Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem
| Autor: | Mostafa Jourhmane, A. Naji, Fatima Ghafrani, Mohammed Hamaidi |
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| Rok vydání: | 2020 |
| Předmět: |
Well-posed problem
Article Subject Computer science General Engineering Stability (learning theory) Inverse QA75.5-76.95 02 engineering and technology Inverse problem 01 natural sciences Computer Science Applications 010101 applied mathematics 020303 mechanical engineering & transports 0203 mechanical engineering Electronic computers. Computer science Modeling and Simulation Collocation method Convergence (routing) Applied mathematics Radial basis function Boundary value problem 0101 mathematics |
| Zdroj: | Modelling and Simulation in Engineering, Vol 2020 (2020) |
| ISSN: | 1687-5605 1687-5591 |
| DOI: | 10.1155/2020/5046286 |
| Popis: | In many references, both the ill-posed and inverse boundary value problems are solved iteratively. The iterative procedures are based on firstly converting the problem into a well-posed one by assuming the missing boundary values. Then, the problem is solved by using either a developed numerical algorithm or a conventional optimization scheme. The convergence of the technique is achieved when the approximated solution is well compared to the unused data. In the present paper, we present a different way to solve an ill-posed problem by applying the localized and space-time localized radial basis function collocation method depending on the problem considered and avoiding the iterative procedure. We demonstrate that the solution of certain ill-posed and inverse problems can be accomplished without iterations. Three different problems have been investigated: problems with missing boundary condition and internal data, problems with overspecified boundary condition, and backward heat conduction problem (BHCP). It has been demonstrated that the presented method is efficient and accurate and overcomes the stability analysis that is required in iterative techniques. |
| Databáze: | OpenAIRE |
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