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10.21105/joss.05946 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.10763375 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/5946 + + + + 10.21105/joss.05946 + https://joss.theoj.org/papers/10.21105/joss.05946 + + + https://joss.theoj.org/papers/10.21105/joss.05946.pdf + + + + + + Model and computational advancements to full +vectorial Maxwell model for studying fiber amplifiers + Henneking + Computers & Mathematics with +Applications + 85 + 10.1016/j.camwa.2021.01.006 + 2021 + Henneking, S., Grosek, J., & +Demkowicz, L. (2021). Model and computational advancements to full +vectorial Maxwell model for studying fiber amplifiers. Computers & +Mathematics with Applications, 85, 30–41. +https://doi.org/10.1016/j.camwa.2021.01.006 + + + A scalable hp-adaptive finite element +software with applications in fiber optics + Henneking + 10.26153/tsw/13716 + 2021 + Henneking, S. (2021). A scalable +hp-adaptive finite element software with applications in fiber optics +[PhD thesis, The University of Texas at Austin]. +https://doi.org/10.26153/tsw/13716 + + + Parallel simulations of high-power optical +fiber amplifiers + Henneking + Spectral and high order methods for partial +differential equations ICOSAHOM 2020+1 + 10.1007/978-3-031-20432-6_22 + 2022 + Henneking, S., Grosek, J., & +Demkowicz, L. (2022). Parallel simulations of high-power optical fiber +amplifiers. Spectral and High Order Methods for Partial Differential +Equations ICOSAHOM 2020+1, 349–360. +https://doi.org/10.1007/978-3-031-20432-6_22 + + + Scalable DPG multigrid solver for Helmholtz +problems: A study on convergence + Badger + Computers & Mathematics with +Applications + 148 + 10.1016/j.camwa.2023.07.006 + 2023 + Badger, J., Henneking, S., Petrides, +S., & Demkowicz, L. (2023). Scalable DPG multigrid solver for +Helmholtz problems: A study on convergence. Computers & Mathematics +with Applications, 148, 81–92. +https://doi.org/10.1016/j.camwa.2023.07.006 + + + An anisotropic hp-adaptation framework for +ultraweak discontinuous Petrov–Galerkin formulations + Chakraborty + arXiv preprint +arXiv:2309.00726 + 10.48550/arXiv.2309.00726 + 2023 + Chakraborty, A., Henneking, S., & +Demkowicz, L. (2023). An anisotropic hp-adaptation framework for +ultraweak discontinuous Petrov–Galerkin formulations. arXiv Preprint +arXiv:2309.00726. +https://doi.org/10.48550/arXiv.2309.00726 + + + hp3D: A scalable MPI/OpenMP hp-adaptive +finite element software library for complex multiphysics applications +(v1.0) + Henneking + 10.5281/zenodo.10763375 + 2024 + Henneking, S., Petrides, S., Fuentes, +F., Badger, J., & Demkowicz, L. (2024). hp3D: A scalable MPI/OpenMP +hp-adaptive finite element software library for complex multiphysics +applications (v1.0). +https://doi.org/10.5281/zenodo.10763375 + + + hp3D User Manual + Henneking + arXiv preprint +arXiv:2207.12211 + 10.48550/arXiv.2207.12211 + 2022 + Henneking, S., & Demkowicz, L. +(2022). hp3D User Manual. arXiv Preprint arXiv:2207.12211. +https://doi.org/10.48550/arXiv.2207.12211 + + + Computing with hp Finite Elements. III. +Parallel hp3D Code + Henneking + 2024 + Henneking, S., Demkowicz, L., +Petrides, S., Fuentes, F., Keith, B., & Gatto, P. (2024). Computing +with hp Finite Elements. III. Parallel hp3D Code. In +preparation. + + + Computing with hp Finite Elements. II. +Frontiers: Three Dimensional Elliptic and Maxwell Problems with +Applications + Demkowicz + 10.1201/9781420011692 + 2007 + Demkowicz, L., Kurtz, J., Pardo, D., +Paszyński, M., Rachowicz, W., & Zdunek, A. (2007). Computing with hp +Finite Elements. II. Frontiers: Three Dimensional Elliptic and Maxwell +Problems with Applications. Chapman & Hall/CRC. +https://doi.org/10.1201/9781420011692 + + + Computing with hp Finite Elements. I. One and +Two Dimensional Elliptic and Maxwell Problems + Demkowicz + 10.1201/9781420011685 + 2006 + Demkowicz, L. (2006). Computing with +hp Finite Elements. I. One and Two Dimensional Elliptic and Maxwell +Problems. Chapman & Hall/CRC Press, Taylor; Francis. +https://doi.org/10.1201/9781420011685 + + + An adaptive multigrid solver for DPG methods +with applications in linear acoustics and +electromagnetics + Petrides + Computers & Mathematics with +Applications + 87 + 10.1016/j.camwa.2021.01.017 + 2021 + Petrides, S., & Demkowicz, L. +(2021). An adaptive multigrid solver for DPG methods with applications +in linear acoustics and