Abstract
In this paper the method of fundamental solutions (MFS) and the method of particular solution (MPS) are combined as a one-stage approach to solve the Cauchy problem for Poisson's equation. The main idea is to approximate the solution of Poisson's equation using a linear combination of fundamental solutions and radial basis functions. As a result, we provide a direct and effective meshless method for solving inverse problems with inhomogeneous terms. Numerical results in 2D and 3D show that our proposed method is effective for Cauchy problems. © 2010 Elsevier Ltd. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 499-506 |
| Journal | Engineering Analysis with Boundary Elements |
| Volume | 35 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Mar 2011 |
Research Keywords
- Cauchy problem
- Inverse problem
- Meshless methods
- Method of fundamental solutions
- Radial basis functions
- The method of particular solutions
- Tikhonov's regularization
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