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

Tsung-Min Hwang, Feng Nan Hwang, Sheng Hong Lai, Weichung Wang, Zih Hao Wei

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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
Volume45
Issue number1
DOIs
Publication statusPublished - 2011 Jun 1

Fingerprint

Acoustics
Polynomials
Distributed computer systems
Parallel processing systems
Scalability
Finite element method
Experiments

Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Engineering(all)

Cite this

A parallel polynomial Jacobi-Davidson approach for dissipative acoustic eigenvalue problems. / Hwang, Tsung-Min; Hwang, Feng Nan; Lai, Sheng Hong; Wang, Weichung; Wei, Zih Hao.

In: Computers and Fluids, Vol. 45, No. 1, 01.06.2011, p. 207-214.

Research output: Contribution to journalArticle

Hwang, Tsung-Min ; Hwang, Feng Nan ; Lai, Sheng Hong ; Wang, Weichung ; Wei, Zih Hao. / A parallel polynomial Jacobi-Davidson approach for dissipative acoustic eigenvalue problems. In: Computers and Fluids. 2011 ; Vol. 45, No. 1. pp. 207-214.
@article{a201d9d1a8234d5998bb1b04888499b6,
title = "A parallel polynomial Jacobi-Davidson approach for dissipative acoustic eigenvalue problems",
abstract = "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.",
keywords = "Acoustic wave equation, Additive Schwarz preconditioner, Cubic eigenvalue problems, Domain decomposition, Jacobi-Davidson methods, Parallel computing",
author = "Tsung-Min Hwang and Hwang, {Feng Nan} and Lai, {Sheng Hong} and Weichung Wang and Wei, {Zih Hao}",
year = "2011",
month = "6",
day = "1",
doi = "10.1016/j.compfluid.2010.11.020",
language = "English",
volume = "45",
pages = "207--214",
journal = "Computers and Fluids",
issn = "0045-7930",
publisher = "Elsevier Limited",
number = "1",

}

TY - JOUR

T1 - A parallel polynomial Jacobi-Davidson approach for dissipative acoustic eigenvalue problems

AU - Hwang, Tsung-Min

AU - Hwang, Feng Nan

AU - Lai, Sheng Hong

AU - Wang, Weichung

AU - Wei, Zih Hao

PY - 2011/6/1

Y1 - 2011/6/1

N2 - 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.

AB - 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.

KW - Acoustic wave equation

KW - Additive Schwarz preconditioner

KW - Cubic eigenvalue problems

KW - Domain decomposition

KW - Jacobi-Davidson methods

KW - Parallel computing

UR - http://www.scopus.com/inward/record.url?scp=79954598117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79954598117&partnerID=8YFLogxK

U2 - 10.1016/j.compfluid.2010.11.020

DO - 10.1016/j.compfluid.2010.11.020

M3 - Article

AN - SCOPUS:79954598117

VL - 45

SP - 207

EP - 214

JO - Computers and Fluids

JF - Computers and Fluids

SN - 0045-7930

IS - 1

ER -