Reconstruction of an Unknown Boundary Portion From Cauchy Data in N-dimensions

Authors

Kurt M. Bryan, Rose-Hulman Institute of TechnologyFollow
Lester Caudill

Document Type

Article

Publication Date

7-8-2004

Abstract

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

Comments

MSTR 04-01

Recommended Citation

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.
https://scholar.rose-hulman.edu/math_mstr/40