Journal Article10.1016/J.AMC.2007.07.018
A new gradient regularization algorithm for source term inversion in 1D solute transportation with final observations
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TL;DR: The new gradient regularization algorithm is introduced and applied to solve an inverse problem of determining source terms in one-dimensional advection–dispersion equation with final observations and gives a possible approach to the precise choices of optimal regularization parameters.
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About: This article is published in Applied Mathematics and Computation. The article was published on 01 Mar 2008. The article focuses on the topics: Gradient method & Regularization perspectives on support vector machines.
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Citations
A Tikhonov regularized penalty function approach for solving polylinear programming problems
TL;DR: It is proved that if the penalty parameter μ tends to zero then the solution of the original problem converges to a unique solution with the minimal weighted norm.
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Identification of time-dependent convection coefficient in a time-fractional diffusion equation
TL;DR: The existence, uniqueness, regularity, and uniqueness of solution for the direct problem are proved by using the fixed point theorem and the stability of inverse convection coefficient problem is obtained based on the regularity of Solution for thedirect problem and some generalized Gronwall’s inequalities.
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A direct numerical method for solving inverse heat source problems
Xiong Xiangtuan,Yan Yaomei,Wang Junxia +2 more
- 01 Apr 2011
TL;DR: In this article, the inverse heat source problem is transferred to the problems of numerical differentiation and stable solutions are obtained by simple and effective methods which are used to regularize the problems for numerical differentiation before.
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A non-iterative method for recovering the space-dependent source and the initial value simultaneously in a parabolic equation
TL;DR: In this article, the inverse problem for determining the space-dependent source and the initial value simultaneously in a parabolic equation from two over-specified measurements is formulated as a regularized minimization problem, which is implemented by the finite element method based on solving a sequence of well-posed direct problems.
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•Journal Article
Chaos-regularization hybrid algorithm for nonlinear two-dimensional inverse heat conduction problem
TL;DR: In this article, a chaos-regularization hybrid algorithm was proposed to solve the nonlinear two-dimensional steady inverse heat conduction problem considering the thermal conductivity changing with temperature, which can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method.
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References
•Book
An Introduction to the Mathematical Theory of Inverse Problems
Andreas Kirsch
- 26 Sep 1996
TL;DR: Inverse Eigenvalue Problems and Inverse Problem in Electrical Impedance Tomography Inverse Scattering Problem as mentioned in this paper is a regularization theory for Equations of the First Kind.
Data compatibility and conditional stability for an inverse source problem in the heat equation
TL;DR: Data compatibilities are obtained with which the inverse source problem here is proved to be solvable and with aid of an integral identity that connects unknown source terms with the known data, a conditional stability is constructed.
47
Determining magnitude of groundwater pollution sources by data compatibility analysis
TL;DR: In this article, a new approach called data compatibility analysis methodology is presented and applied to solve the inverse source problem, where the unknown is confined to an explicit admissible set which can be easily estimated through the compatible conditions.
35
One-dimensional equilibrium model and source parameter determination for soil-column experiment
TL;DR: The inversion results show that for such inverse source coefficient problems with limited additional data, some optimal methods could be more efficient than regularization strategies, and for some real equilibrium soil-column experiments, the process of source (sink) reactions could be a key factor in the solute transportation.
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•Journal Article
Model parameter inversion for cadmium ion transport through unsaturated soils
TL;DR: In this article, a gradient regularization method is adopted as the inversion method for inversing parameter values of the parameter mentioned above for cadmium ion transport in 8 Portugal soils samples and 1 Belgium soils sample under different experimental conditions.
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