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Application of meshfree methods for solving the inverse one-dimensional Stefan problem

机译:无网格方法在求解一维反斯蒂芬反问题中的应用

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摘要

This work is motivated by studies of numerical simulation for solving the inverse one and two-phase Stefan problem. The aim is devoted to employ two special interpolation techniques to obtain space-time approximate solution for temperature distribution on irregular domains, as well as for the reconstruction of the functions describing the temperature and the heat flux on the fixed boundary x=0 when the position of the moving interface is given as extra specification. The advantage of applying the methods is producing the shape functions which provide the important delta function property to ensure that the essential conditions are fulfilled. Due to ill-posedness of the problem, the process is intractable numerically, so special optimization technique is used to obtain the regularized solution. Numerical results for the typical benchmark test examples, which have the input measured data perturbed by increasing amounts of noise and continuity to the input data in the presence of additive noise, are obtained, which present the efficiency of the proposed method.
机译:这项工作的动机是通过数值模拟研究来解决一阶和二阶反Stefan问题。该目标致力于采用两种特殊的插值技术来获得时空近似值解,以用于不规则区域上的温度分布,以及用于重构描述位置固定位置x = 0时温度和热通量的函数。移动接口的接口是额外的规范。应用该方法的优点是产生形状函数,该形状函数提供重要的增量函数属性以确保满足基本条件。由于问题的不适性,该过程在数值上难以处理,因此使用特殊的优化技术来获得正则解。获得了典型基准测试示例的数值结果,这些示例的输入测量数据受到噪声量的增加的干扰,并且在存在附加噪声的情况下与输入数据保持连续性,从而证明了所提方法的有效性。

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