A Global Time Treatment for Inverse Heat Conduction Problems
- 1 November 1997
- journal article
- research article
- Published by ASME International in Journal of Heat Transfer
- Vol. 119 (4) , 673-683
- https://doi.org/10.1115/1.2824171
Abstract
A new global time treatment is proposed and demonstrated for inverse heat conduction problems. This exposition illustrates the methodology by carefully and meticulously investigating the classic Beck’s problem. It is shown that accurate and stable numerical results occur without resorting to any stabilizing scheme beyond the implementation of a global basis representation for the temperature distribution. As a global time method the entire space-time domain is resolved in a simultaneous fashion. The approach is also extendable to multidimensional and multiprobe situations without difficulty. In direct problems the method has been successively applied to initial value problems, Volterra integral equations, and parabolic and hyperbolic partial and integro-partial differential equations.Keywords
This publication has 7 references indexed in Scilit:
- A NEW APPROACH FOR SOLVING INVERSE SOLIDIFICATION DESIGN PROBLEMSNumerical Heat Transfer, Part B: Fundamentals, 1996
- Direct least-square solutions to integral equations containing discrete dataJournal of Thermophysics and Heat Transfer, 1996
- Cumulative variable formulation for transient conductive and radiative transport in participating mediaJournal of Thermophysics and Heat Transfer, 1995
- A Galerkin solution to a regularized Cauchy singular integro-differential equationQuarterly of Applied Mathematics, 1995
- A Primer on Integral Equations of the First KindPublished by Society for Industrial & Applied Mathematics (SIAM) ,1991
- On the solution of integral equations with strongly singular kernelsQuarterly of Applied Mathematics, 1987
- Accurate solution of the Orr–Sommerfeld stability equationJournal of Fluid Mechanics, 1971