Berljafa, Mario and Wortmann, Daniel and Di Napoli, Edoardo
(2014)
*An optimized and scalable eigensolver for sequences of eigenvalue problems.*
[MIMS Preprint]

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## Abstract

In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution of one problem fosters the initialization of the next. In addition, in some eigenproblem sequences there is a connection between the solutions of adjacent eigenproblems. Whenever it is possible to unravel the existence of such a connection, the eigenproblem sequence is said to be correlated. When facing with a sequence of correlated eigenproblems the current strategy amounts to solving each eigenproblem in isolation. We propose a alternative approach which exploits such correlation through the use of an eigensolver based on subspace iteration and accelerated with Chebyshev polynomials (ChFSI). The resulting eigensolver is optimized by minimizing the number of matrix-vector multiplications and parallelized using the Elemental library framework. Numerical results show that ChFSI achieves excellent scalability and is competitive with current dense linear algebra parallel eigensolvers.

Item Type: | MIMS Preprint |
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Subjects: | PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 02 Mathematical methods in physics PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 70 CONDENSED MATTER - ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES > 71 Electronic structure of bulk materials |

Depositing User: | Mr Mario Berljafa |

Date Deposited: | 11 Jul 2014 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2151 |

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