A local meshless collocation method for solving certain inverse problems. (English) Zbl 1403.65120
Summary: In this paper, we propose a meshless scheme based on compactly supported radial basis functions (CS-RBFs) for solving the Cauchy problem of Poisson’s equation and the inverse heat conduction problems in 2D. By assuming the unknown boundary condition to be a polynomial function, the inverse problems can be solved using a procedure similar to the process for solving forward problems. We employ Tikhonov regularization technique under L-curve regularization parameter to obtain a stable numerical solution. Numerical results verify the effectiveness and stability of this method.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
Keywords:
inverse problem; compactly supported radial basis functions; local meshless method; Tikhonov regularization; L-curveReferences:
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