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Reconstruction Of Partially Conductive Cracks Using Boundary Data, David Mccune, Janine Haugh
Reconstruction Of Partially Conductive Cracks Using Boundary Data, David Mccune, Janine Haugh
Mathematical Sciences Technical Reports (MSTR)
This paper develops an algorithm for finding one or more non-insulated, pair-wise disjoint, linear cracks in a two dimensional region using boundary measurements.
Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N-Dimensions, Kurt M. Bryan, Lester Caudill
Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N-Dimensions, Kurt M. Bryan, Lester Caudill
Mathematical Sciences Technical Reports (MSTR)
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
Determining The Length Of A One-Dimensional Bar, Natalya Yarlikina, Holly Walrath
Determining The Length Of A One-Dimensional Bar, Natalya Yarlikina, Holly Walrath
Mathematical Sciences Technical Reports (MSTR)
In this paper we examine the inverse problem of determining the length of a one-dimensional bar from thermal measurements (temperature and heat flux) at one end of the bar (the "accessible" end); the other inaccessible end of the bar is assumed to be moving. We develop two different approaches to estimating the length of the bar, and show how one approach can also be adapted to find unknown boundary conditions at the inaccessible end of the bar.