Splitting-based conjugate gradient method for a multi-dimensional linear inverse heat conduction problem
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TL;DR: This paper considers a multi-dimensional inverse heat conduction problem with time-dependent coefficients in a box by a variational method, and applies the conjugate gradient method with a stopping rule to the discretized inverse problem rather than to the continuous one.
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About: This article is published in Journal of Computational and Applied Mathematics. The article was published on 01 Oct 2009. and is currently open access. The article focuses on the topics: Gradient method & Nonlinear conjugate gradient method.
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Citations
An inverse problem of parameter estimation for time-fractional heat conduction in a composite medium using carbon-carbon experimental data
Qiao Zhuang,Bo Yu,Xiaoyun Jiang +2 more
TL;DR: In this paper, a time-fractional heat conduction model is proposed for an experimental heat conduct process in a 3-layer composite medium. And the optimal order of Caputo fractional derivative is estimated with Levenberg-Marquardt method.
43
A boundary element method for a multi-dimensional inverse heat conduction problem
TL;DR: A variational method for a multi-dimensional inverse heat conduction problem in Lipschitz domains is investigated using the boundary element method coupled with the conjugate gradient method and it is proved the convergence of this scheme with and without Tikhonov regularization.
32
Review of Computational Schemes in Inverse Heat Conduction Problems
TL;DR: A review of the current computational methods and applications of inverse heat conduction problems (IHCPs) in different fields is presented in this paper, where two major so-called major problems are discussed.
25
A backward parabolic equation with a time-dependent coefficient: Regularization and error estimates
TL;DR: In this paper, a modified method for regularizing the problem and derive an optimal stability estimation is presented, and a numerical experiment is presented for illustrating the estimate, where the solution does not depend continuously on the given data.
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Determination of the initial condition in parabolic equations from integral observations
TL;DR: In this article, a variational method in combination with Tikhonov regularization was proposed to solve the problem of determining the initial condition in parabolic equations with integral observations.
17
References
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James V. Beck,Ben Blackwell,Charles R. St. Clair +2 more
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TL;DR: In this paper, the Inverse Heat Conduction Problem (IHCP) is formulated as a two-dimensional Inverse Convolutional Problem (ICP) and the solution of the one-dimensional IHCP is described.
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Victor Isakov
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