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Numerical solution of the variation boundary integral equation for inverse problems
Author(s) -
Gallego Rafael,
Suárez Javier
Publication year - 2000
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 - 10.1002/1097-0207(20001010)49:4<501::aid-nme971>3.0.co;2-7
Subject(s) - mathematics , inverse problem , linearization , boundary (topology) , inverse , domain (mathematical analysis) , shape optimization , mathematical analysis , boundary value problem , variation (astronomy) , minification , integral equation , geometry , mathematical optimization , finite element method , nonlinear system , physics , quantum mechanics , thermodynamics , astrophysics
In this paper a procedure to solve the identification inverse problems for two‐dimensional potential fields is presented. The procedure relies on a boundary integral equation (BIE) for the variations of the potential, flux, and geometry. This equation is a linearization of the regular BIE for small changes in the geometry. The aim in the identification inverse problems is to find an unknown part of the boundary of the domain, usually an internal flaw, using experimental measurements as additional information. In this paper this problem is solved without resorting to a minimization of a functional, but by an iterative algorithm which alternately solves the regular BIE and the variation BIE. The variation of the geometry of the flaw is modelled by a virtual strainfield, which allows for greater flexibility in the shape of the assumed flaw. Several numerical examples demonstrate the effectiveness and reliability of the proposed approach. Copyright © 2000 John Wiley & Sons, Ltd.