二阶伴随灵敏度分析方法（2nd-asam）用于大规模非线性系统：II. 非线性热传导基准的应用
Second-order adjoint sensitivity analysis methodology (2nd-asam) for large-scale nonlinear systems: II. Application to a nonlinear heat conduction benchmark
AI总结：
本文展示将Cacuci（2015）提出的二阶伴随灵敏度分析方法应用于非线性热传导基准，该基准模拟含加热棒的液态铅铋合金实验段，具有精确解，揭示了数学推导。通过六个大规模伴随计算，精确计算了温度响应对五个模型参数的五阶一阶和十五阶二阶导数，仅需修改热传导微分算子的右端源项。
摘要：
本文展示了Cacuci（2015）提出的二阶伴随灵敏度分析方法（2nd-ASAM）在非线性热传导基准中的应用，该基准模拟包含加热棒的液态铅铋合金实验段。该基准具有精确解，从而清晰揭示了底层数学推导。对于此示例问题，六个大规模伴随计算足以精确计算温度响应对五个模型参数的五阶一阶和十五阶不同的二阶导数。非常显著的是，仅需修改热传导微分算子的右端源项；左端的微分方程（以及因此在大规模实际应用中的求解器）保持不变。
英文摘要：
This work presents an illustrative application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci (2015) to a paradigm nonlinear heat conduction benchmark, which models a conceptual experimental test section containing heated rods immersed in liquid lead-bismuth eutectic. This benchmark admits an exact solution, thereby making transparent the underlying mathematical derivations. For this illustrative problem, six large-scale adjoint computations sufficed to compute exactly all five 1st-order and fifteen distinct 2nd-order derivatives of the temperature response to the five model parameters. Very significantly, only the sources on the right-sides of the heat conduction differential operator need to be modified; the left-side of the differential equations (and hence the solver in large-scale practical applications) remains unchanged.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
