The deal.II library, Version 9.1

References

[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, http://www.mcs.anl.gov/petsc, 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, https://github.com/jlblancoc/nanoflann, 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, https://docs.nvidia.com/cuda/cusolver/index.html.Search in Google Scholar

[19] CuSPARSE Library, https://docs.nvidia.com/cuda/cusparse/index.html.Search in Google Scholar

[20] T. A. Davis, Algorithm 832: UMFPACK V4.3.an 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, http://trilinos.org.Search 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, https://github.com/ginkgo-project/ginkgo.Search 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, https://www.dealii.org/developer/doxygen/deal.II/changes_between_9_0_1_and_9_1_0.html.Search 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, http://graal.ens-lyon.fr/MUMPS/.Search in Google Scholar

[47] Muparser: Fast Math Parser Library, http://muparser.beltoforion.de/.Search in Google Scholar

[48] OpenCASCADE: Open CASCADE Technology, 3D Modeling & Numerical Simulation, http://www.opencascade.org/.Search 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: https://github.com/assimp/assimp (2012).Search in Google Scholar

[54] SymEngine: Fast Symbolic Manipulation Library, Written in C++, https://github.com/symengine/symengine, http://sympy.org/.Search in Google Scholar

[55] The HDF Group, Hierarchical Data Format, Version 5, 1997-2018, http://www.hdfgroup.org/HDF5/.Search 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