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On the determination of a Robin boundary coefficient in an elastic cavity using the MFS. (English) Zbl 1157.74015
Ferreira, A. J. M. (ed.) et al., Progress on meshless methods. Invited papers based on the presentations at the 2nd ECCOMAS thematic conference on meshless methods, Porto, Portugal, July 9–11, 2007. Dordrecht: Springer (ISBN 978-1-4020-8820-9/hbk). Computational Methods in Applied Sciences (Springer) 11, 125-139 (2009).
Summary: We address a problem of recovering a boundary condition on an elastic cavity from a single boundary measurement on an external part of the boundary. The boundary condition is given by a Robin condition, and we aim to identify its Robin coefficient (matrix). We discuss the uniqueness question for this inverse problem and present several numerical simulations, based on two different reconstruction approaches: an approach by solving the Cauchy problem, and an iterative Newton type approach (that requires the computation of several direct problems). To solve the mentioned (direct and inverse) problems, we propose the method of fundamental solutions (MFS) whose properties will be discussed.
For the entire collection see [Zbl 1151.65003].

MSC:
74G75 Inverse problems in equilibrium solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74B05 Classical linear elasticity
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
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