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Publications on details of deal.II

deal.II is documented in a large number of publications in the scientific literature. Publications that provide a top-level overview and that document specific versions are listed on a separate page. This page shows publications that explain in great detail the implementation of algorithms and data structures of various components of deal.II:

  • M. Fehling, W. Bangerth
    Algorithms for Parallel Generic hp-adaptive Finite Element Software
    ACM Transactions on Mathematical Software, vol. 49, issue 3, article 25, pp. 1-26, 2023.
    DOI: 10.1145/3603372

  • L. Heltai, W. Bangerth, M. Kronbichler, A. Mola
    Propagating geometry information to finite element computations
    ACM Transactions on Mathematical Software, vol. 47, issue 4, article 32, 1-30, 2021.
    DOI: 10.1145/3468428

  • T. C. Clevenger, T. Heister, G. Kanschat, M. Kronbichler
    A Flexible, Parallel, Adaptive Geometric Multigrid Method for FEM
    ACM Transactions on Mathematical Software, vol. 47, 1, Article 7, 2020.
    DOI: 10.1145/3425193

  • A. Sartori, N. Giuliani, M. Bardelloni, L. Heltai
    deal2lkit: A toolkit library for high performance programming in deal.II
    SoftwareX, vol. 7, pp. 318-327, 2018.
    DOI: 10.1016/j.softx.2018.09.004

  • R. Agelek, M. Anderson, W. Bangerth, W. L. Barth
    On orienting edges of unstructured two- and three-dimensional meshes
    ACM Transactions on Mathematical Software, vol. 44, article 5, 2017.
    DOI: 10.1145/3061708

  • D. Davydov, T. Gerasimov, J.-P. Pelteret, P. Steinmann
    Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics
    Advanced Modeling and Simulation in Engineering Sciences, vol. 4, pp. 2213-7467. 2017.
    DOI: 10.1186/s40323-017-0093-0

  • B. Turcksin, M. Kronbichler, W. Bangerth
    WorkStream — a design pattern for multicore-enabled finite element computations
    ACM Transactions on Mathematical Software, vol. 43, pp. 2/1-29, 2016.
    DOI: 10.1145/2851488

  • M. Maier, M. Bardelloni, L. Heltai
    LinearOperator — a generic, high-level expression syntax for linear algebra
    Computers and Mathematics with Applications, vol. 72, issue 1, pp. 1-24, 2016.
    DOI: 10.1016/j.camwa.2016.04.024

  • W. Bangerth, T. Heister
    What makes computational open source software libraries successful?
    Computational Science & Discovery, vol. 6, article 015010, 2013.
    DOI: 10.1088/1749-4699/6/1/015010

  • W. Bangerth, C. Burstedde, T. Heister, M. Kronbichler
    Algorithms and Data Structures for Massively Parallel Generic Adaptive Finite Element Codes
    ACM Transactions on Mathematical Software, vol. 38, No. 2, pp. 14/1-28, 2012.
    DOI: 10.1145/2049673.2049678

  • M. Kronbichler, K. Kormann
    A generic interface for parallel cell-based finite element operator application
    Computers and Fluids, vol. 63, pp. 135-147, 2012.
    DOI: 10.1016/j.compfluid.2012.04.012

  • B. Janssen, G. Kanschat
    Adaptive Multilevel Methods with Local Smoothing for H1- and Hcurl-Conforming High Order Finite Element Methods
    SIAM J. Sci. Comput., vol. 33/4, pp. 2095-2114, 2011.
    DOI: 10.1137/090778523

  • W. Bangerth, O. Kayser-Herold
    Data Structures and Requirements for hp Finite Element Software
    ACM Transactions on Mathematical Software, vol. 36, pp. 4/1-31, 2009.
    DOI: 10.1145/1486525.1486529

  • G. Kanschat
    Multilevel methods for discontinuous Galerkin FEM on locally refined meshes
    Comput. & Struct., vol. 82, pp. 2437-2445, 2004.
    DOI: 10.1016/j.compstruc.2004.04.015

For massively parallel computations, deal.II builds on the p4est library. If you use this functionality, please also cite the p4est paper listed at their website.

deal.II is a component of the SPEC CPU2006 and SPEC CPU2017 benchmark suites. There are hundreds of papers that use and describe this testsuite as a reference for compiler and hardware optimizations. The following special issue gives a detailed comparison with respect to many different metrics of the benchmarks in SPEC CPU2006, including deal.II:

  • Special Issue: SPEC CPU2006 analysis (Editor: John Henning)
    ACM SIGARCH Computer Architecture News, vol. 35, issue 1, 2007.