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

Zih Hao Wei, Feng Nan Hwang, Tsung Ming Huang, Weichung Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XIX
Pages157-164
Number of pages8
DOIs
Publication statusPublished - 2010 Dec 3
Event19th International Conference on Domain Decomposition, DD19 - Zhanjiajie, China
Duration: 2009 Aug 172009 Aug 22

Publication series

NameLecture Notes in Computational Science and Engineering
Volume78 LNCSE
ISSN (Print)1439-7358

Other

Other19th International Conference on Domain Decomposition, DD19
CountryChina
CityZhanjiajie
Period09/8/1709/8/22

Fingerprint

Jacobi-Davidson
Quantum Dots
Semiconductor quantum dots
Additive Schwarz
Polynomials
Polynomial
Polynomial Eigenvalue Problem
Simulation
Sparse Polynomials
Newton-type Methods
Computational Science
Krylov Subspace Methods
Quintic
Parameter Tuning
Preconditioner
Eigenvalue Problem
Accelerate
Scalability
Interior
Physics

ASJC Scopus subject areas

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

Cite this

Wei, Z. H., Hwang, F. N., Huang, T. M., & Wang, W. (2010). A parallel scalable PETSc-based Jacobi-Davidson polynomial Eigensolver with application in quantum dot simulation. In 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.

Domain Decomposition Methods in Science and Engineering XIX. 2010. p. 157-164 (Lecture Notes in Computational Science and Engineering; Vol. 78 LNCSE).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Wei, ZH, Hwang, FN, Huang, TM & Wang, W 2010, A parallel scalable PETSc-based Jacobi-Davidson polynomial Eigensolver with application in quantum dot simulation. in 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
Wei ZH, Hwang FN, Huang TM, Wang W. A parallel scalable PETSc-based Jacobi-Davidson polynomial Eigensolver with application in quantum dot simulation. In Domain Decomposition Methods in Science and Engineering XIX. 2010. p. 157-164. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-642-11304-8_16
Wei, Zih Hao ; Hwang, Feng Nan ; Huang, Tsung Ming ; Wang, Weichung. / A parallel scalable PETSc-based Jacobi-Davidson polynomial Eigensolver with application in quantum dot simulation. Domain Decomposition Methods in Science and Engineering XIX. 2010. pp. 157-164 (Lecture Notes in Computational Science and Engineering).
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