具Robin条件的高维扩散方程反问题正则化算法OACHSSCDCSTPCD
Regularization Algorithms for Inverse Problems of High-dimensional Diffusion Equations with Robin Boundary Conditions
初始热场和热源同时识别问题是一类热传导方程反问题.通过两个固定时刻的温度测量数据同时反演初始温度和热源项,提出了改进的正则化方法,获得了稳定化算法,给出了正则化参数的选取策略及正则化解的误差估计,对带噪声干扰的测量数据进行预处理以提高数据精度.数值算例验证了算法的有效性.
The simultaneous identification of the initial heat field and the heat source is a class of inverse prob-lems in heat conduction equations.By utilizing temperature measurements at two fixed moments,an improved regularization method is proposed to stably determine both the initial temperature and heat source terms.A sta-bilization algorithm is thus obtained.Strategies for selecting regularization parameters and error estimates for the regularization solutions are provided.Additionally,pre-processing is performed on the measurement data with noise interference to improve accuracy.Numerical experiments verify the effectiveness of the algorithm.
郭琴;徐定华
浙江理工大学 理学院,浙江 杭州 310018
数学
高维热传导方程Robin边界条件改进正则化方法数据预处理误差估计
high-dimensional heat conduction equationsRobin boundary conditionsimproved regularization methodsdata pre-processingerror estimation
《宁夏大学学报（自然科学版）》 2024 (002)
97-106 / 10
国家自然科学基金资助项目(12371428,11871435)
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