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Physical Sciences and Mathematics Commons™
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Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
An Inverse Problem In Thermal Language, Kurt M. Bryan, Lester Caudill
An Inverse Problem In Thermal Language, Kurt M. Bryan, Lester Caudill
Mathematical Sciences Technical Reports (MSTR)
This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring of the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has of data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.
A Direct Method For The Inversion Of Physical Systems, Lester Caudill, Herschel Rabitz, Attila Askar
A Direct Method For The Inversion Of Physical Systems, Lester Caudill, Herschel Rabitz, Attila Askar
Department of Math & Statistics Faculty Publications
A general algorithm for the direct inversion of data to yield unknown functions entering physical systems is presented. Of particular interest are linear and non-linear dynamical systems. The potential broad applicability of this method is examined in the context of a number of coefficient-recovery problems for partial differential equations. Stability issues are addressed and a stabilization approach, based on inverse asymptotic tracking, is proposed. Numerical examples for a simple illustration are presented, demonstrating the effectiveness of the algorithm.