We consider the inverse problem of determining the shape of some inacces sible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples
Bryan, Kurt M. and Caudill, Lester, "Reconstruction of an Unknown Boundary Portion From Cauchy Data in N-dimensions" (2004). Mathematical Sciences Technical Reports (MSTR). 40.