FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 209-230

**A Richardson-type iterative approach for identification of
delamination boundaries**

E. Schnack

T.-A. Langhoff

S. Dimitrov

Abstract

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A \textit direct problem of particular mathematical modelling is
to determine the response of a system, given the governing
partial differential equations, the geometry under interest, the
complete boundary and initial conditions, and material properties.
When one or more of the conditions for the solution of the direct
problem are unknown, an \textit inverse problem can be formulated.
One of the methods frequently used for the solution of inverse
problems involves finding the values of the unknowns in
a mathematical formulation such that the behavior calculated with
the model matches the measured response at degree evaluated in terms
of the classical $L$_{2} norm.
Considered in this sense, the inverse problem is equivalent to an
\textit ill-posed optimization problem for the estimation of
parameters whose solution in predominant part of cases is a real
mathematical challenge.
In this contribution, we report a novel approach which avoids the
mathematical difficulties inspired by ill-posed character of the
model.
Our method is devoted to the computation of inverse problems furnished
by second-order elliptical systems of partial differential equations
and falls in the same conceptual line with the method initiated by
Kozlov et al.
and further extended and algorithmized by Weikl et al.

We construct and employ a weak version of the algorithm found by
Weikl et al.
Proofs for the convergence and regularity of this version are given
for the case of a single layer.

The computational realization of the algorithm (called briefly AICRA)
is applied and numerical results are obtained.
The comparison with experiments demonstrates a good significance and
representativeness.

Location: http://mech.math.msu.su/~fpm/eng/k06/k064/k06414h.htm

Last modified: February 17, 2007