A boundary-type meshless method for the Robin inverse problem - Dong, Chao-Feng (Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban, 2013)
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.