A variational method for identifying a spacewise-dependent heat source

被引：0

作者：

Johansson, B. Tomas ^{[1
]}

Lesnic, Daniel ^{[2
]}

机构：

[1] School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom

[2] Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

来源：

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) | 2007年 / 72卷 / 06期

关键词：

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution; but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Journal article (JA)

引用

页码：748 / 760

共 50 条

[21] A unified approach to identifying an unknown spacewise dependent source in a variable coefficient parabolic equation from final and integral overdeterminations
Hasanov, Alemdar
Pektas, Burhan
APPLIED NUMERICAL MATHEMATICS, 2014, 78 : 49 - 67
[22] Simultaneous identification of diffusion coefficient, spacewise dependent source and initial value for one-dimensional heat equation
Zhao, Zhi-Xue
Banda, Mapundi K.
Guo, Bao-Zhu
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (10) : 3552 - 3565
[23] Some uniqueness theorems for inverse spacewise dependent source problems in nonlinear PDEs
Slodicka, M.
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2014, 22 (01) : 2 - 9
[24] The modified polynomial expansion method for identifying the time dependent heat source in two-dimensional heat conduction problems
Kuo, Chung-Lun
Liu, Chein-Shan
Chang, Jiang-Ren
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2016, 92 : 658 - 664
[25] Application of the variational iteration method to inverse heat source problems
Geng, Fazhan
Lin, Yingzhen
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (11-12) : 2098 - 2102
[26] Identification of spacewise and time dependent source terms in 1D heat conduction equation from temperature measurement at a final time
Hasanov, Alemdar
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2012, 55 (7-8) : 2069 - 2080
[27] Identifying an unknown source term in a heat equation with time-dependent coefficients
Duc, Nguyen Van
Nhat Minh, Luong Duy
Thanh, Nguyen Trung
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2021, 29 (05) : 609 - 635
[28] Research on multi-heat source arrangement optimization based on equivalent heat source method and reconstructed variational autoencoder
Yang, Yide
Gong, Mali
Ma, Jianshe
SCIENTIFIC REPORTS, 2024, 14 (01):
[29] The homotopy method for identifying the radiative source term in the heat conduction problem
Zhang, Wenyu
Ma, Fuming
Sun, Yao
APPLICABLE ANALYSIS, 2016, 95 (04) : 842 - 859
[30] INVERSE PROBLEMS OF IDENTIFYING THE TIME-DEPENDENT SOURCE COEFFICIENT FOR SUBELLIPTIC HEAT EQUATIONS
Ismailov, Mansur i.
Ozawa, Tohru
Suragan, Durvudkhan
INVERSE PROBLEMS AND IMAGING, 2024, 18 (04) : 813 - 823

← 1 2 3 4 5 →