Recovering Heat Source from Fourth-Order Inverse Problems by Weighted Gradient Collocation

Judy P. Yang*, Hsiang Ming Li

*此作品的通信作者

研究成果: Article同行評審

2 引文 斯高帕斯(Scopus)

摘要

The weighted gradient reproducing kernel collocation method is introduced to recover the heat source described by Poisson’s equation. As it is commonly known that there is no unique solution to the inverse heat source problem, the weak solution based on a priori assumptions is considered herein. In view of the fourth-order partial differential equation (PDE) in the mathematical model, the high-order gradient reproducing kernel approximation is introduced to efficiently untangle the problem without calculating the high-order derivatives of reproducing kernel shape functions. The weights of the weighted collocation method for high-order inverse analysis are first determined. In the benchmark analysis, the unclear illustration in the literature is clarified, and the correct interpretation of numerical results is given particularly. Two mathematical formulations with four examples are provided to demonstrate the viability of the method, including the extreme cases of the limited accessible boundary.

原文English
文章編號241
期刊Mathematics
10
發行號2
DOIs
出版狀態Published - 1 1月 2022

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