Optimal choice of descent steps in gradient methods of solution of inverse heat-conduction problems

1980 ◽  
Vol 39 (2) ◽  
pp. 865-869
Author(s):  
E. A. Artyukhin ◽  
S. V. Rumyantsev
Keyword(s):  
Heat Conduction ◽  
Gradient Methods ◽  
Optimal Choice ◽  
Inverse Heat Conduction ◽  
Inverse Heat Conduction Problems

A Modified Conjugate Gradient Method for Transient Nonlinear Inverse Heat Conduction Problems: A Case Study for Identifying Temperature-Dependent Thermal Conductivities

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Miao Cui ◽  
Qianghua Zhu ◽  
Xiaowei Gao
Keyword(s):  
Heat Conduction ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Adjoint Problem ◽  
Inverse Heat Conduction ◽  
Temperature Dependent ◽  
Sensitivity Problem ◽  
Inverse Heat Conduction Problems ◽  
Thermal Conductivities

Despite numerous studies of conjugate gradient methods (CGMs), the “sensitivity problem” and the “adjoint problem” are inevitable for nonlinear inverse heat conduction problems (IHCPs), which are accompanied by some assumptions and complicated differentiating processes. In this paper, a modified CGM (MCGM) is presented for the solution of a specified transient nonlinear IHCP, to recover temperature-dependent thermal conductivities for a case study. By introducing the complex-variable-differentiation method (CVDM) for sensitivity analysis, the sensitivity problem and the adjoint problem are circumvented. Five test examples are given to validate and assess the performance of the MCGM.

Efficient Numerical Solution of Inverse Heat Conduction Problems

1995 ◽  
Author(s):  
Hans-Jürgen Reinhardt ◽  
Dinh Nho Hao
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Numerical Methods ◽  
Stationary Point ◽  
Forthcoming Paper ◽  
Inverse Heat Conduction ◽  
Piecewise Constant ◽  
Numerical Tests ◽  
Inverse Heat Conduction Problems ◽  
Special Case

Abstract In this contribution we propose new numerical methods for solving inverse heat conduction problems. The methods are constructed by considering the desired heat flux at the boundary as piecewise constant (in time) and then deriving an explicit expression for the solution of the equation for a stationary point of the minimizing functional. In a very special case the well-known Beck method is obtained. For the time being, numerical tests could not be included in this contribution but will be presented in a forthcoming paper.

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