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Efficient approximation algorithm for the Schrödinger–Possion system
Author(s) -
He Xuefei,
Wang Kun
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22534
Subject(s) - mathematics , convergence (economics) , polygon mesh , nonlinear system , algorithm , geometry , physics , quantum mechanics , economics , economic growth
In this article, we study an efficient approximation algorithm for the Schrödinger–Possion system arising in the resonant tunneling diode (RTD) structure. By following the classical Gummel iterative procedure, we first decouple this nonlinear system and prove the convergence of the iteration method. Then via introducing a novel spatial discrete method, we solve efficiently the decoupled Schrödinger and Possion equations with discontinuous coefficients on no‐uniform meshes at each iterative step, respectively. Compared with the traditional ones, the algorithm considered here not only has a less restriction on the discrete mesh, but also is more accurate. Finally, some numerical experiments are shown to confirm the efficiency of the proposed algorithm.