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Awad Nasser, Ahmed, Allame, Masoud, Abed Kadhim Aal-Rkhais, Habeeb, Tavassoli-Kajani, Majid. (1404). Numerical solution of obstacle problem by using the mesh-free radial point interpolation method. فیزیولوژی و بیوتکنولوژی آبزیان, 13(4), 929-942. doi: 10.22124/jmm.2025.29905.2671
Ahmed Awad Nasser; Masoud Allame; Habeeb Abed Kadhim Aal-Rkhais; Majid Tavassoli-Kajani. "Numerical solution of obstacle problem by using the mesh-free radial point interpolation method". فیزیولوژی و بیوتکنولوژی آبزیان, 13, 4, 1404, 929-942. doi: 10.22124/jmm.2025.29905.2671
Awad Nasser, Ahmed, Allame, Masoud, Abed Kadhim Aal-Rkhais, Habeeb, Tavassoli-Kajani, Majid. (1404). 'Numerical solution of obstacle problem by using the mesh-free radial point interpolation method', فیزیولوژی و بیوتکنولوژی آبزیان, 13(4), pp. 929-942. doi: 10.22124/jmm.2025.29905.2671
Awad Nasser, Ahmed, Allame, Masoud, Abed Kadhim Aal-Rkhais, Habeeb, Tavassoli-Kajani, Majid. Numerical solution of obstacle problem by using the mesh-free radial point interpolation method. فیزیولوژی و بیوتکنولوژی آبزیان, 1404; 13(4): 929-942. doi: 10.22124/jmm.2025.29905.2671

Numerical solution of obstacle problem by using the mesh-free radial point interpolation method

Journal of Mathematical Modeling
مقاله 12، دوره 13، شماره 4، اسفند 2025، صفحه 929-942    اصل مقاله (546.13 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2025.29905.2671
نویسندگان
Ahmed Awad Nasser1؛ Masoud Allame* 2؛ Habeeb Abed Kadhim Aal-Rkhais3؛ Majid Tavassoli-Kajani1
1Department of Mathematics, Isfahan (Khorasgan) branch, Islamic Azad University, Isfahan, Iran
2Department of Mathematics, Isfahan (Khorasgan) branch, Islamic Azad University, Isfahan, Iran
3Department of Mathematics, College of Computer and Mathematics, University of Thi-Qar, Iraq
چکیده
The obstacle problem is a well-known type of elliptic variational inequality that originally arose from contact issues in solid mechanics. The solutions to the obstacle problem often have irregularities along a free boundary, which can be effective in designing an appropriate numerical method for these problems.  In this paper, we present a  mesh-free method based on the radial point interpolation method for numerically solving an obstacle problem. In the proposed method, the  radial point interpolating shape functions are utilized in the global weak form of the obstacle problem, based on the element-free Galerkin method. This approach is combined with an active set strategy to address the obstacle problem. One of the key benefits of the proposed method is its independence from any mesh of the computing domain, along with its straightforward implementation and  high numerical stability. To ensure the efficiency of the presented method, we have investigated the convergence of  the proposed method.  The  obtained numerical results confirm the theoretical achievements and demonstrate the method's effectiveness and accuracy.
کلیدواژه‌ها
Obstacle problem, variational inequality؛ meshfree method؛ radial points interpolation method
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