Abstract
Nano-scale quantum dot simulations result in large-scale polynomial eigenvalue problems. It remains unclear how these problems can be solved efficiently. We fill this gap in capability partially by proposing a polynomial Jacobi-Davidson method framework, including several varied schemes for solving the associated correction equations. We investigate the performance of the proposed Jacobi-Davidson methods for solving the polynomial eigenvalue problems and several Krylov subspace methods for solving the linear eigenvalue problems with the use of various linear solvers and preconditioning schemes. This study finds the most efficient scheme combinations for different types of target problems.
| Original language | English |
|---|---|
| Pages (from-to) | 999-1021 |
| Number of pages | 23 |
| Journal | Taiwanese Journal of Mathematics |
| Volume | 14 |
| Issue number | 3 A |
| DOIs | |
| Publication status | Published - 2010 Jun |
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Keywords
- Correction equations
- Jacobi-davidson methods
- Krylov subspace methods
- Polynomial eigenvalue problems
- Quantum dot
- Schr̈odinger equation
ASJC Scopus subject areas
- Mathematics(all)
Cite this
An efficiency study of polynomial eigenvalue problem solvers for quantum dot simulations. / Huang, Tsung Ming; Wang, Weichung; Lee, Chang Tse.
In: Taiwanese Journal of Mathematics, Vol. 14, No. 3 A, 06.2010, p. 999-1021.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An efficiency study of polynomial eigenvalue problem solvers for quantum dot simulations
AU - Huang, Tsung Ming
AU - Wang, Weichung
AU - Lee, Chang Tse
PY - 2010/6
Y1 - 2010/6
N2 - Nano-scale quantum dot simulations result in large-scale polynomial eigenvalue problems. It remains unclear how these problems can be solved efficiently. We fill this gap in capability partially by proposing a polynomial Jacobi-Davidson method framework, including several varied schemes for solving the associated correction equations. We investigate the performance of the proposed Jacobi-Davidson methods for solving the polynomial eigenvalue problems and several Krylov subspace methods for solving the linear eigenvalue problems with the use of various linear solvers and preconditioning schemes. This study finds the most efficient scheme combinations for different types of target problems.
AB - Nano-scale quantum dot simulations result in large-scale polynomial eigenvalue problems. It remains unclear how these problems can be solved efficiently. We fill this gap in capability partially by proposing a polynomial Jacobi-Davidson method framework, including several varied schemes for solving the associated correction equations. We investigate the performance of the proposed Jacobi-Davidson methods for solving the polynomial eigenvalue problems and several Krylov subspace methods for solving the linear eigenvalue problems with the use of various linear solvers and preconditioning schemes. This study finds the most efficient scheme combinations for different types of target problems.
KW - Correction equations
KW - Jacobi-davidson methods
KW - Krylov subspace methods
KW - Polynomial eigenvalue problems
KW - Quantum dot
KW - Schr̈odinger equation
UR - http://www.scopus.com/inward/record.url?scp=77954061260&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77954061260&partnerID=8YFLogxK
U2 - 10.11650/twjm/1500405878
DO - 10.11650/twjm/1500405878
M3 - Article
AN - SCOPUS:77954061260
VL - 14
SP - 999
EP - 1021
JO - Taiwanese Journal of Mathematics
JF - Taiwanese Journal of Mathematics
SN - 1027-5487
IS - 3 A
ER -