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The deal.II library, Version 9.1

Daniel Arndt , Wolfgang Bangerth , Thomas C. Clevenger , Denis Davydov , Marc Fehling , Daniel Garcia-Sanchez , Graham Harper , Timo Heister EMAIL logo , Luca Heltai , Martin Kronbichler , Ross Maguire Kynch , Matthias Maier , Jean-Paul Pelteret , Bruno Turcksin and David Wells


This paper provides an overview of the new features of the finite element library deal.II, version 9.1.

JEL Classification: 65M60; 65N30; 65Y05


This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (


[1] G. Alzetta, D. Arndt, W. Bangerth, V. Boddu, B. Brands, D. Davydov, R. Gassmoeller, T. Heister, L. Heltai, K. Kormann, M. Kronbichler, M.Maier, J.-P. Pelteret, B. Turcksin, and D. Wells, The deal.II library, Version 9.0, J. Numer. Math. 26 (2018), No. 4, 173–184.10.1515/jnma-2018-0054Search in Google Scholar

[2] P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. ĽfExcellent, A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM J. Matrix Anal. Appl. 23 (2001), No. 1, 15–41.10.1137/S0895479899358194Search in Google Scholar

[3] P. R. Amestoy, I. S. Duff, and J.-Y. ĽfExcellent, Multifrontal parallel distributed symmetric and unsymmetric solvers, Comput. Methods Appl. Mech. Eng. 184 (2000), 501–520.10.1016/S0045-7825(99)00242-XSearch in Google Scholar

[4] P. R. Amestoy, A. Guermouche, J.-Y. ĽfExcellent, and S. Pralet, Hybrid scheduling for the parallel solution of linear systems, Parallel Computing32 (2006), No. 2, 136–156.10.1016/j.parco.2005.07.004Search in Google Scholar

[5] E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S.Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999.10.1137/1.9780898719604Search in Google Scholar

[6] D. Arndt, W. Bangerth, D. Davydov, T. Heister, L. Heltai, M. Kronbichler, M.Maier, J.-P. Pelteret, B. Turcksin, and D. Wells, The deal.II library, Version 8.5, J. Numer. Math. 25 (2017), No. 3, 137–146.10.1515/jnma-2017-0058Search in Google Scholar

[7] S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijkhout, W. D. Gropp, D. Karpeyev, D. Kaushik, M. G. Knepley, D.May, L. Curfman McInnes, R. Mills, T.Munson, K. Rupp, P. Sanan B. F. Smith, S. Zampini, H. Zhang, and H. Zhang, PETSc Users Manual, Argonne National Laboratory, Report No. ANL-95/11 - Revision 3.9, 2018.10.2172/1409218Search in Google Scholar

[8] S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijkhout, W. D. Gropp, D. Karpeyev, D. Kaushik, M. G. Knepley, D.May, L. Curfman McInnes, R. Mills, T.Munson, K. Rupp, P. Sanan B. F. Smith, S. Zampini, H. Zhang, and H. Zhang, PETSc Web Page,, 2018.Search in Google Scholar

[9] W. Bangerth, C. Burstedde, T. Heister, and M. Kronbichler, Algorithms and data structures for massively parallel generic adaptive finite element codes, ACM Trans. Math. Softw. 38 (2011), 14/1–14/28.10.1145/2049673.2049678Search in Google Scholar

[10] W. Bangerth, R. Hartmann, and G. Kanschat, deal.II – a general purpose object oriented finite element library, ACM Trans. Math. Softw. 33 (2007), No. 4, 24/1–24/27.10.1145/1268776.1268779Search in Google Scholar

[11] W. Bangerth and O. Kayser-Herold, Data Structures and Requirements for hp Finite Element Software, ACM Trans. Math. Softw. 36 (2009), No. 1, 4/1–4/31.10.1145/1486525.1486529Search in Google Scholar

[12] C. Bernardi and G. Raugel, Analysis of some finite elements for the Stokes problem, Math. Comp. 44 (1985), No. 169, 71–79.10.1090/S0025-5718-1985-0771031-7Search in Google Scholar

[13] L. S. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S.Hammarling, G. Henry, A. Petitet, K. Stanley, D.Walker, and R. C.Whaley, ScaLAPACK Users’ Guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1997.10.1137/1.9780898719642Search in Google Scholar

[14] J. L. Blanco and P. K. Rai, Nanoflann: a C++ Header-Only Fork of FLANN, a Library for Nearest Neighbor (NN) with KD-Trees,, 2014.Search in Google Scholar

