Applying the meshless Fragile Points method to solve the two-dimensional linear Schrödinger equation on arbitrary domains

Iranian Journal of Numerical Analysis and Optimization

مقاله 13، دوره 13، شماره 1 - شماره پیاپی 24، خرداد 2023، صفحه 1-18   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.72900.1063

نویسندگان

D. Haghighi؛ S. Abbasbandy^* ؛ E. Shivanian

Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran.

چکیده

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.

کلیدواژه‌ها

Fragile Points Method؛ Numerical Fluxes؛ Schrödinger equa-tion؛ Voronoi Diagram

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