A Numerical Algorithm Based on RBFs for Solving an Inverse Source Problem

作者：Shidfar A^*; Darooghehgimofrad Z

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2017, 40(3): 1149-1158.

DOI：10.1007/s40840-016-0358-7

• Inverse problem
• Radial basis function
• Tikhonov regularization
• Meshless method
• Thin plate splines

In this paper, a meshless numerical scheme for solving an inverse source problem is considered. The proposed scheme is based on approximating the solution employing the thin plate spline (TPS) radial basis RBF). Applying this radial basis function results in a badly ill-condition system of equations. The Tikhonov regularization method is employed for solving this system of equations. Determination of regularization parameter is based on generalized cross-validation (GCV) technique. Some numerical examples are presented to demonstrate the accuracy and ability of this method.

• 出版日期2017-7