A numerical computation for inverse boundary determination problem

Abstract

Based on the idea of radial basis interpolation for Hermite–Birkhoff data and the shift invariability of harmonic function space, a new computational method is developed to determine an unknown boundary of a domain from given values of the solution and its derivatives on only a part of the other boundary. This is a well-known inverse boundary determination problem that arises from using non-destructive evaluation techniques in the engineering industry. Error estimation of the computational method is also given and the numerical results indicate that the method provides an accurate approximation of the unknown boundary.