electromagnetics. Computers & Mathematics +with Applications, 87, 12–26. +https://doi.org/10.1016/j.camwa.2021.01.017 + + + A fully asynchronous multifrontal solver +using distributed dynamic scheduling + Amestoy + SIAM Journal on Matrix Analysis and +Applications + 1 + 23 + 10.1137/s0895479899358194 + 2001 + Amestoy, P. R., Duff, I. S., +L’Excellent, J. Y., & Koster, J. (2001). A fully asynchronous +multifrontal solver using distributed dynamic scheduling. SIAM Journal +on Matrix Analysis and Applications, 23(1), 15–41. +https://doi.org/10.1137/s0895479899358194 + + + PT-Scotch: A tool for efficient parallel +graph ordering + Chevalier + Parallel Computing + 6-8 + 34 + 10.1016/j.parco.2007.12.001 + 2008 + Chevalier, C., & Pellegrini, F. +(2008). PT-Scotch: A tool for efficient parallel graph ordering. +Parallel Computing, 34(6-8), 318–331. +https://doi.org/10.1016/j.parco.2007.12.001 + + + A fast and high quality multilevel scheme for +partitioning irregular graphs + Karypis + SIAM Journal on Scientific +Computing + 1 + 20 + 10.1137/s1064827595287997 + 1998 + Karypis, G., & Kumar, V. (1998). +A fast and high quality multilevel scheme for partitioning irregular +graphs. SIAM Journal on Scientific Computing, 20(1), 359–392. +https://doi.org/10.1137/s1064827595287997 + + + Hierarchical data format version +5 + The HDF Group + 1997 + The HDF Group. (1997). Hierarchical +data format version 5. +http://www.hdfgroup.org/HDF5 + + + PETSc/TAO users manual + Balay + 10.2172/2205494 + 2023 + Balay, S., Abhyankar, S., Adams, M. +F., Benson, S., Brown, J., Brune, P., Buschelman, K., Constantinescu, +E., Dalcin, L., Dener, A., Eijkhout, V., Faibussowitsch, J., Gropp, W. +D., Hapla, V., Isaac, T., Jolivet, P., Karpeev, D., Kaushik, D., +Knepley, M. G., … Zhang, J. (2023). PETSc/TAO users manual (ANL-21/39 - +Revision 3.20). Argonne National Laboratory. +https://doi.org/10.2172/2205494 + + + Mathematical theory of finite +elements + Demkowicz + 10.1137/1.9781611977738 + 2023 + Demkowicz, L. (2023). Mathematical +theory of finite elements. Society for Industrial; Applied Mathematics. +https://doi.org/10.1137/1.9781611977738 + + + Polynomial exact sequences and +projection-based interpolation with application to Maxwell +equations + Demkowicz + Mixed finite elements, compatibility +conditions, and applications + 10.1007/978-3-540-78319-0_3 + 2008 + Demkowicz, L. (2008). Polynomial +exact sequences and projection-based interpolation with application to +Maxwell equations. In Mixed finite elements, compatibility conditions, +and applications (pp. 101–158). Springer. +https://doi.org/10.1007/978-3-540-78319-0_3 + + + Toward a universal hp adaptive finite element +strategy. Part 1: Constrained approximation and data +structure + Demkowicz + Computer Methods in Applied Mechanics and +Engineering + 77 + 10.1016/0045-7825(89)90129-1 + 1989 + Demkowicz, L., Oden, J. T., & +Rachowicz, W. (1989). Toward a universal hp adaptive finite element +strategy. Part 1: Constrained approximation and data structure. Computer +Methods in Applied Mechanics and Engineering, 77, 79–112. +https://doi.org/10.1016/0045-7825(89)90129-1 + + + Toward a universal hp adaptive finite element +strategy. Part 2: A posteriori error estimation + Oden + Computer Methods in Applied Mechanics and +Engineering + 77 + 10.1016/0045-7825(89)90130-8 + 1989 + Oden, J. T., Demkowicz, L., +Rachowicz, R., & Westermann, T. A. (1989). Toward a universal hp +adaptive finite element strategy. Part 2: A posteriori error estimation. +Computer Methods in Applied Mechanics and Engineering, 77, 113–180. +https://doi.org/10.1016/0045-7825(89)90130-8 + + + Toward a universal hp adaptive finite element +strategy. Part 3: Design of hp meshes + Rachowicz + Computer Methods in Applied Mechanics and +Engineering + 77 + 10.1016/0045-7825(89)90131-X + 1989 + Rachowicz, W., Oden, J. T., & +Demkowicz, L. (1989). Toward a universal hp adaptive finite element +strategy. Part 3: Design of hp meshes. Computer Methods in Applied +Mechanics and Engineering, 77, 181–212. +https://doi.org/10.1016/0045-7825(89)90131-X + + + Discontinuous Petrov–Galerkin (DPG) +method + Demkowicz + Encyclopedia of Computational Mechanics +Second Edition + 10.1002/9781119176817.ecm2105 + 2017 + Demkowicz, L., & Gopalakrishnan, +J. (2017). Discontinuous Petrov–Galerkin (DPG) method. Encyclopedia of +Computational Mechanics Second Edition, 1–15. +https://doi.org/10.1002/9781119176817.ecm2105 + + + Using a DPG