Numerical Homogenization and Model Order Reduction for Multiscale Inverse Problems
| العنوان: | Numerical Homogenization and Model Order Reduction for Multiscale Inverse Problems |
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| المؤلفون: | Assyr Abdulle, Andrea Di Blasio |
| المصدر: | Multiscale Modeling & Simulation. 17:399-433 |
| بيانات النشر: | Society for Industrial & Applied Mathematics (SIAM), 2019. |
| سنة النشر: | 2019 |
| مصطلحات موضوعية: | Model order reduction, determining conductivity, inverse problems, Ecological Modeling, Numerical analysis, homogenization, General Physics and Astronomy, General Chemistry, Inverse problem, reduced basis, Homogenization (chemistry), boundary, Computer Science Applications, Modeling and Simulation, multiscale methods, Applied mathematics, global uniqueness, Mathematics |
| الوصف: | A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. We assume that the micro structure is known and seek to recover a macroscopic scalar parameterization of the microscale tensor (e.g., volume fraction). Departing from the full fine-scale model, which would require mesh resolution for the forward problem down to the finest scale, we solve the inverse problem for a coarse model obtained by numerical homogenization. The input data, i.e., measurement from the Dirichlet-to-Neumann map, are solely based on the original fine-scale model. Furthermore, reduced basis techniques are used to avoid computing effective coefficients for the forward solver at each integration point of the macroscopic mesh. Uniqueness and stability of the effective inverse problem is established based on standard assumptions for the fine-scale model, and a link to this latter model is established by means of G-convergence. A priori error estimates are established for our method. Numerical experiments illustrate the efficiency of the proposed scheme and confirm our theoretical findings. |
| تدمد: | 1540-3467 1540-3459 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd752b0bf696934f552d935c82da8ee4Test https://doi.org/10.1137/16m1091320Test |
| حقوق: | CLOSED |
| رقم الانضمام: | edsair.doi.dedup.....bd752b0bf696934f552d935c82da8ee4 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15403467 15403459 |
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