### Abstract

The Jacobi-Davidson (JD) algorithm recently has gained popularity for finding a few selected interior eigenvalues of large sparse polynomial eigenvalue problems, which commonly appear in many computational science and engineering PDE based applications. As other inner-outer algorithms like Newton type method, the bottleneck of the JD algorithm is to solve approximately the inner correction equation. In the previous work, [Hwang, Wei, Huang, and Wang, A Parallel Additive Schwarz Preconditioned Jacobi-Davidson (ASPJD) Algorithm for Polynomial Eigenvalue Problems in Quantum Dot (QD) Simulation, Journal of Computational Physics (2010)], the authors proposed a parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method to accelerate the convergence of the JD algorithm. Based on the previous computational experiences on the algorithmic parameter tuning for the ASPJD algorithm, we further investigate the parallel performance of a PETSc based ASPJD eigensolver on the Blue Gene/P, and a QD quintic eigenvalue problem is used as an example to demonstrate its scalability by showing the excellent strong scaling up to 2,048 cores.

Original language | English |
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Title of host publication | Domain Decomposition Methods in Science and Engineering XIX |

Pages | 157-164 |

Number of pages | 8 |

DOIs | |

Publication status | Published - 2010 Dec 3 |

Event | 19th International Conference on Domain Decomposition, DD19 - Zhanjiajie, China Duration: 2009 Aug 17 → 2009 Aug 22 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 78 LNCSE |

ISSN (Print) | 1439-7358 |

### Other

Other | 19th International Conference on Domain Decomposition, DD19 |
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Country | China |

City | Zhanjiajie |

Period | 09/8/17 → 09/8/22 |

### Fingerprint

### ASJC Scopus subject areas

- Modelling and Simulation
- Engineering(all)
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Mathematics

### Cite this

*Domain Decomposition Methods in Science and Engineering XIX*(pp. 157-164). (Lecture Notes in Computational Science and Engineering; Vol. 78 LNCSE). https://doi.org/10.1007/978-3-642-11304-8_16

**A parallel scalable PETSc-based Jacobi-Davidson polynomial Eigensolver with application in quantum dot simulation.** / Wei, Zih Hao; Hwang, Feng Nan; Huang, Tsung Ming; Wang, Weichung.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Domain Decomposition Methods in Science and Engineering XIX.*Lecture Notes in Computational Science and Engineering, vol. 78 LNCSE, pp. 157-164, 19th International Conference on Domain Decomposition, DD19, Zhanjiajie, China, 09/8/17. https://doi.org/10.1007/978-3-642-11304-8_16

}

TY - GEN

T1 - A parallel scalable PETSc-based Jacobi-Davidson polynomial Eigensolver with application in quantum dot simulation

AU - Wei, Zih Hao

AU - Hwang, Feng Nan

AU - Huang, Tsung Ming

AU - Wang, Weichung

PY - 2010/12/3

Y1 - 2010/12/3

N2 - The Jacobi-Davidson (JD) algorithm recently has gained popularity for finding a few selected interior eigenvalues of large sparse polynomial eigenvalue problems, which commonly appear in many computational science and engineering PDE based applications. As other inner-outer algorithms like Newton type method, the bottleneck of the JD algorithm is to solve approximately the inner correction equation. In the previous work, [Hwang, Wei, Huang, and Wang, A Parallel Additive Schwarz Preconditioned Jacobi-Davidson (ASPJD) Algorithm for Polynomial Eigenvalue Problems in Quantum Dot (QD) Simulation, Journal of Computational Physics (2010)], the authors proposed a parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method to accelerate the convergence of the JD algorithm. Based on the previous computational experiences on the algorithmic parameter tuning for the ASPJD algorithm, we further investigate the parallel performance of a PETSc based ASPJD eigensolver on the Blue Gene/P, and a QD quintic eigenvalue problem is used as an example to demonstrate its scalability by showing the excellent strong scaling up to 2,048 cores.

AB - The Jacobi-Davidson (JD) algorithm recently has gained popularity for finding a few selected interior eigenvalues of large sparse polynomial eigenvalue problems, which commonly appear in many computational science and engineering PDE based applications. As other inner-outer algorithms like Newton type method, the bottleneck of the JD algorithm is to solve approximately the inner correction equation. In the previous work, [Hwang, Wei, Huang, and Wang, A Parallel Additive Schwarz Preconditioned Jacobi-Davidson (ASPJD) Algorithm for Polynomial Eigenvalue Problems in Quantum Dot (QD) Simulation, Journal of Computational Physics (2010)], the authors proposed a parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method to accelerate the convergence of the JD algorithm. Based on the previous computational experiences on the algorithmic parameter tuning for the ASPJD algorithm, we further investigate the parallel performance of a PETSc based ASPJD eigensolver on the Blue Gene/P, and a QD quintic eigenvalue problem is used as an example to demonstrate its scalability by showing the excellent strong scaling up to 2,048 cores.

UR - http://www.scopus.com/inward/record.url?scp=78651521932&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651521932&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-11304-8_16

DO - 10.1007/978-3-642-11304-8_16

M3 - Conference contribution

AN - SCOPUS:78651521932

SN - 9783642113031

T3 - Lecture Notes in Computational Science and Engineering

SP - 157

EP - 164

BT - Domain Decomposition Methods in Science and Engineering XIX

ER -