method to validate DMA +experimental calibration of viscoelastic materials + Fuentes + Computers & Mathematics with +Applications + 325 + 10.1016/j.cma.2017.07.012 + 2017 + Fuentes, F., Demkowicz, L., & +Wilder, A. (2017). Using a DPG method to validate DMA experimental +calibration of viscoelastic materials. Computers & Mathematics with +Applications, 325, 748–765. +https://doi.org/10.1016/j.cma.2017.07.012 + + + Deal.II–general-purpose object-oriented +finite element library + Bangerth + ACM Transactions on Mathematical +Software + 4 + 33 + 10.1145/1268776.1268779 + 2007 + Bangerth, W., Hartmann, R., & +Kanschat, G. (2007). Deal.II–general-purpose object-oriented finite +element library. ACM Transactions on Mathematical Software, 33(4), +24–es. https://doi.org/10.1145/1268776.1268779 + + + MFEM: A modular finite element methods +library + Anderson + Computers & Mathematics with +Applications + 81 + 10.1016/j.camwa.2020.06.009 + 2021 + Anderson, R., Andrej, J., Barker, A., +Bramwell, J., Camier, J.-S., Cerveny, J., Dobrev, V., Dudouit, Y., +Fisher, A., Kolev, T., & others. (2021). MFEM: A modular finite +element methods library. Computers & Mathematics with Applications, +81, 42–74. +https://doi.org/10.1016/j.camwa.2020.06.009 + + + Zoltan data management services for parallel +dynamic applications + Devine + Computing in Science and +Engineering + 2 + 4 + 10.1109/5992.988653 + 2002 + Devine, K., Boman, E., Heaphy, R., +Hendrickson, B., & Vaughan, C. (2002). Zoltan data management +services for parallel dynamic applications. Computing in Science and +Engineering, 4(2), 90–97. +https://doi.org/10.1109/5992.988653 + + + Paraview: An end-user tool for large data +visualization + Ahrens + The visualization handbook + 10.1016/b978-012387582-2/50038-1 + 2005 + Ahrens, J., Geveci, B., & Law, C. +(2005). Paraview: An end-user tool for large data visualization. In The +visualization handbook. Elsevier. +https://doi.org/10.1016/b978-012387582-2/50038-1 + + + Orientation embedded high order shape +functions for the exact sequence elements of all shapes + Fuentes + Computers & Mathematics with +Applications + 4 + 70 + 10.1016/j.camwa.2015.04.027 + 2015 + Fuentes, F., Keith, B., Demkowicz, +L., & Nagaraj, S. (2015). Orientation embedded high order shape +functions for the exact sequence elements of all shapes. Computers & +Mathematics with Applications, 70(4), 353–458. +https://doi.org/10.1016/j.camwa.2015.04.027 + + + Adaptive multilevel solvers for the +discontinuous Petrov–Galerkin method with an emphasis on high-frequency +wave propagation problems + Petrides + 10.26153/tsw/2153 + 2019 + Petrides, S. (2019). Adaptive +multilevel solvers for the discontinuous Petrov–Galerkin method with an +emphasis on high-frequency wave propagation problems [PhD thesis, The +University of Texas at Austin]. +https://doi.org/10.26153/tsw/2153 + + + Finite element modeling of electromagnetic +radiation and induced heat transfer in the human body + Kim + 2013 + Kim, K. (2013). Finite element +modeling of electromagnetic radiation and induced heat transfer in the +human body [PhD thesis, The University of Texas at Austin]. +https://hdl.handle.net/2152/21292 + + + Modeling bone conduction of sound in the +human head using hp-finite elements + Gatto + 2012 + Gatto, P. (2012). Modeling bone +conduction of sound in the human head using hp-finite elements [PhD +thesis, The University of Texas at Austin]. +https://hdl.handle.net/2152/19517 + + + A 3D DPG Maxwell approach to nonlinear Raman +gain in fiber laser amplifiers + Nagaraj + Journal of Computational +Physics + 2 + 10.1016/j.jcpx.2019.100002 + 2019 + Nagaraj, S., Grosek, J., Petrides, +S., Demkowicz, L., & Mora, J. D. (2019). A 3D DPG Maxwell approach +to nonlinear Raman gain in fiber laser amplifiers. Journal of +Computational Physics, 2, 100002. +https://doi.org/10.1016/j.jcpx.2019.100002 + + + + + + From 7fe8be0408d0ad75fe09f713a609bbe433e003f5 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Mon, 4 Mar 2024 15:37:56 +0000 Subject: [PATCH 3/3] Creating 10.21105.joss.05946.jats --- joss.05946/10.21105.joss.05946.jats | 872 ++++++++++++++++++++++++++++ 1 file changed, 872 insertions(+) create mode 100644 joss.05946/10.21105.joss.05946.jats diff --git a/joss.05946/10.21105.joss.05946.jats b/joss.05946/10.21105.joss.05946.jats new file mode 100644 index 0000000000..f27911005a --- /dev/null +++ b/joss.05946/10.21105.joss.05946.jats @@ -0,0 +1,872 @@ + + +

