Radial basis functions method for parabolic inverse problem

Abstract

The radial basis functions (RBFs) method is employed to handle a class of multi-dimensional parabolic inverse problems. Because they are not modelled by classical parabolic initial-boundary value problems, theoretical behaviour and numerical approximation of these problems have been active areas of research. Based on the idea of RBF approximation, a fast and highly accurate meshless method is developed for solving an inverse problem with a control parameter. Moreover, with the meshless property, it can be used to handle multi-dimensional parabolic inverse problems defined on very complicated geometries.

Keywords:

• interpolation
• radial basis functions
• inverse problem
• parabolic equations
• meshless methods

2000 AMS Subject Classifications :

• 41A05
• 65D05
• 65M70

Acknowledgements

We are grateful for the anonymous reviewers for their valuable comments and suggestions. This work is supported by 973program-2006CB303102, SSTC 08DZ 2271900.