带有移动边界的热传导反问题有限点法OA
Finite Point Method for Inverse Heat Conduction Problem with Moving Boundary
对带有移动边界的非齐次热传导方程反问题进行研究,利用一种基于动态节点布置策略的无网格有限点法求解该问题.当带有噪声数据时,求解源项为不适定问题,结合磨光正则化方法,对方程的源项以及精确解进行同时反演.通过数值算例验证,文中所用方法对于求解此类带有移动边界的热传导方程反问题是稳定有效的.
The inverse problem of non-homogeneous heat conduction equation with moving boundaries is studied,and a meshless finite point method based on dynamic node arrangement strategy is used to solve the problem.When there is noisy data,solving the source term is an ill-posed problem.In this paper,combining the smoothing regulariza-tion method,the source term and the exact solution of the equation are simultaneously inverted.Numerical examples show that the method used in the article is stable and effective for solving inverse problems of heat conduction equa-tions with moving boundaries.
高佳兴;张永富
内蒙古民族大学 数学科学学院,内蒙古 通辽 028043内蒙古民族大学 数学科学学院,内蒙古 通辽 028043
数理科学
热传导反问题有限点法移动边界磨光正则化方法
heat conduction inverse problemfinite point methodmobile boundarysmoothing regularization method
《内蒙古民族大学学报（自然科学版）》 2026 (1)
75-82,8
国家自然科学基金项目(11961053)内蒙古自治区直属高校基本科研业务费项目(GXKY252013)
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