinet  zmath  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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