Identifier: 2008-6
Author(s): W. Wang and C.-W. Shu
Title: The WKB local discontinuous Galerkin method for the simulation of Schrodinger equation in a resonant tunneling diode
Page count: 21 pp.
Abstract:
In this paper, we develop a multiscale local discontinuous Galerkin (LDG) method to simulate the one-dimensional stationary Schrodinger-Poisson problem. The stationary Schrodinger equation is discretized by the WKB local discontinuous Galerkin (WKB-LDG) method, and the Poisson potential equation is discretized by the minimal dissipa- tion LDG (MD-LDG) method. The WKB-LDG method we propose in our work provides a significant reduction of both the computational cost and memory in solving the Schrodinger equation. Comparing with traditional continuous finite element Galerkin methodology, the WKB-LDG method has the advantages of the DG methods including their flexibility in h-p adaptivity and allowance of complete disconti- nuity at element interfaces. Although not addressed in this paper, a ma jor advantage of the WKB-LDG method is its feasibility for two- dimensional devices.
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