A finite element method with energy-adaptive grids for the coupled Schrodinger-Poisson-drift-diffusion model

被引:0
|
作者
Mu, Pengcong [1 ,2 ]
Wu, Xinming [3 ]
Zheng, Weiying [1 ,2 ]
机构
[1] Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, LSEC,NCMIS, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[3] Fudan Univ, Sch Math Sci, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China
关键词
Schrodinger-Poisson model; Drift-diffusion model; Finite element method; Energy-adaptive grid; Resonant tunneling diode; SIMULATION; TRANSPORT; EQUATION;
D O I
10.1016/j.jcp.2023.112528
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In this paper, we propose a finite element method for solving the coupled model of classical drift-diffusion equations and Schrodinger-Poisson equations in simulating a resonant tunneling diode (RTD). The coupling coefficient Theta and the quantum electron density n(qu) are defined by weighted integrals of vertical bar psi(p)vertical bar(2) where psi(p) is the wave function of Schrodinger equation for each momentum p is an element of R. We first prove a growth rate of vertical bar psi(p)vertical bar as vertical bar p vertical bar -> +infinity. This enables us to truncate the momentum space R to a bounded interval [-P, P], which corresponds to an energy interval [0, E-P]. We propose an energy-adaptive algorithm based on a posteriori error estimate for computing Theta and n(qu) approximately on [0, E-P]. The algorithm reduces the number of nodes greatly by capturing resonance peaks accurately and adjusting the partition of [0, E-P] adaptively. Numerical experiment for an RTD shows that, based on energy-adaptive grids, the Gummel method for solving the coupled model is robust and can converge in several iterative steps.
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页数:17
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