Parameter identification in PDEs by the solution of monotone inclusion problems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915171827449856 |
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| author | Gautam, Pankaj Grasmair, Markus |
| author_facet | Gautam, Pankaj Grasmair, Markus |
| contents | In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total variation based regularization method requiring the solution of a monotone inclusion problem. We show well-posedness in the sense of inverse problems of the resulting regularization scheme. In addition, we introduce and analyze a numerical algorithm for the solution of this inclusion problem using a nested inertial primal dual method. We demonstrate by means of numerical examples the convergence of both the numerical algorithm and the regularization method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_04557 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parameter identification in PDEs by the solution of monotone inclusion problems Gautam, Pankaj Grasmair, Markus Numerical Analysis Analysis of PDEs Optimization and Control 65J20, 47H05, 47J06, 49J20 In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total variation based regularization method requiring the solution of a monotone inclusion problem. We show well-posedness in the sense of inverse problems of the resulting regularization scheme. In addition, we introduce and analyze a numerical algorithm for the solution of this inclusion problem using a nested inertial primal dual method. We demonstrate by means of numerical examples the convergence of both the numerical algorithm and the regularization method. |
| title | Parameter identification in PDEs by the solution of monotone inclusion problems |
| topic | Numerical Analysis Analysis of PDEs Optimization and Control 65J20, 47H05, 47J06, 49J20 |
| url | https://arxiv.org/abs/2403.04557 |