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A Highly Scalable Matrix-Free Multigrid Solver for μFE Analysis Based on a Pointer-Less Octree

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Large-Scale Scientific Computing (LSSC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7116))

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Abstract

The state of the art method to predict bone stiffness is micro finite element (μFE) analysis based on high-resolution computed tomography (CT). Modern parallel solvers enable simulations with billions of degrees of freedom. In this paper we present a conjugate gradient solver that works directly on the CT image and exploits the geometric properties of the regular grid and the basic element shapes given by the 3D pixel. The data is stored in a pointer-less octree. The tree data structure provides different resolutions of the image that are used to construct a geometric multigrid preconditioner. It enables the use of matrix-free representation of all matrices on all levels. The new solver reduces the memory footprint by more than a factor of 10 compared to our previous solver ParFE. It allows to solve much bigger problems than before and scales excellently on a Cray XT-5 supercomputer.

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Authors and Affiliations

  1. Computational Science, ETH Zürich, 8092, Zürich, Switzerland

    Cyril Flaig & Peter Arbenz

Authors
  1. Cyril Flaig
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  2. Peter Arbenz
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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Block 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov  & Svetozar Margenov  & 

  2. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads, Building 321,, 2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Flaig, C., Arbenz, P. (2012). A Highly Scalable Matrix-Free Multigrid Solver for μFE Analysis Based on a Pointer-Less Octree. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_56

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  • DOI: https://doi.org/10.1007/978-3-642-29843-1_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29842-4

  • Online ISBN: 978-3-642-29843-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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