• Login
    View Item 
    •   Home
    • Research
    • Articles
    • View Item
    •   Home
    • Research
    • Articles
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesTitleAuthorsKAUST AuthorsIssue DateSubmit DateSubjectsThis CollectionTitleAuthorsKAUST AuthorsIssue DateSubmit DateSubjects

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguidePlumX LibguideSubmit an Item

    Statistics

    Display statistics

    Refined isogeometric analysis for a preconditioned conjugate gradient solver

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    1-s2.0-S004578251830077X-main.pdf
    Size:
    428.2Kb
    Format:
    PDF
    Description:
    Accepted Manuscript
    Embargo End Date:
    2020-02-12
    Download
    Type
    Article
    Authors
    Garcia, Daniel
    Pardo, D. cc
    Dalcin, Lisandro cc
    Calo, Victor M. cc
    KAUST Department
    Extreme Computing Research Center
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Numerical Porous Media SRI Center (NumPor)
    Date
    2018-02-12
    Permanent link to this record
    http://hdl.handle.net/10754/627135
    
    Metadata
    Show full item record
    Abstract
    Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the total computational cost required to solve the corresponding system of equations using a direct LU factorization solver dramatically reduces (up to a factor of 55) Garcia et al. (2017). At the same time, rIGA enriches the IGA spaces, thus improving the best approximation error. In this work, we extend the complexity analysis of rIGA to the case of iterative solvers. We build an iterative solver as follows: we first construct the Schur complements using a direct solver over small subdomains (macro-elements). We then assemble those Schur complements into a global skeleton system. Subsequently, we solve this system iteratively using Conjugate Gradients (CG) with an incomplete LU (ILU) preconditioner. For a 2D Poisson model problem with a structured mesh and a uniform polynomial degree of approximation, rIGA achieves moderate savings with respect to IGA in terms of the number of Floating Point Operations (FLOPs) and computational time (in seconds) required to solve the resulting system of linear equations. For instance, for a mesh with four million elements and polynomial degree p=3, the iterative solver is approximately 2.6 times faster (in time) when applied to the rIGA system than to the IGA one. These savings occur because the skeleton rIGA system contains fewer non-zero entries than the IGA one. The opposite situation occurs for 3D problems, and as a result, 3D rIGA discretizations provide no gains with respect to their IGA counterparts when considering iterative solvers.
    Citation
    Garcia D, Pardo D, Dalcin L, Calo VM (2018) Refined isogeometric analysis for a preconditioned conjugate gradient solver. Computer Methods in Applied Mechanics and Engineering. Available: http://dx.doi.org/10.1016/j.cma.2018.02.006.
    Sponsors
    David Pardo has received funding from the Project of the Spanish Ministry of Economy and Competitiveness with reference MTM2016-76329-R (AEI/FEDER, EU), and MTM2016-81697-ERC/AEI, the BCAM “Severo Ocho” accreditation of excellenceSEV-2013-0323, and the Basque Government through the BERC 2014-2017 program and the Consolidated Research Group Grant IT649-13 on “Mathematical Modeling, Simulation, and Industrial Applications (M2SI)”. This publication was also made possible in part by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 644602, the CSIRO Professorial Chair in Computational Geoscience at Curtin University, the Deep Earth Imaging Enterprise Future Science Platforms of the Commonwealth Scientific Industrial Research Organisation, CSIRO, of Australia, the Mega-grant of the Russian Federation Government ( N14.Y26.31.0013) and the Curtin Institute for Computation. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper.
    Publisher
    Elsevier BV
    Journal
    Computer Methods in Applied Mechanics and Engineering
    ISSN
    0045-7825
    DOI
    10.1016/j.cma.2018.02.006
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S004578251830077X
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cma.2018.02.006
    Scopus Count
    Collections
    Articles; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

    entitlement

     
    DSpace software copyright © 2002-2019  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.