+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +5946 +10.21105/joss.05946 + + + +hp3D: +A Scalable MPI/OpenMP + +hp-Adaptive +Finite Element Software Library for Complex Multiphysics +Applications + + + +https://orcid.org/0000-0003-2177-8519 + +Henneking +Stefan + + +* + + +https://orcid.org/0000-0002-1284-5495 + +Petrides +Socratis + + + + +https://orcid.org/0000-0002-4039-082X + +Fuentes +Federico + + + + +https://orcid.org/0000-0001-6482-105X + +Badger +Jacob + + + + +https://orcid.org/0000-0001-7839-8037 + +Demkowicz +Leszek + + + + + +Oden Institute, The University of Texas at Austin, +USA + + + + +Lawrence Livermore National Laboratory, USA + + + + +Institute for Mathematical and Computational Engineering, +Pontificia Universidad Católica de Chile, Chile + + + + +* E-mail: + + +2 +10 +2023 + +9 +95 +5946 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +finite element +hp-adaptivity +DPG method + + + + + + Summary +

The + + hp3D + finite element (FE) library is a tool for computational modeling of + engineering applications. The library provides a framework for + discretization of + three-dimensional1 multiphysics + problems described by systems of partial differential equations. + + + hp3D + can be compiled in real or complex mode to accommodate the need for + real- or complex-valued physics variables, respectively. The library + is written entirely in Fortran; user applications interfacing with the + library are also written in Fortran. The + + + hp3D + software can be installed and runs efficiently on various CPU-based + compute architectures, from laptops and single workstations to + state-of-the-art supercomputers.

