A Domain Decomposition Based Jacobi-Davidson Algorithm for Quantum Dot Simulation

  • Tao ZhaoEmail author
  • Feng-Nan Hwang
  • Xiao-Chuan Cai
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)


In this paper, we develop an overlapping domain decomposition (DD) based Jacobi-Davidson (JD) algorithm for a polynomial eigenvalue problem arising from quantum dot simulation. Both DD and JD have several adjustable components. The goal of the work is to figure out if it is possible to choose the right components of DD and JD such that the resulting approach has a near linear speedup for a fine mesh calculation. Through experiments, we find that the key is to use two different coarse meshes. One is used to obtain a good initial guess that helps to achieve quadratic convergence of the nonlinear JD iterations. The other guarantees scalable convergence of the linear solver of the correction equation. We report numerical experiments carried out on a supercomputer with over 10,000 processors.


Finite Volume Method Domain Decomposition Fine Mesh Coarse Mesh Correction Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of ColoradoBoulderUSA
  2. 2.Department of MathematicsNational Central UniversityJhongliTaiwan

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