[15] C. Burstedde, Parallel tree algorithms for AMR and non-standard data access, arXiv e-prints (2018), arXiv:1803.08432.10.1145/3401990Search in Google Scholar

[16] C. Burstedde, L. C.Wilcox, and O. Ghattas, p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees, SIAM J. Sci. Comput. 33 (2011), No. 3, 1103–1133.10.1137/100791634Search in Google Scholar

[17] T. C. Clevenger, T. Heister, G. Kanschat, and M. Kronbichler, A Flexible, Parallel, Adaptive Geometric Multigrid Method for FEM, arXiv:1904.03317, Report, 2019.10.1145/3425193Search in Google Scholar

[18] CuSOLVER Library, in Google Scholar

[19] CuSPARSE Library, in Google Scholar

[20] T. A. Davis, Algorithm 832: UMFPACK unsymmetric-pattern multifrontal method, ACM Trans. Math. Softw. 30 (2004), 196–199.10.1145/992200.992206Search in Google Scholar

[21] D. Davydov, T. Gerasimov, J.-P. Pelteret, and P. Steinmann, Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics, Adv. Modeling Simul. Eng. Sci. 4 (2017), No. 1, 7.10.1186/s40323-017-0093-0Search in Google Scholar PubMed PubMed Central

[22] A. DeSimone, L. Heltai, and C.Manigrasso, Tools for the Solution of PDEs Defined on Curved Manifolds with Deal.II, SISSA, Report No. 42/2009/M, 2009.Search in Google Scholar

[23] M. A. Heroux et al., Trilinos Web Page, 2018, in Google Scholar

[24] MGalassi, J Davies, J Theiler, B Gough, G Jungman, P Alken, MBooth, F Rossi, and R Ulerich, GNU Scientific Library Reference Manual (Edition 2.3), 2016.Search in Google Scholar

[25] C. Geuzaine and J.-F. Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities, Int. J. Numer. Meth. Eng. 79 (2009), No. 11, 1309–1331.10.1002/nme.2579Search in Google Scholar

[26] Ginkgo: High-Performance Linear Algebra Library for Manycore Systems, in Google Scholar

[27] N. Giuliani, A.Mola, and L. Heltai, π-BEM: A flexible parallel implementation for adaptive, geometry aware, and high order boundary element methods, Advances in Engineering Software121 (2018), No.March, 39–58.10.1016/j.advengsoft.2018.03.008Search in Google Scholar

[28] A. Griewank, D. Juedes, and J. Utke, Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++, ACM Trans. Math. Software (TOMS)22 (1996), No. 2, 131–167.10.1145/229473.229474Search in Google Scholar

[29] L. Heltai and A.Mola, Towards the Integration of CAD and FEM Using Open Source Libraries: a Collection of Deal.II Manifold Wrappers for the OpenCASCADE Library, SISSA, Report, 2015.Search in Google Scholar

[30] V. Hernandez, J. E. Roman, and V. Vidal, SLEPc: A Scalable and Flexible Toolkit for the Solution of Eigenvalue Problems, ACM Trans. Math. Software31 (2005), No. 3, 351–362.10.1145/1089014.1089019Search in Google Scholar

[31] M. A. Heroux, R. A. Bartlett, V. E. Howle, R. J. Hoekstra, J. J. Hu, T. G. Kolda, R. B. Lehoucq, K. R. Long, R. P. Pawlowski, E. T. Phipps, A. G. Salinger, H. K. Thornquist, R. S. Tuminaro, J. M.Willenbring, A.Williams, and K. S. Stanley, An overview of the Trilinos project, ACM Trans. Math. Softw. 31 (2005), 397–423.10.1145/1089014.1089021Search in Google Scholar

[32] A. C. Hindmarsh, P. N. Brown, K. Ei. Grant, S. Li. Lee, R. Serban, D. E. Shumaker, and C. S. Woodward, SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers, ACM Trans. Math. Software (TOMS)31 (2005), No. 3, 363–396.10.1145/1089014.1089020Search in Google Scholar

[33] B. Janssen and G. Kanschat, Adaptive multilevel methods with local smoothing for H1- and Hcurl-conforming high order finite element methods, SIAM J. Sci. Comput. 33 (2011), No. 4, 2095–2114.10.1137/090778523Search in Google Scholar

[34] G. Kanschat, Multi-level methods for discontinuous Galerkin FEM on locally refined meshes, Comput. & Struct. 82 (2004), No. 28, 2437–2445.10.1016/j.compstruc.2004.04.015Search in Google Scholar

[35] G. Karypis and V. Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM J. Sci. Comput. 20 (1998), No. 1, 359–392.10.1137/S1064827595287997Search in Google Scholar

