Numerical computation for pyramid quantum dot

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

Research output: Contribution to conferencePaper

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 languageEnglish
Publication statusPublished - 2004 Dec 1
EventEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 - Jyvaskyla, Finland
Duration: 2004 Jul 242004 Jul 28

Other

OtherEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004
CountryFinland
CityJyvaskyla
Period04/7/2404/7/28

Fingerprint

Polynomial Eigenvalue Problem
Switching Systems
Jacobian matrices
Heterostructures
Switching systems
Quintic
Jacobian matrix
Finite volume method
Pyramid
Quantum Dots
Computational methods
Finite Volume Method
Computational Methods
Numerical Computation
Semiconductor quantum dots
Schrödinger Equation
Heterojunctions
Jacobi-Davidson
Polynomials
Cuboid

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

Hwang, T-M., Lin, W. W., Wang, W. C., & Wang, W. (2004). Numerical computation for pyramid quantum dot. Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland.

Numerical computation for pyramid quantum dot. / Hwang, Tsung-Min; Lin, Wen Wei; Wang, Wei Cheng; Wang, Weichung.

2004. Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland.

Research output: Contribution to conferencePaper

Hwang, T-M, Lin, WW, Wang, WC & Wang, W 2004, 'Numerical computation for pyramid quantum dot' Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland, 04/7/24 - 04/7/28, .
Hwang T-M, Lin WW, Wang WC, Wang W. Numerical computation for pyramid quantum dot. 2004. Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland.
Hwang, Tsung-Min ; Lin, Wen Wei ; Wang, Wei Cheng ; Wang, Weichung. / Numerical computation for pyramid quantum dot. Paper presented at European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, Finland.
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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.

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