Efficient approximation algorithm for the Schrödinger–Possion system

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....

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Bibliographic Details
Published in:Numerical methods for partial differential equations Vol. 37; no. 1; pp. 422 - 443
Main Authors: He, Xuefei, Wang, Kun
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.01.2021
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Subjects:
Algorithms
Approximation
discontinuous coefficient
finite difference method
Gummel iterative method
Iterative methods
Nonlinear systems
non‐uniform mesh
Resonant tunneling
resonant tunneling diode
Schröginger–Possion system
Tunnel diodes
ISSN:0749-159X, 1098-2426
Online Access:Get full text
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Summary: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.
Bibliography:Funding information
Chongqing University Graduate Key Courses, 201805032; Fundamental Research Funds for the Central Universities, 2019CDXYST0016; National Natural Science Foundation of China, 91630205
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ISSN:0749-159X
1098-2426
DOI:10.1002/num.22534