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.

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Post-print Article

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Copyright © 2005 IOP Publishing. Article first published online: 6 DEC 2004. DOI: doi:10.1088/0266-5611/21/1/015.

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Full citation:

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.