+
+ + Statement of need +

+ + hp3D + combines a list of unique features and algorithms setting it apart + from other publicly available finite element libraries. The software + supports hybrid meshes combining elements of “all shapes:” hexahedra, + tetrahedra, prisms, and pyramids. The internal Geometric Modeling + Package (GMP) provides support for exact geometry + elements and isoparametric elements. Exact geometry + elements directly use the parametrizations provided by GMP resulting + in computations with no geometry error; isoparametric elements + approximate the geometry maps with polynomials spanning the element + space of shape functions. + + hp3D’s + shape functions package provides compatible discretization of energy + spaces forming the + + H1H(curl)H(div)L2 + exact sequence + (Demkowicz, + 2023; + Fuentes + et al., 2015). Additionally, the + + hp3D + FE code sets itself apart from other advanced FE libraries (e.g., MFEM + (Anderson + et al., 2021) or deal.II + (Bangerth + et al., 2007)) by supporting + + + hp-adaptive + solutions with anisotropic refinements in both + element size + + h + and polynomial order + + p. + Such + + hp-adaptive + methods are the most efficient way to converge to difficult solutions, + e.g., resolving solutions with boundary layers, adapting toward + geometric singularities, etc. + (Chakraborty + et al., 2023). + + hp3D + features a number of unique algorithms, including constrained + approximation routines for assembling elements with hanging + nodes + (Demkowicz + et al., 1989; + Oden + et al., 1989; + Rachowicz + et al., 1989), and projection-based + interpolation for computation of nodal constraints + (Demkowicz, + 2008). Besides discretization with the standard Bubnov-Galerkin + FE method, the + + hp3D + library also supports discretization with the discontinuous + Petrov-Galerkin (DPG) method + (Demkowicz + & Gopalakrishnan, 2017). The + + hp3D + software leverages hybrid MPI/OpenMP parallelism to run efficiently on + large-scale computing facilities + (Badger + et al., 2023; + Henneking, + 2021).

+
+ + Dependencies +

+ + hp3D + interfaces with several well-established third-party libraries: for + mesh partitioning (ParMETIS + (Karypis + & Kumar, 1998), PT-Scotch + (Chevalier + & Pellegrini, 2008)), for dynamic load balancing (Zoltan + (Devine + et al., 2002)), for linear solvers (MUMPS + (Amestoy + et al., 2001), PETSc + (Balay + et al., 2023)), and for I/O (pHDF5 + (The + HDF Group, 1997)). We note that all of these dependencies can + be directly installed via PETSc. Additionally, the geometry mesh and + the solution can be exported to VTK and visualized with ParaView + (Ahrens + et al., 2005).

+
+ + Examples of applications +

Some examples of 3D applications that have been implemented in + + + hp3D + include modeling of acoustic wave propagation in the human head + (Gatto, + 2012), modeling of electromagnetic waves with thermal effects + in the human head + (Kim, + 2013), electromagnetic and acoustic scattering and + high-frequency beams + (Petrides, + 2019; + Petrides + & Demkowicz, 2021), modeling of insulators in high-energy + density electric motors (thermo-viscoelasticity) + (Fuentes + et al., 2017), and modeling of optical amplifiers (nonlinear + Maxwell equations coupled with the heat equation) + (Henneking + et al., 2022, + 2021; + Nagaraj + et al., 2019).

+
+ + Further reading +

Instructions on installing and using the code are available in the + + + hp3D + user manual + (Henneking + & Demkowicz, 2022). + + hp3D’s + underlying algorithms are described in various published articles and + books. Many parts of the current version of the + + + hp3D + software are based on the algorithms described in the two-volume + + + hp + book series + (Demkowicz, + 2006; + Demkowicz + et al., 2007) on the former 2D and 3D versions of the code + (which were not published as open-source libraries). A third + + + hp + book volume detailing the additions and modifications of the newest + version, including its MPI/OpenMP parallel algorithms, will be + published soon + (Henneking, + Demkowicz, et al., 2024). The orientation-embedded shape + functions package is described in Fuentes et al. + (2015). + Details on the FE methodology and conforming discretization of + exact-sequence elements are given in Demkowicz + (2023).

+

The source code for + + hp3D + has been archived to Zenodo + (Henneking, + Petrides, et al., 2024).

+
+ + Acknowledgements +

We acknowledge contributions from Ankit Chakraborty, Paolo Gatto, + Brendan Keith, Kyungjoo Kim, Jaime D. Mora, and Sriram Nagaraj for + this project. The development and open-sourcing of the + + + hp3D + FE code are supported by NSF award 2103524. This work was performed + under the auspices of the U.S. Department of Energy by Lawrence + Livermore National Laboratory under Contract DE-AC52-07NA27344, + LLNL-JRNL-855288.

