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
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.
nonlinear optimization, gradient method, finite deformation elasticity theory, polyconvex functionals, grid optimization.
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Computational Mathematics and Mathematical Physics, 2005, 45:8, 1400–1415
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
\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.
\jour Comput. Math. Math. Phys.
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