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

N1 - Funding Information:
The authors are grateful to the anonymous reviewers for their valuable comments, to So-Hsiang Chou for helpful discussions, and to the Computer and Information Networking Center, National Taiwan University for providing high-performance computing resource. This work is partially supported by the National Science Council , the Taida Institute of Mathematical Sciences , and the National Center for Theoretical Sciences in Taiwan .

PY - 2011/6

Y1 - 2011/6

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

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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 -