Numerical computation for pyramid quantum dot

Tsung Min Hwang; Wen Wei Lin; Wei Cheng Wang; Weichung Wang

Numerical computation for pyramid quantum dot

Tsung Min Hwang, Wen Wei Lin, Wei Cheng Wang, Weichung Wang

Department of Mathematics

Research output: Contribution to conference › Paper › peer-review

Abstract

We present a simple and efficient numerical method for the simulation of the three-dimensional pyramid quantum dot which is placed in a cuboid box. The corresponding Schrödinger equation is discretized using the finite volume method with uniform mesh in Cartesian coordinates and the interface conditions are incorporated into the discretization scheme without explicitly enforcing them. The resulting matrix eigenvalue problem is then solved using a Jacobi-Davidson based method. Both linear and quintic polynomial eigenvalue problems are simulated. The scheme is 2nd order accurate and converges extremely fast. The superior performance is a combined effect of the uniform spacing of the grids and the nice structure of the resulting matrices. We have successfully simulated a variety of test problems, including a quintic polynomial eigenvalue problem with more than 32 million variables.

Original language	English
Publication status	Published - 2004
Event	European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 - Jyvaskyla, Finland Duration: 2004 Jul 24 → 2004 Jul 28

Conference

Conference	European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004
Country/Territory	Finland
City	Jyvaskyla
Period	2004/07/24 → 2004/07/28

Keywords

Finite volume method
Heterostructure
Large scale polynomial eigenvalue problem
Schrödinger equation
Semiconductor pyramid quantum dot

ASJC Scopus subject areas

Artificial Intelligence
Applied Mathematics

Cite this

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title = "Numerical computation for pyramid quantum dot",

abstract = "We present a simple and efficient numerical method for the simulation of the three-dimensional pyramid quantum dot which is placed in a cuboid box. The corresponding Schr{\"o}dinger equation is discretized using the finite volume method with uniform mesh in Cartesian coordinates and the interface conditions are incorporated into the discretization scheme without explicitly enforcing them. The resulting matrix eigenvalue problem is then solved using a Jacobi-Davidson based method. Both linear and quintic polynomial eigenvalue problems are simulated. The scheme is 2nd order accurate and converges extremely fast. The superior performance is a combined effect of the uniform spacing of the grids and the nice structure of the resulting matrices. We have successfully simulated a variety of test problems, including a quintic polynomial eigenvalue problem with more than 32 million variables.",

keywords = "Finite volume method, Heterostructure, Large scale polynomial eigenvalue problem, Schr{\"o}dinger equation, Semiconductor pyramid quantum dot",

author = "Hwang, {Tsung Min} and Lin, {Wen Wei} and Wang, {Wei Cheng} and Weichung Wang",

year = "2004",

language = "English",

note = "European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 ; Conference date: 24-07-2004 Through 28-07-2004",

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TY - CONF

T1 - Numerical computation for pyramid quantum dot

AU - Hwang, Tsung Min

AU - Lin, Wen Wei

AU - Wang, Wei Cheng

AU - Wang, Weichung

PY - 2004

Y1 - 2004

N2 - We present a simple and efficient numerical method for the simulation of the three-dimensional pyramid quantum dot which is placed in a cuboid box. The corresponding Schrödinger equation is discretized using the finite volume method with uniform mesh in Cartesian coordinates and the interface conditions are incorporated into the discretization scheme without explicitly enforcing them. The resulting matrix eigenvalue problem is then solved using a Jacobi-Davidson based method. Both linear and quintic polynomial eigenvalue problems are simulated. The scheme is 2nd order accurate and converges extremely fast. The superior performance is a combined effect of the uniform spacing of the grids and the nice structure of the resulting matrices. We have successfully simulated a variety of test problems, including a quintic polynomial eigenvalue problem with more than 32 million variables.

AB - We present a simple and efficient numerical method for the simulation of the three-dimensional pyramid quantum dot which is placed in a cuboid box. The corresponding Schrödinger equation is discretized using the finite volume method with uniform mesh in Cartesian coordinates and the interface conditions are incorporated into the discretization scheme without explicitly enforcing them. The resulting matrix eigenvalue problem is then solved using a Jacobi-Davidson based method. Both linear and quintic polynomial eigenvalue problems are simulated. The scheme is 2nd order accurate and converges extremely fast. The superior performance is a combined effect of the uniform spacing of the grids and the nice structure of the resulting matrices. We have successfully simulated a variety of test problems, including a quintic polynomial eigenvalue problem with more than 32 million variables.

KW - Finite volume method

KW - Heterostructure

KW - Large scale polynomial eigenvalue problem

KW - Schrödinger equation

KW - Semiconductor pyramid quantum dot

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UR - http://www.scopus.com/inward/citedby.url?scp=84893441965&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84893441965

T2 - European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004

Y2 - 24 July 2004 through 28 July 2004

ER -

Numerical computation for pyramid quantum dot

Abstract

Conference

Keywords

ASJC Scopus subject areas

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