Applying the meshless Fragile Points method to solve the two-dimensional linear Schrödinger equation on arbitrary domains
The meshless Fragile Points method (FPM) is applied to find the numerical solutions of the Schrödinger equation on arbitrary domains. This method is based on Galerkin’s weak-form formulation, and the generalized finite difference method has been used to obtain the test and trial functions. For parti...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2023-03-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_41896_f5e983fd6b63a55ba1297dd5d2152990.pdf |
| _version_ | 1827997355984551936 |
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| author | D. Haghighi S. Abbasbandy E. Shivanian |
| author_facet | D. Haghighi S. Abbasbandy E. Shivanian |
| author_sort | D. Haghighi |
| collection | DOAJ |
| description | The meshless Fragile Points method (FPM) is applied to find the numerical solutions of the Schrödinger equation on arbitrary domains. This method is based on Galerkin’s weak-form formulation, and the generalized finite difference method has been used to obtain the test and trial functions. For partitioning the problem domain into subdomains, Voronoi diagram has been applied. These functions are simple, local, and discontinuous poly-nomials. Because of the discontinuity of test and trial functions, FPM may be inconsistent. To deal with these inconsistencies, we use numerical flux corrections. Finally, numerical results are presented for some exam-ples of domains with different geometric shapes to demonstrate accuracy, reliability, and efficiency. |
| first_indexed | 2024-04-10T05:28:18Z |
| format | Article |
| id | doaj.art-b0e4f606b7864c3aba0aadcea41108e0 |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-04-10T05:28:18Z |
| publishDate | 2023-03-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-b0e4f606b7864c3aba0aadcea41108e02023-03-07T09:30:31ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692023-03-0113111810.22067/ijnao.2022.72900.106341896Applying the meshless Fragile Points method to solve the two-dimensional linear Schrödinger equation on arbitrary domainsD. Haghighi0S. Abbasbandy1E. Shivanian2Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran.Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran.Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran.The meshless Fragile Points method (FPM) is applied to find the numerical solutions of the Schrödinger equation on arbitrary domains. This method is based on Galerkin’s weak-form formulation, and the generalized finite difference method has been used to obtain the test and trial functions. For partitioning the problem domain into subdomains, Voronoi diagram has been applied. These functions are simple, local, and discontinuous poly-nomials. Because of the discontinuity of test and trial functions, FPM may be inconsistent. To deal with these inconsistencies, we use numerical flux corrections. Finally, numerical results are presented for some exam-ples of domains with different geometric shapes to demonstrate accuracy, reliability, and efficiency.https://ijnao.um.ac.ir/article_41896_f5e983fd6b63a55ba1297dd5d2152990.pdffragile points methodnumerical fluxesschrödinger equa-tionvoronoi diagram |
| spellingShingle | D. Haghighi S. Abbasbandy E. Shivanian Applying the meshless Fragile Points method to solve the two-dimensional linear Schrödinger equation on arbitrary domains Iranian Journal of Numerical Analysis and Optimization fragile points method numerical fluxes schrödinger equa-tion voronoi diagram |
| title | Applying the meshless Fragile Points method to solve the two-dimensional linear Schrödinger equation on arbitrary domains |
| title_full | Applying the meshless Fragile Points method to solve the two-dimensional linear Schrödinger equation on arbitrary domains |
| title_fullStr | Applying the meshless Fragile Points method to solve the two-dimensional linear Schrödinger equation on arbitrary domains |
| title_full_unstemmed | Applying the meshless Fragile Points method to solve the two-dimensional linear Schrödinger equation on arbitrary domains |
| title_short | Applying the meshless Fragile Points method to solve the two-dimensional linear Schrödinger equation on arbitrary domains |
| title_sort | applying the meshless fragile points method to solve the two dimensional linear schrodinger equation on arbitrary domains |
| topic | fragile points method numerical fluxes schrödinger equa-tion voronoi diagram |
| url | https://ijnao.um.ac.ir/article_41896_f5e983fd6b63a55ba1297dd5d2152990.pdf |
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