We consider the inverse problem of determining the shape of some inaccessible 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.
Copyright © 2005 IOP Publishing. Article first published online: 6 DEC 2004. DOI: doi:10.1088/0266-5611/21/1/015.
The definitive version is available at:
Bryan, Kurt, and Lester Caudill. "Reconstruction of an Unknown Boundary Portion from Cauchy Data in N-Dimensions." Inverse Problems 21, no. 1 (February 2005): 239-55. doi:10.1088/0266-5611/21/1/015.
Bryan, Kurt and Caudill, Lester, "Reconstruction of an Unknown Boundary Portion from Cauchy Data in N- Dimensions" (2005). Math and Computer Science Faculty Publications. 99.