The Local Radial Basis Function Collocation Method for Solving Two-Dimensional Inverse Cauchy Problems
Authors:
- 15 April 2013
- journal article
- research article
- Published by Taylor & Francis in Numerical Heat Transfer, Part B: Fundamentals
- Vol. 63 (4) , 284-303
Abstract
In this study, inverse Cauchy problems, which are governed by the Poisson equation, inhomogeneous Helmholtz equation, and inhomogeneous convection-diffusion-reaction equation, are analyzed by the local radial basis function collocation method (LRBFCM). In the inverse Cauchy problem, overspecified boundary conditions are given along part of the boundary and no boundary condition is imposed on the rest of the boundary. The inverse problems are generally very unstable and ill-posed, so the inverse Cauchy problem is very difficult to solve stably using any numerical scheme. The LRBFCM is one kind of domain-type meshless method and can get rid of mesh generation and numerical quadrature. In addition, the localization in LRBFCM can reduce the ill-conditioning problem and full matrix. Therefore, in this study the LRBFCM is adopted to analyze two-dimensional inverse Cauchy problems. Five numerical examples are provided to verify the proposed meshless scheme. In addition, the stability of the proposed scheme is validated by adding noise into boundary conditions.Keywords
This publication has 19 references indexed in Scilit:
- The Method of Fundamental Solutions for Solving the Backward Heat Conduction Problem with Conditioning by a New Post-ConditionerNumerical Heat Transfer, Part B: Fundamentals, 2011
- Modified Collocation Trefftz Method for the Geometry Boundary Identification Problem of Heat ConductionNumerical Heat Transfer, Part B: Fundamentals, 2011
- Equivalence between the Trefftz method and the method of fundamental solution for the annular Green's function using the addition theorem and image conceptEngineering Analysis with Boundary Elements, 2009
- Meshless Method for Geometry Boundary Identification Problem of Heat ConductionNumerical Heat Transfer, Part B: Fundamentals, 2009
- Some comments on the ill-conditioning of the method of fundamental solutionsEngineering Analysis with Boundary Elements, 2006
- Direct solution of ill-posed boundary value problems by radial basis function collocation methodInternational Journal for Numerical Methods in Engineering, 2005
- Eigensolutions of multiply connected membranes using the method of fundamental solutionsEngineering Analysis with Boundary Elements, 2005
- Numerical comparisons of two meshless methods using radial basis functionsEngineering Analysis with Boundary Elements, 2002
- Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson's equationsEngineering Analysis with Boundary Elements, 2002
- An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equationEngineering Analysis with Boundary Elements, 1997