共轭梯度法求解非线性多宗量稳态传热反问题

应用共轭梯度法求解非线性多宗量稳态热传导反问题。采用八节点的等参单元在空间上进行离散，建立了便于敏度分析的非线性正演和反演的有限元模型，可直接求导进行敏度分析。给出了相关的数值验证，对测量误差及测点数目的影响作了初步探讨，结果表明，采用的算法能够对非线性稳态热传导中导热系数和边界条件联合反问题进行有效的求解，并具有较高精度。

Solving non-linear inverse heat conduction problems with multi-variables in steady state via conjugate gradient method

In this paper the conjugate gradient method is employed to solve non-linear inverse heat conduction problems with multi-variables in the steady state. The eight-point finite element is used for the discretization in the space system. The finite element model is given, facilitating to sensitivity analysis for non-linear direct and inverse problems. Several numerical examples are introduced to successfully verify the results in the paper. The preliminary investigation of effect of noise data and the number of sample points on the results are given. Results show that the proposed method can identify single and combined non-linear thermal parameters and boundary conditions for non-linear inverse conduction problems in the steady state with high precision.