Trusted frequency region of convergence for the enclosure method in thermal imaging

Abstract

This study deals with the numerical implementation of a formula in the enclosure method as applied to a prototype inverse initial boundary value problem for thermal imaging in a one-space dimension. A precise error estimate of the formula is given and the effect on the discretization of the used integral of the measured data in the formula is studied. The formula requires a large frequency to converge; however, the number of time interval divisions grows exponentially as the frequency increases. Therefore, for a given number of divisions, we fixed the trusted frequency region of convergence with some given error bound. The trusted frequency region is computed theoretically using the theorems provided in this paper and is numerically implemented for various cases.