eprintid: 19104 rev_number: 22 eprint_status: archive userid: 1903 dir: disk0/00/01/91/04 datestamp: 2014-04-07 16:45:17 lastmod: 2016-04-21 17:21:04 status_changed: 2014-04-07 16:45:17 type: article metadata_visibility: show item_issues_count: 0 creators_name: Paredes Gonzalez, Pedro creators_name: Hermanns Navarro, Miguel creators_name: Le Clainche Martínez, Soledad creators_name: Theofilis, Vassilios title: Order 10 4 speedup in global linear instability analysis using matrix formation ispublished: pub subjects: mecanica keywords: Global linear flow instability analysis High-order finite-differences Large-scale eigenvalue problems Sparse linear algebra 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. date: 2013-01 date_type: published publisher: Elsevier official_url: http://www.sciencedirect.com/science/article/pii/S0045782512002964 id_number: 10.1016/j.cma.2012.09.014 full_text_status: public publication: Computer Methods in Applied Mechanics and Engineering volume: 253 pagerange: 287-304 institution: Aeronauticos department: Motopropulsion refereed: TRUE issn: 0045-7825 referencetext: [1] V. Theofilis, Global linear instability, Annu. Rev. Fluid Mech. 43 (2011) 319–352. [2] N. Abdessemed, S.J. Sherwin, V. Theofilis, Linear instability analysis of low pressure turbine flows, J. 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Walker, ScaLAPACK: a portable linear algebra library for distributed memory computers – design issues and performance, http://www.netlib.org/scalapack/, 1996. rights: by-nc-nd citation: Paredes Gonzalez, Pedro, Hermanns Navarro, Miguel, 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 . document_url: https://oa.upm.es/19104/1/INVE_MEM_2013_141203.pdf