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Numerical multiscale methods to determine the coefficient in diffusion problems | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 دی 1403 اصل مقاله (2.42 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.59745.2547 | ||
| نویسندگان | ||
| Marzieh Tavakolian1؛ Ali Hatam* 1؛ Morteza Fotouhi2؛ Edmund Chadwick3 | ||
| 1Department of Applied Mathematics, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran, Iran 1591634311. | ||
| 2Department of Mathematical Sciences, Sharif University of Technology, Tehran 11365-9415, Iran. | ||
| 3School of Science, Engineering & Environment, University of Salford, Salford, M5 4WT, UK. | ||
| چکیده | ||
| Here we study the inverse problem of determining the highly oscillatory coefficient $a^\varepsilon$ in some PDEs of the form $ u^\varepsilon_t - \nabla .(a^\varepsilon(x) \nabla u^\varepsilon)=0$, in a bounded domain $\Omega \subset\mathbb{R}^d $; $\varepsilon$ indicates the smallest characteristic wavelength in the problem ($0 < \varepsilon \ll 1$). Assume that $g(t, x)$ is given input data for $(t, x) \in (0,T) \times\partial \Omega$ and the associated output is the thermal flux $a^\varepsilon(x)\nabla u(T_0,x)\cdot n(x)$ measured on the boundary at a given time $T_0$. Because of ill-posedness of the inverse problem, we reduce the dimension by seeking effective parameters. For forward solver, we apply either analytic homogenization or some numerical multiscale methods such as FE-HMM and LOD method. | ||
| کلیدواژه‌ها | ||
| 35B27؛ 35K20؛ 35R30؛ 65L60؛ 65M32 | ||
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آمار تعداد مشاهده مقاله: 91 تعداد دریافت فایل اصل مقاله: 144 |
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