Regularization Algorithms for Inverse Problems of High-dimensional Diffusion Equations with Robin Boundary Conditions
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.
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