A parallel polynomial Jacobi-Davidson approach for dissipative acoustic eigenvalue problems

Tsung Ming Huang, Feng Nan Hwang*, Sheng Hong Lai, Weichung Wang, Zih Hao Wei

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We consider a rational algebraic large sparse eigenvalue problem arising in the discretization of the finite element method for the dissipative acoustic model in the pressure formulation. The presence of nonlinearity due to the frequency-dependent impedance poses a challenge in developing an efficient numerical algorithm for solving such eigenvalue problems. In this article, we reformulate the rational eigenvalue problem as a cubic eigenvalue problem and then solve the resulting cubic eigenvalue problem by a parallel restricted additive Schwarz preconditioned Jacobi-Davidson algorithm (ASPJD). To validate the ASPJD-based eigensolver, we numerically demonstrate the optimal convergence rate of our discretization scheme and show that ASPJD converges successfully to all target eigenvalues. The extraneous root introduced by the problem reformulation does not cause any observed side effect that produces an undesirable oscillatory convergence behavior. By performing intensive numerical experiments, we identify an efficient correction-equation solver, an effective algorithmic parameter setting, and an optimal mesh partitioning. Furthermore, the numerical results suggest that the ASPJD-based eigensolver with an optimal mesh partitioning results in superlinear scalability on a distributed and parallel computing cluster scaling up to 192 processors.

Original languageEnglish
Pages (from-to)207-214
Number of pages8
JournalComputers and Fluids
Issue number1
Publication statusPublished - 2011 Jun


  • Acoustic wave equation
  • Additive Schwarz preconditioner
  • Cubic eigenvalue problems
  • Domain decomposition
  • Jacobi-Davidson methods
  • Parallel computing

ASJC Scopus subject areas

  • General Computer Science
  • General Engineering


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