On the Determination of a Robin Boundary Coefficient in an Elastic Cavity Using the MFS
In this work, 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.
KeywordsInverse problems Robin boundary conditions Lamé system method of fundamental solutions
Unable to display preview. Download preview PDF.
- 2.C. J. S. Alves and N. F. M. Martins, The Direct Method of Fundamental Solutions and the Inverse Kirsch-Kress Method for the Reconstruction of Elastic Inclusions or Cavities, Preprint (22), Department of Mathematics, FCT/UNL, Caparica, Portugal, 2007Google Scholar
- 3.C. J. S. Alves and N. F. M. Martins, Reconstruction of inclusions or cavities in potential problems using the MFS, Submitted Google Scholar
- 13.K. Madsen, H. B. Nielsen and O. Tingleff, Methods for non-linear least squares problems, IMM, 60 pages, Denmark, 2004Google Scholar