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

Document Type : Research Article

Authors

• D. Haghighi
• S. Abbasbandy
• E. Shivanian

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

10.22067/ijnao.2022.72900.1063

Abstract

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.

Keywords

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

20.1001.1.24236977.2023.13.1.1.2

Main Subjects

• Numerical methods for differential equations and its applications

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