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RBF partition of unity methods for solving the Poison equation on irregular domains | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 مهر 1404 اصل مقاله (2.53 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.65004.2967 | ||
| نویسندگان | ||
| Fariba Fathi Dopolani؛ Mohammadreza Ahmadi Darani* | ||
| Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University , P.O. Box. 115, Shahrekord, Iran. | ||
| چکیده | ||
| This paper presents a novel approach for solving the {Poisson} equation on arbitrary domains using a direct Radial Basis Function (DRBF) partition of unity technique. The method involves dividing the primary domain into overlapping subdomains, calculating local approximations within each {subdomain}, and then combining these approximations through discontinuous weight functions to form a global solution. We also use polyharmonic spline (PHS) kernels, {with} scaling properties. This strategy improves stability, lowers computational costs, and replaces a single ill-conditioned linear system with several smaller, well-conditioned linear systems. Numerical experiments are performed to confirm the efficacy of the proposed method. | ||
| کلیدواژه‌ها | ||
| radial basis function (RBF) Methods؛ Partition of unity (PU)؛ Direct Radial Basis Function Partition of Unity (D-RBF-PU) | ||
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آمار تعداد مشاهده مقاله: 42 تعداد دریافت فایل اصل مقاله: 70 |
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