The DEAL.II finite element library: Design, features, and insights

Arndt, Daniel; Bangerth, Wolfgang; Davydov, Denis; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Maier, Matthias; Pelteret, Jean-Paul; Turcksin, Bruno; Wells, David

doi:10.1016/j.camwa.2020.02.022

Title: The DEAL.II finite element library: Design, features, and insights

Abstract

DEAL.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. In this paper, we outline its primary design considerations and its sophisticated features such as distributed meshes, $h p$ -adaptivity, support for complex geometries, and matrix-free algorithms. But DEAL.II is more than just a software library: It is also a diverse and worldwide community of developers and users, as well as an educational platform. We therefore also discuss some of the technical and social challenges and lessons learned in running a large community software project over the course of two decades.

Authors:

^[1];

^[2]; Davydov, Denis ^[3];

^[4];

^[5];

^[6];

^[7]; Pelteret, Jean-Paul ^[3];

^[1]; Wells, David ^[8]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computational Engineering and Energy Sciences Group
Colorado State Univ., Fort Collins, CO (United States). Dept. of Mathematics
Independent Researcher
Clemson Univ., SC (United States). School of Mathematical and Statistical Sciences
International School for Advanced Studies, Trieste (Italy)
Technical Univ. of Munich, Garching (Germany). Inst. for Computational Mechanics
Texas A & M Univ., College Station, TX (United States). Dept. of Mathematics
Univ. of North Carolina, Chapel Hill, NC (United States). Dept. of Mathematics

Publication Date:: Mon Mar 16 00:00:00 EDT 2020

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR); Italian Ministry of Instruction, University and Research (MIUR); German Research Foundation (DFG); US Army Research Office (ARO)

OSTI Identifier:: 1651382

Grant/Contract Number:: AC05-00OR22725; OAC-1835673; DMS-1821210; EAR-0949446; EAR-1550901; DMS-1901529; OAC2015848; EAR-1925575; DMS-1912847; OAC-1450327; STTR-N16A-T003; NA-FROMPDEs-MIUR-PE1; W911NF14-1-0247

Resource Type:: Accepted Manuscript

Journal Name:: Computers and Mathematics with Applications (Oxford)

Additional Journal Information:: Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 81; Journal ID: ISSN 0898-1221

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; finite elements; mathematical software; scientific computing; software design

Citation Formats


                    Arndt, Daniel, Bangerth, Wolfgang, Davydov, Denis, Heister, Timo, Heltai, Luca, Kronbichler, Martin, Maier, Matthias, Pelteret, Jean-Paul, Turcksin, Bruno, and Wells, David. The DEAL.II finite element library: Design, features, and insights.  United States: N. p., 2020. 
Web.  doi:10.1016/j.camwa.2020.02.022.

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                    Arndt, Daniel, Bangerth, Wolfgang, Davydov, Denis, Heister, Timo, Heltai, Luca, Kronbichler, Martin, Maier, Matthias, Pelteret, Jean-Paul, Turcksin, Bruno, & Wells, David. The DEAL.II finite element library: Design, features, and insights.  United States.  https://doi.org/10.1016/j.camwa.2020.02.022

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                    Arndt, Daniel, Bangerth, Wolfgang, Davydov, Denis, Heister, Timo, Heltai, Luca, Kronbichler, Martin, Maier, Matthias, Pelteret, Jean-Paul, Turcksin, Bruno, and Wells, David. Mon .  
"The DEAL.II finite element library: Design, features, and insights".  United States.  https://doi.org/10.1016/j.camwa.2020.02.022.  https://www.osti.gov/servlets/purl/1651382.

