An efficiency study of polynomial eigenvalue problem solvers for quantum dot simulations

Tsung Ming Huang, Weichung Wang, Chang Tse Lee

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)999-1021
Number of pages23
JournalTaiwanese Journal of Mathematics
Volume14
Issue number3 A
DOIs
Publication statusPublished - 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)

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