[36] M. Kronbichler and K. Kormann, A generic interface for parallel cell-based finite element operator application, Comput. Fluids63 (2012), 135–147.10.1016/j.compfluid.2012.04.012Search in Google Scholar

[37] M. Kronbichler and K. Kormann, Fast matrix-free evaluation of discontinuous Galerkin finite element operators, ACM Trans. Math. Soft. 45 (2019), No. 3, 29/1–29/40.10.1145/3325864Search in Google Scholar

[38] M. Kronbichler and K. Ljungkvist, Multigrid for Matrix-Free High-Order Finite Element Computations on Graphics Processors, ACM Trans. Parallel Comput. 6 (2019), No. 1, 2/1–2/32.10.1145/3322813Search in Google Scholar

[39] M. Kronbichler and W. A.Wall, A performance comparison of continuous and discontinuous Galerkin methods with fast multigrid solvers, SIAM J. Sci. Comput. 40 (2018), No. 5, A3423–A3448.10.1137/16M110455XSearch in Google Scholar

[40] R. M. Kynch and P. D. Ledger, Resolving the sign conflict problem for hp.hexahedral Nedelec elements with application to eddy current problems, Computers & Structures181 (2017), 41–54.10.1016/j.compstruc.2016.05.021Search in Google Scholar

[41] R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, SIAM, Philadelphia, 1998.10.1137/1.9780898719628Search in Google Scholar

[42] List of Changes for 9.1, in Google Scholar

[43] K. Ljungkvist, Matrix-free Finite-element Computations on Graphics Processors with Adaptively Refined Unstructured Meshes, In: Proceedings of the 25th High Performance Computing Symposium, HPC’17, pp. 1:1–1:12, Society for Computer Simulation International, San Diego, CA, USA, 2017.Search in Google Scholar

[44] M.Maier, M. Bardelloni, and L. Heltai, LinearOperator – a generic, high-level expression syntax for linear algebra, Comp. & Math. Appl. 72 (2016), No. 1, 1–24.10.1016/j.camwa.2016.04.024Search in Google Scholar

[45] M.Maier, M. Bardelloni, and L. Heltai, LinearOperator Benchmarks, Version 1.0.0, March 2016.Search in Google Scholar

[46] MUMPS: a MUltifrontal Massively Parallel Sparse Direct Solver, in Google Scholar

[47] Muparser: Fast Math Parser Library, in Google Scholar

[48] OpenCASCADE: Open CASCADE Technology, 3D Modeling & Numerical Simulation, in Google Scholar

[49] J. Reinders, Intel Threading Building Blocks, O’Reilly, 2007.Search in Google Scholar

[50] R. Rew and G. Davis, NetCDF: an interface for scientific data access, Computer Graphics and Applications, IEEE10 (1990), No. 4, 76–82.10.1109/38.56302Search in Google Scholar

[51] D. Ridzal and D. P. Kouri, Rapid Optimization Library, Sandia National Laboratories (SNL-NM), Albuquerque, NM, USA, Report, 2014.Search in Google Scholar

[52] A. Sartori, N. Giuliani, M. Bardelloni, and L. Heltai, deal2lkit: A toolkit library for high performance programming in deal.II, SoftwareX7 (2018), 318–327.10.1016/j.softx.2018.09.004Search in Google Scholar

[53] T. Schulze, A. Gessler, K. Kulling, D. Nadlinger, J. Klein, M. Sibly, and M. Gubisch, Open asset import library (assimp), Computer Software, URL: (2012).Search in Google Scholar

[54] SymEngine: Fast Symbolic Manipulation Library, Written in C++,, in Google Scholar

[55] The HDF Group, Hierarchical Data Format, Version 5, 1997-2018, in Google Scholar

[56] B. Turcksin, M. Kronbichler, and W. Bangerth, WorkStream – a design pattern for multicore-enabled finite element computations, ACM Trans. Math. Software43 (2016), No. 1, 2/1–2/29.10.1145/2851488Search in Google Scholar

[57] A.Walther and A. Griewank, Getting started with ADOL-C, In: Combinatorial Scientific Computing, Chapman-Hall CRC Computational Science, pp. 181–202, U. Naumann and O. Schenk, 2012.10.1201/b11644-8Search in Google Scholar

[58] S. Zaglmayr, High Order Finite Element Methods for Electromagnetic Field Computation, Ph.D. thesis, Johannes Kepler University, Linz, Austria, 2006.Search in Google Scholar

Received: 2019-06-14
Accepted: 2019-06-16
Published Online: 2019-06-30
Published in Print: 2019-12-18

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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