Parallel two-level domain decomposition based Jacobi-Davidson algorithms for pyramidal quantum dot simulation

Tao Zhao, Feng Nan Hwang, Xiao Chuan Cai

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We consider a quintic polynomial eigenvalue problem arising from the finite volume discretization of a quantum dot simulation problem. The problem is solved by the Jacobi-Davidson (JD) algorithm. Our focus is on how to achieve the quadratic convergence of JD in a way that is not only efficient but also scalable when the number of processor cores is large. For this purpose, we develop a projected two-level Schwarz preconditioned JD algorithm that exploits multilevel domain decomposition techniques. The pyramidal quantum dot calculation is carefully studied to illustrate the efficiency of the proposed method. Numerical experiments confirm that the proposed method has a good scalability for problems with hundreds of millions of unknowns on a parallel computer with more than 10,000 processor cores.

Original languageEnglish
Pages (from-to)74-81
Number of pages8
JournalComputer Physics Communications
Volume204
DOIs
StatePublished - 1 Jul 2016

Keywords

  • Jacobi-Davidson algorithm
  • Parallel performance
  • Polynomial eigenvalue problem
  • Quantum dot simulation
  • Two-level Schwarz preconditioner

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