基于复变量求导法的共轭梯度法及其在热传导反问题边界条件辨识中的应用

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。

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

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.