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Density results and the method of fundamental solutions for Cauchy data reconstruction

Alves, Carlos J. S.; Martins, Nuno F. M.

Advances in Boundary Element and Meshless Techniques XIV (A. Sellier and M.H. Aliabadi, Eds.), EC Ltd, Eastleigh, UK (2013), pp. 323-328

In this work we address the problem that consists in fitting Cauchy boundary data using the method of fundamental solutions (MFS). We study some density properties in order to justify the MFS fitting for full and partial Cauchy data. We focus on fitting partial data and in particular we will present some theoretical and numerical results concerning the reconstruction of data in an inaccessible part of
the boundary.