A Tikhonov regularized penalty function approach for solving polylinear programming problems

Identification of time-dependent convection coefficient in a time-fractional diffusion equation

Inverse source problems is a classical ill-posed problem. There exist several literatures on inverse heat source problems. In this study we use some stable methods to deal with the inverse problems of determining space-wise and time-wise dependent heat source in the heat diffusion equation. The problems of inverse heat source sources are transferred to the problems of numerical differentiation. By simple and effective methods which are used to regularize the problems of numerical differentiation before, we can obtain stable solutions. The numerical results show that our proposed procedure yields stable and accurate approximation.

A direct numerical method for solving inverse heat source problems

Abstract This paper is concerned with the inverse problem for determining the space-dependent source and the initial value simultaneously in a parabolic equation from two over-specified measurements. By means of transforming information of the initial value into the source term and obtaining a combined source term, the parabolic equation problem is converted into a parabolic problem with homogeneous conditions. Then the considered inverse problem is formulated into a regularized minimization problem, which is implemented by the finite element method based on solving a sequence of well-posed direct problems. The uniqueness of inverse solutions are proved by the solvability of the corresponding variational problem, and the conditional stability as well as the convergence rate of regularized solutions are also provided. Then the error estimate of approximate regularization solutions is presented in the finite-dimensional space. The proposed method is a very fast non-iterative algorithm, and it can successfully solve the multi-dimensional inverse problem for recovering the space-dependent source and the initial value simultaneously. Numerical results of five examples including one- and two-dimensional cases show that the proposed method is efficient and robust with respect to data noise.

A non-iterative method for recovering the space-dependent source and the initial value simultaneously in a parabolic equation

Electrical structures in the central part of the North China Craton and their implications for the mechanism of Craton destruction

A new gradient regularization algorithm for source term inversion in 1D solute transportation with final observations

Three-Dimensional Electrical Structure and Seismogenic Environment of the Crust–Mantle in the Lushan Earthquake Region, China

Deep electrical structure and thermodynamic mechanism of the high-temperature geothermal field in Kangding, Western Sichuan, China

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A new gradient regularization algorithm for source term inversion in 1D solute transportation with final observations

Three-Dimensional Electrical Structure and Seismogenic Environment of the Crust–Mantle in the Lushan Earthquake Region, China

Deep electrical structure and thermodynamic mechanism of the high-temperature geothermal field in Kangding, Western Sichuan, China