A boundary-type meshless method for the Robin inverse problem

• Published in: Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Vol. 40; no. 1; pp. 29 - 34
• Main Author: Dong, Chao-Feng
• Format: Journal Article
• Language: Chinese
• Published: Zhejiang University Press 01.01.2013
• Subjects: Boundaries; Finite element method; Inverse problems; Mathematical analysis; Mathematical models; Meshless methods; Newton Theory; Regularization; robin反问题; 基本解方法; 截断奇异值分解; 无网格方法; 边界粒子法
• ISSN: 1008-9497
• DOI: 10.3785/j.issn.1008-9497.2013.01.008

A boundary-type meshless method is proposed to solve the Robin inverse problem associated with inhomogeneous steady-state heat conduction. In the present method, the problem is transformed into the inverse Cauchy problem by Newton's law of convective heat transfer; the boundary particle method is used to handle the inhomogeneous term in order to avoid the requirement of inner nodes; a method of fundamental solutions is then employed to evaluate the particular solution and the corresponding homogenous solution. Since the inverse problem is ill-posed, the truncated singular value decomposition with the regularization parameter given by the L-curve method is introduced to solve the resultant highly ill-conditioned system of linear equations. Numerical results are presented to verify the reliability and efficiency of the proposed method.