关于环形区域内逆热传导问题的李群打靶方法

Inverse heat conduction problems (IHCP) are well known for being ill-posed，i.e., the solution of the problem does not continuously depend on the measurement data. In this paper, the Lie-group shooting method and quasi-boundary regularization method (QBRM) are employed to solve a two-dimensional inverse heat conduction problem (IHCP) in annular domain. On one hand, A quasi-boundary regularization leads to a two-point boundary value problem of the inverse heat conduction equation. On the other hand, the illposed problem is analyzed by using the semi-discretization numerical schemes. The key point of the LGSM is based on the erection of a one-step Lie group element and the formation of a generalized mid-point Lie group element. By imposing one-step Lie group element being equal to the generalized mid-point Lie group element, we can obtain system of nonlinear algebraic equations on the temperature and the heat flux of the inner boundary, and we choose a suitable weighting factor through a minimum discrepancy to solve the ill-posed problem by the iteration method. Several numerical examples show that the LGSM has good effectiveness and stability.