Abstract A novel domain propulsion and adaptive modified inversion method based on the least square error method and the precise integration finite element method is firstly proposed to identify the geometries of two-dimensional and three-dimensional models made of functional gradient materials. After introducing concept of virtual boundary, the inverse geometry problems can be solved only by the two processes, which are the domain propulsion process and the adaptive modified process. The first process is getting a better shape and position of virtual boundary through propulsion scheme. After that, the geometry can be identified by modifying the shape of virtual boundary and searching the isotherm or isothermal surface. To improve the ill-posedness of problems, the truncated singular value decomposition method and the coefficient expending scheme are adopted in inversing process. The results of some typical numerical examples show that the present method can obtain the great performance on both the inversing accuracy and the computing efficiency by discussing the influence of some factors such as the different approximation functions, the measurement errors, the number of measurement points and so on.

中文翻译：

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一种新的域推进和自适应修正反演方法用于 FGM 的逆几何热传导分析

摘要 首次提出了一种基于最小二乘误差法和精密积分有限元法的域推进和自适应修正反演新方法，用于识别功能梯度材料的二维和三维模型的几何形状。引入虚拟边界的概念后，逆几何问题只能通过域推进过程和自适应修正过程两个过程来解决。第一个过程是通过推进方案获得更好的虚拟边界形状和位置。之后，可以通过修改虚拟边界的形状并搜索等温线或等温面来识别几何形状。为了改善问题的不适定性，反演过程采用截断奇异值分解法和系数展开方案。一些典型数值算例的结果表明，通过讨论不同的逼近函数、测量误差、测量点数和测量点数等因素的影响，该方法在反演精度和计算效率方面都取得了很好的效果。很快。