DOI
10.1088/0266-5611/21/1/015
Abstract
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.
Document Type
Post-print Article
Publication Date
2-2005
Publisher Statement
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:
http://iopscience.iop.org/0266-5611/21/1/003/pdf/0266-5611_21_1_003.pdf
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.
Recommended Citation
Bryan, Kurt and Caudill, Lester, "Reconstruction of an Unknown Boundary Portion from Cauchy Data in N- Dimensions" (2005). Department of Math & Statistics Faculty Publications. 99.
https://scholarship.richmond.edu/mathcs-faculty-publications/99
Included in
Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Physics Commons