Duality based domain decomposition with proportioning for the solution of free boundary problems
type: Item
instance of: scholarly article
title: Duality based domain decomposition with proportioning for the solution of free boundary problems
zbMATH Open document ID: 0859.65056
DOI: 10.1016/0377-0427(96)80912-5
published in: Journal of Computational and Applied Mathematics
publication date: 1997-04-07T00:00:00Z
review text: The author proposes an algorithm for solving the quadratic programming problem \(\min\{f(x): x\in {\mathcal B}\}\), where \(f(x)={1\over 2} x^T Ax-x^Tb\) and \({\mathcal B}=\{x:Bx\leq c\}\), \(b\in \mathbb{R}^n\), \(c\in \mathbb{R}^m\). Furthermore, \(B\) denotes an \(m\times n\) full rank matrix and the symmetric positive semidefinite matrix \(A\) is given as \(A=\text{diag}(A_1,\dots,A_p)\). The author assumes that the problem arises from a discretization of free boundary problems (contact problems of a system of \(p\) elastic bodies) with a spatial domain comprising \(p\) subdomains (\(A_i\) are band matrices, \(m\ll n\)). After the introduction of the dual problem and a brief description of the domain decomposition in Section 2, Section 3 is concerned with the discussion of the algorithm and its main properties applied to the original problem. The algorithm is characterized by a sequence of auxiliary problems, where the precision of their solution is controlled by the norm of the so-called unbalanced contact residuals. For details the reader is referred to another paper by the author. In Section 4 the application of the algorithm to the dual problem is discussed and finally numerical results for a model problem are presented to illustrate the good properties of the proposed algorithm.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 903498
zbMATH Keywords: numerical examples
zbMATH Keywords: complementarity problem
zbMATH Keywords: contact problems
zbMATH Keywords: quadratic programming
zbMATH Keywords: free boundary problems
zbMATH Keywords: domain decomposition
zbMATH Keywords: algorithm
author: Z. Dostál
MaRDI profile type: Publication
full work available at URL: 0377-0427(96)80912-5
OpenAlex ID: W2071561302
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description: scientific article; zbMATH DE number 903498