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@article{osti_1651382,

  title        = {The DEAL.II finite element library: Design, features, and insights},

  author       = {Arndt, Daniel and Bangerth, Wolfgang and Davydov, Denis and Heister, Timo and Heltai, Luca and Kronbichler, Martin and Maier, Matthias and Pelteret, Jean-Paul and Turcksin, Bruno and Wells, David},

  abstractNote = {DEAL.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. In this paper, we outline its primary design considerations and its sophisticated features such as distributed meshes, hp-adaptivity, support for complex geometries, and matrix-free algorithms. But DEAL.II is more than just a software library: It is also a diverse and worldwide community of developers and users, as well as an educational platform. We therefore also discuss some of the technical and social challenges and lessons learned in running a large community software project over the course of two decades.},

  doi          = {10.1016/j.camwa.2020.02.022},

  journal      = {Computers and Mathematics with Applications (Oxford)},

  number       = ,

  volume       = 81,

  place        = {United States},

  year         = {Mon Mar 16 00:00:00 EDT 2020},

  month        = {Mon Mar 16 00:00:00 EDT 2020}

}

Copy to clipboard

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Title: The DEAL.II finite element library: Design, features, and insights

Abstract

Citation Formats

Kokkos: Enabling manycore performance portability through polymorphic memory access patterns journal, December 2014

A Performance Comparison of Continuous and Discontinuous Galerkin Methods with Fast Multigrid Solvers journal, January 2018

Data structures and requirements for hp finite element software journal, March 2009

Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methods journal, January 2011

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The TUBA Family of Plate Elements for the Matrix Displacement Method journal, August 1968

deal2lkit: A toolkit library for high performance programming in deal.II journal, January 2018

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p4est : Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees journal, January 2011

Guest editor's introduction journal, March 2007

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Multilevel methods for discontinuous Galerkin FEM on locally refined meshes journal, November 2004

The deal.II library, Version 9.0 journal, December 2018

WorkStream -- A Design Pattern for Multicore-Enabled Finite Element Computations journal, August 2016

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libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations journal, November 2006

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The deal.II library, Version 9.1 journal, December 2019

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Research and Education in Computational Science and Engineering journal, January 2018

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π-BEM: A flexible parallel implementation for adaptive, geometry aware, and high order boundary element methods journal, July 2018

Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics journal, December 2017

Algorithms and data structures for massively parallel generic adaptive finite element codes journal, December 2011

Algorithm 755; ADOL-C: a package for the automatic differentiation of algorithms written in C/C++ journal, June 1996

An overview of the Trilinos project journal, September 2005

DFT-FE – A massively parallel adaptive finite-element code for large-scale density functional theory calculations journal, January 2020

A generic interface for parallel cell-based finite element operator application journal, June 2012

Fast Matrix-Free Evaluation of Discontinuous Galerkin Finite Element Operators journal, August 2019

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Algorithms and data structures for massively parallel generic adaptive finite element codes journal, December 2011

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Kokkos: Enabling manycore performance portability through polymorphic memory access patterns
journal, December 2014

A Performance Comparison of Continuous and Discontinuous Galerkin Methods with Fast Multigrid Solvers
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Data structures and requirements for hp finite element software
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journal, January 2011

Basic Linear Algebra Subprograms for Fortran Usage
journal, September 1979

The TUBA Family of Plate Elements for the Matrix Displacement Method
journal, August 1968

deal2lkit: A toolkit library for high performance programming in deal.II
journal, January 2018

The deal.II library, version 8.5
journal, January 2017

`p4est` : Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
journal, January 2011

Guest editor's introduction
journal, March 2007

High accuracy mantle convection simulation through modern numerical methods: High accuracy mantle convection simulation
journal, August 2012

Multilevel methods for discontinuous Galerkin FEM on locally refined meshes
journal, November 2004

The deal.II library, Version 9.0
journal, December 2018

WorkStream -- A Design Pattern for Multicore-Enabled Finite Element Computations
journal, August 2016

LinearOperator—A generic, high-level expression syntax for linear algebra
journal, July 2016

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journal, November 2006

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journal, May 2006

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journal, August 2016

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journal, December 2019

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journal, May 2019

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journal, January 2018

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journal, August 2007

π-BEM: A flexible parallel implementation for adaptive, geometry aware, and high order boundary element methods
journal, July 2018

Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics
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journal, November 2004

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