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A variational framework for distance‐minimizing data‐driven method for linear elasticity
Author(s) -
Nguyen Lu Trong Khiem,
Rambausek Matthias,
Keip MarcAndré
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800354
Subject(s) - uniqueness , mathematical optimization , minification , convexity , mathematics , interpolation (computer graphics) , lagrange polynomial , lagrange multiplier , penalty method , polynomial , convergence (economics) , sequence (biology) , function (biology) , computer science , mathematical analysis , animation , computer graphics (images) , evolutionary biology , biology , financial economics , economics , genetics , economic growth
A variational framework for the distance‐minimizing data‐driven computing method is proposed based on the method of Lagrange multipliers. The data‐driven solution is defined as an optimization solution of a double‐minimization problem. A staggered scheme is employed to decompose the original problem into a sequence of single‐minimization problems. As an advantage, the variational formulation renders straightforward implementation of the high‐order polynomial interpolation. The non‐uniqueness of the data‐driven solution is the consequence of the use of the current solution strategy and non‐convexity of the data function space. A convergence study of the solution with respect to the data size is presented. The decrease of mean values and standard deviations of errors with respect to the reference solution justify the variational formulation.