Efficient preconditioning of hphp-FEM matrix sequences with slowly-varying coefficients: An application to topology optimization

P. Gatto, J. S. Hesthaven, Rasmus Ellebæk Christiansen

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    Abstract

    We previously introduced a preconditioner that has proven effective for hphp-FEM discretizations of various challenging elliptic and hyperbolic problems. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated, to high precision, by Hierarchically-Semi-Separable matrices. The preconditioner is built as an approximate LDMtLDMt factorization through a divide-and-conquer approach. This implies an enhanced flexibility which allows to handle unstructured geometric meshes, anisotropies, and discontinuities. We build on our previous numerical experiments and develop a preconditioner-update strategy that allows us handle matrix sequences arising from problems with slowly-varying coefficients. We investigate the performance of the preconditioner along with the update strategy in context of topology optimization of an acoustic cavity.
    Original languageEnglish
    JournalComputer Methods in Applied Mechanics and Engineering
    Volume322
    Pages (from-to)81-96
    Number of pages16
    ISSN0045-7825
    DOIs
    Publication statusPublished - 2017

    Keywords

    • Preconditioned GMRES
    • Interpolative decomposition
    • Indefinite operators
    • Acoustic Topology Optimization

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