Large-Scale Eigenvalue Calculations for Stability Analysis of Steady Flows on Massively Parallel Computers

PDF Version Also Available for Download.

Description

We present an approach for determining the linear stability of steady states of PDEs on massively parallel computers. Linearizing the transient behavior around a steady state leads to a generalized eigenvalue problem. The eigenvalues with largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation to recast the problem as an ordinary eigenvalue problem. The Cayley transformation requires the solution of a linear system at each Arnoldi iteration, which must be done iteratively for the algorithm to scale with problem size. A representative model problem of 3D incompressible flow and heat transfer in ... continued below

Physical Description

26 p.

Creation Information

Lehoucq, Richard B. & Salinger, Andrew G. August 1, 1999.

Context

This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this report can be viewed below.

Who

People and organizations associated with either the creation of this report or its content.

Sponsor

Publisher

  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM, and Livermore, CA (United States)
    Place of Publication: Albuquerque, New Mexico

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this report. Follow the links below to find similar items on the Digital Library.

Description

We present an approach for determining the linear stability of steady states of PDEs on massively parallel computers. Linearizing the transient behavior around a steady state leads to a generalized eigenvalue problem. The eigenvalues with largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation to recast the problem as an ordinary eigenvalue problem. The Cayley transformation requires the solution of a linear system at each Arnoldi iteration, which must be done iteratively for the algorithm to scale with problem size. A representative model problem of 3D incompressible flow and heat transfer in a rotating disk reactor is used to analyze the effect of algorithmic parameters on the performance of the eigenvalue algorithm. Successful calculations of leading eigenvalues for matrix systems of order up to 4 million were performed, identifying the critical Grashof number for a Hopf bifurcation.

Physical Description

26 p.

Notes

OSTI as DE00010357

Medium: P; Size: 26 pages

Source

  • Other Information: PBD: 1 Aug 1999

Language

Item Type

Identifier

Unique identifying numbers for this report in the Digital Library or other systems.

  • Report No.: SAND99-1593
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/10357 | External Link
  • Office of Scientific & Technical Information Report Number: 10357
  • Archival Resource Key: ark:/67531/metadc621041

Collections

This report is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this report?

When

Dates and time periods associated with this report.

Creation Date

  • August 1, 1999

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

Description Last Updated

  • April 10, 2017, 6:27 p.m.

Usage Statistics

When was this report last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 4

Interact With This Report

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Lehoucq, Richard B. & Salinger, Andrew G. Large-Scale Eigenvalue Calculations for Stability Analysis of Steady Flows on Massively Parallel Computers, report, August 1, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc621041/: accessed October 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.