In this paper we examine the inverse problem of determining the amount of corrosion/disbonding which has occurred on the boundary of a single circular (or nearly circular) inclusion D in a two-dimensional domain Omega , using Cauchy data for the steady-state heat equation. We develop an algorithm for reconstructing a function which quantifies the level of corrosion/disbonding at each point on the boundary of D. We also address the issue of ill-posedness and develop a simple regularization scheme, then provide several numerical examples. We also show a simple procedure for recovering the center of D assuming that Omega and D have the same thermal conductivity.
Kurt Bryan, Department of Mathematics, Rose-Hulman Institute of Technology firstname.lastname@example.org
Christian, Nicholas and Johnson, Mathew
"Non-Destructive Testing of Thermal Resistances for a Single Inclusion in a 2-Dimensional Domain,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 6
, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol6/iss1/7