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Free surfaces: shape sensitivity analysis and numerical methods
Author(s) -
Kärkkäinen Kari T.,
Tiihonen Timo
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990320)44:8<1079::aid-nme543>3.0.co;2-i
Subject(s) - sensitivity (control systems) , convergence (economics) , linearization , mathematical optimization , boundary (topology) , numerical analysis , simplicity , mathematics , shape optimization , boundary value problem , computer science , nonlinear system , finite element method , mathematical analysis , engineering , structural engineering , electronic engineering , philosophy , physics , epistemology , quantum mechanics , economics , economic growth
In this paper we consider numerical methods for stationary free boundary problems. We start by analysing systematically different shape optimization formulations of a model problem and show how the optimality conditions relate to construction of trial type methods. Shape sensitivity analysis of the free boundary leads also to the so‐called total linearization method which combines the good properties of Newton method and trial methods, i.e. fast convergence and relative simplicity of implementation. Detailed implementation for a model problem together with numerical tests is presented. Copyright © 1999 John Wiley & Sons, Ltd.