Order 10 4 speedup in global linear instability analysis using matrix formation

Paredes Gonzalez, Pedro and Hermanns Navarro, Miguel and Le Clainche Martínez, Soledad and Theofilis, Vassilios (2013). Order 10 4 speedup in global linear instability analysis using matrix formation. "Computer Methods in Applied Mechanics and Engineering", v. 253 ; pp. 287-304. ISSN 0045-7825. https://doi.org/10.1016/j.cma.2012.09.014.

Description

Title: Order 10 4 speedup in global linear instability analysis using matrix formation
Author/s:
  • Paredes Gonzalez, Pedro
  • Hermanns Navarro, Miguel
  • Le Clainche Martínez, Soledad
  • Theofilis, Vassilios
Item Type: Article
Título de Revista/Publicación: Computer Methods in Applied Mechanics and Engineering
Date: January 2013
ISSN: 0045-7825
Volume: 253
Subjects:
Freetext Keywords: Global linear flow instability analysis High-order finite-differences Large-scale eigenvalue problems Sparse linear algebra
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Motopropulsión y Termofluidodinámica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.

More information

Item ID: 19104
DC Identifier: http://oa.upm.es/19104/
OAI Identifier: oai:oa.upm.es:19104
DOI: 10.1016/j.cma.2012.09.014
Official URL: http://www.sciencedirect.com/science/article/pii/S0045782512002964
Deposited by: Memoria Investigacion
Deposited on: 07 Apr 2014 16:45
Last Modified: 21 Apr 2016 17:21
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