Conjugate gradient method based on complex-variable-differentiation method and its application for identification of boundary conditions in inverse heat conduction problems

CUI Miao; DUAN Weiwei; GAO Xiaowei

doi:10.11949/j.issn.0438-1157.20150308

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Conjugate gradient method based on complex-variable-differentiation method and its application for identification of boundary conditions in inverse heat conduction problems

更新时间：2025-12-10

- Conjugate gradient method based on complex-variable-differentiation method and its application for identification of boundary conditions in inverse heat conduction problems
- CIESC Journal Issue S1, Pages: 106-110(2015)
- 作者机构：
  
  大连理工大学航空航天学院, 工业装备结构分析国家重点实验室,辽宁,大连,116024
- 作者简介：
- 基金信息：
- DOI：10.11949/j.issn.0438-1157.20150308
  CLC： K124
- Online First：30 June 2015，
  
  Published：30 June 2015
- 稿件说明：
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CUI Miao, DUAN Weiwei, GAO Xiaowei. Conjugate gradient method based on complex-variable-differentiation method and its application for identification of boundary conditions in inverse heat conduction problems[J]. CIESC Journal, 2015, (S1): 106-110.
DOI：

CUI Miao, DUAN Weiwei, GAO Xiaowei. Conjugate gradient method based on complex-variable-differentiation method and its application for identification of boundary conditions in inverse heat conduction problems[J]. CIESC Journal, 2015, (S1): 106-110. DOI： 10.11949/j.issn.0438-1157.20150308.

摘要

为了利用共轭梯度法的计算精度高和收敛速度快的优点

避免传统共轭梯度法在求解非线性热传导反问题中的微分处理、复杂的推导过程等问题

给出一种改进的共轭梯度法

即将复变量求导法引入传统的共轭梯度法

准确计算了各灵敏度系数

进而对瞬态非线性热传导反问题进行求解

并对边界条件进行辨识。算例验证了本文方法的有效性与精度。与传统共轭梯度法相比

在处理非线性问题方面

本文方法具有操作简单和精度高的优点。

Abstract

The conventional conjugate gradient method is improved to utilize its advantage of high accuracy and fast convergence

and to avoid the complicated differentiating and derivation processes for solving nonlinear inverse heat conduction problems. In the present work

the complex-variable-differentiation method is introduced into the conventional conjugate gradient method

which is employed to precisely calculate the sensitivity coefficients. Transient nonlinear inverse heat conduction problems are solved

and then the boundary conditions are identified. Numerical examples are given to show the effectiveness and high accuracy. Compared with the conventional conjugate gradient method

the present algorithm has the advantage of easier implementation and higher accuracy.

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