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A Multigrid Solver for Subdiffusion Equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 اردیبهشت 1404 اصل مقاله (1.14 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.65520.3017 | ||
| نویسندگان | ||
| Reza Mokhtari* 1؛ Mohadeseh Ramezani1؛ Gundolf Haase2 | ||
| 1Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran. | ||
| 2Department for Mathematics and Scientific Computing, University of Graz, Graz, Austria. | ||
| چکیده | ||
| In this paper, we investigate the S3-FD method for solving time-fractional diffusion equations in both one-dimensional (1D) and two-dimensional (2D) spatial domains, achieving high-order temporal accuracy. We leverage the S3 formula, which has a temporal accuracy of \(4 - \alpha\), to approximate the Caputo fractional derivative of order \(\alpha \in (0,1)\), and we employ the finite difference approach for spatial discretization. We develop a fully discrete scheme for both uniform and non-uniform spatial meshes. Our analysis begins with the 1D subdiffusion problem, where we employ the cyclic reduction method alongside OpenMP-based parallel programming to reduce computational costs. Leveraging this groundwork, we extend our technique to the 2D subdiffusion problem using a multigrid method and domain decomposition strategy paired with MPI programming. This innovative method yields an impressive temporal convergence order of \(\mathcal{O}(\Delta t^{4-\alpha})\). The performance and efficiency of the proposed S3-FD algorithm are demonstrated through numerical experiments, highlighting its potential for large-scale fractional diffusion problems. | ||
| کلیدواژه‌ها | ||
| Subdiffusion equation؛ S3 formula؛ multigrid method؛ domain decomposition؛ parallel processing | ||
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آمار تعداد مشاهده مقاله: 76 تعداد دریافت فایل اصل مقاله: 66 |
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