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

N1 - Funding Information:
The authors are grateful to the BG/P computer sources provided by IBM during the workshop on computational science: IBM research and BG/P held at National Taiwan University during summer 2009. 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 - 2010

Y1 - 2010

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.

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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

T2 - 19th International Conference on Domain Decomposition, DD19

Y2 - 17 August 2009 through 22 August 2009

ER -