Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data

doi:10.1088/1674-1056/20/10/100201

中国物理B ›› 2011, Vol. 20 ›› Issue (10): 100201-100201.doi: 10.1088/1674-1056/20/10/100201

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Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data

李福乐, 张洪谦

College of Science and Information, Qingdao Agricultural University, Qingdao 266109, China

收稿日期:2010-07-13 修回日期:2011-05-23 出版日期:2011-10-15 发布日期:2011-10-15
基金资助:
Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. ZR2009AL012) and the Science and Technology Program of Education Bureau of Shandong Province, China (Grant No. J09LA12).

Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data

Li Fu-Le(李福乐)^† and Zhang Hong-Qian(张洪谦)

College of Science and Information, Qingdao Agricultural University, Qingdao 266109, China

Received:2010-07-13 Revised:2011-05-23 Online:2011-10-15 Published:2011-10-15
Supported by:
Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. ZR2009AL012) and the Science and Technology Program of Education Bureau of Shandong Province, China (Grant No. J09LA12).

摘要/Abstract

摘要： In this paper, we present a new algorithm to solve a two-dimensional parabolic inverse problem with a source parameter, which appears in many physical phenomena. A linearized compact difference scheme for this problem is constructed using the finite difference method. The discretization accuracy is second-order in time and fourth-order in space. We obtain the unique solvability and present an alternating direction implicit algorithm to solve this difference scheme. The results of numerical experiments are presented to demonstrate the accuracy of this algorithm.

Abstract: In this paper, we present a new algorithm to solve a two-dimensional parabolic inverse problem with a source parameter, which appears in many physical phenomena. A linearized compact difference scheme for this problem is constructed using the finite difference method. The discretization accuracy is second-order in time and fourth-order in space. We obtain the unique solvability and present an alternating direction implicit algorithm to solve this difference scheme. The results of numerical experiments are presented to demonstrate the accuracy of this algorithm.

Key words: control parameter, temperature distribution, finite difference scheme, solvability

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Zz (Inverse problems) 02.60.Cb (Numerical simulation; solution of equations) 02.70.Bf (Finite-difference methods)

李福乐, 张洪谦. Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data[J]. 中国物理B, 2011, 20(10): 100201-100201.

Li Fu-Le(李福乐) and Zhang Hong-Qian(张洪谦) . Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data[J]. Chin. Phys. B, 2011, 20(10): 100201-100201.

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Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data

Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data

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