热传导问题灵敏度分析的伴随法

Adjoint method of heat conduction sensitivity analysis

在热传导灵敏度分析的直接法的研究基础上 ,进一步探讨了稳态和瞬态热传导问题灵敏度分析的伴随法。推导了伴随法的计算列式 ,对于瞬态热传导问题 ,研究了瞬态约束处理的关键点方法 ,并提出伴随方程的精细积分解法。算例表明 ,稳态问题灵敏度计算 ,伴随法与直接法的结果是一致的 ;瞬态问题灵敏度计算 。

Based on research of the direct method for sensitivity analysis of heat conduction, an adjoint method is further investigated. Both the steady state problem and the transient problem are taken into account. After a brief introduction of the finite element method for heat conduction, the sensitivity equations of heat conduction are deduced by the adjoint method. The detail formulations are presented. As for a transient problem, the algorithm of critical time constraint is discussed. And then the precise time integration (PTI) method, is proposed to solve the equations of the adjoint method. The PTI method guarantees the numerical stability and precision in the results. The numerical examples show that the direct method and the adjoint method can achieve the same precision in the results. However as for the transient problem, the adjoint method is easy to implement.