Kurt Bryan and Lester Caudill 2005 Inverse Problems 21 239 doi:10.1088/0266-5611/21/1/015
Kurt Bryan1 and Lester Caudill2
Show affiliationsWe 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.
02.30.Jr Partial differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
Issue 1 (February 2005)
Received 16 August 2004, in final form 31 October 2004
Published 6 December 2004
Kurt Bryan and Lester Caudill 2005 Inverse Problems 21 239
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