+
+ + + + + + + HennekingStefan + GrosekJacob + DemkowiczLeszek + + Model and computational advancements to full vectorial Maxwell model for studying fiber amplifiers + Computers & Mathematics with Applications + Elsevier + 2021 + 85 + 10.1016/j.camwa.2021.01.006 + 30 + 41 + + + + + + HennekingStefan + + A scalable hp-adaptive finite element software with applications in fiber optics + The University of Texas at Austin + 2021 + 10.26153/tsw/13716 + + + + + + HennekingStefan + GrosekJacob + DemkowiczLeszek + + Parallel simulations of high-power optical fiber amplifiers + Spectral and high order methods for partial differential equations ICOSAHOM 2020+1 + Springer + 2022 + 10.1007/978-3-031-20432-6_22 + 349 + 360 + + + + + + BadgerJacob + HennekingStefan + PetridesSocratis + DemkowiczLeszek + + Scalable DPG multigrid solver for Helmholtz problems: A study on convergence + Computers & Mathematics with Applications + Elsevier + 2023 + 148 + 10.1016/j.camwa.2023.07.006 + 81 + 92 + + + + + + ChakrabortyAnkit + HennekingStefan + DemkowiczLeszek + + An anisotropic hp-adaptation framework for ultraweak discontinuous Petrov–Galerkin formulations + arXiv preprint arXiv:2309.00726 + 2023 + 10.48550/arXiv.2309.00726 + + + + + + HennekingStefan + PetridesSocratis + FuentesFederico + BadgerJacob + DemkowiczLeszek + + hp3D: A scalable MPI/OpenMP hp-adaptive finite element software library for complex multiphysics applications (v1.0) + 2024 + 10.5281/zenodo.10763375 + + + + + + HennekingStefan + DemkowiczLeszek + + hp3D User Manual + arXiv preprint arXiv:2207.12211 + 2022 + 10.48550/arXiv.2207.12211 + + + + + + HennekingStefan + DemkowiczLeszek + PetridesSocratis + FuentesFederico + KeithBrendan + GattoPaolo + + Computing with hp Finite Elements. III. Parallel hp3D Code + In preparation + 2024 + + + + + + DemkowiczLeszek + KurtzJason + PardoDavid + PaszyńskiMaciej + RachowiczWaldemar + ZdunekAdam + + Computing with hp Finite Elements. II. Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications + Chapman & Hall/CRC + 2007 + 10.1201/9781420011692 + + + + + + DemkowiczLeszek + + Computing with hp Finite Elements. I. One and Two Dimensional Elliptic and Maxwell Problems + Chapman & Hall/CRC Press, Taylor; Francis + 2006 + 10.1201/9781420011685 + + + + + + PetridesSocratis + DemkowiczLeszek + + An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics + Computers & Mathematics with Applications + 2021 + 87 + 10.1016/j.camwa.2021.01.017 + 12 + 26 + + + + + + AmestoyP. R. + DuffI. S. + L’ExcellentJ. Y. + KosterJ. + + A fully asynchronous multifrontal solver using distributed dynamic scheduling + SIAM Journal on Matrix Analysis and Applications + SIAM + 2001 + 23 + 1 + 10.1137/s0895479899358194 + 15 + 41 + + + + + + ChevalierC. + PellegriniF. + + PT-Scotch: A tool for efficient parallel graph ordering + Parallel Computing + Elsevier + 2008 + 34 + 6-8 + 10.1016/j.parco.2007.12.001 + 318 + 331 + + + + + + KarypisG. + KumarV. + + A fast and high quality multilevel scheme for partitioning irregular graphs + SIAM Journal on Scientific Computing + SIAM + 1998 + 20 + 1 + 10.1137/s1064827595287997 + 359 + 392 + + + + + + The HDF Group + + Hierarchical data format version 5 + 1997 + http://www.hdfgroup.org/HDF5 + + + + + + BalaySatish + AbhyankarShrirang + AdamsMark F. + BensonSteven + BrownJed + BrunePeter + BuschelmanKris + ConstantinescuEmil + DalcinLisandro + DenerAlp + EijkhoutVictor + FaibussowitschJacob + GroppWilliam D. + HaplaVáclav + IsaacTobin + JolivetPierre + KarpeevDmitry + KaushikDinesh + KnepleyMatthew G. + KongFande + KrugerScott + MayDave A. + McInnesLois Curfman + MillsRichard Tran + MitchellLawrence + MunsonTodd + RomanJose E. + RuppKarl + SananPatrick + SarichJason + SmithBarry F. + ZampiniStefano + ZhangHong + ZhangHong + ZhangJunchao + + PETSc/TAO users manual + Argonne National Laboratory + 2023 + 10.2172/2205494 + + + + + + DemkowiczLeszek + + Mathematical theory of finite elements + Society for Industrial; Applied Mathematics + 2023 + 10.1137/1.9781611977738 + + + + + + DemkowiczLeszek + + Polynomial exact sequences and projection-based interpolation with application to Maxwell equations + Mixed finite elements, compatibility conditions, and applications + Springer + 2008 + 10.1007/978-3-540-78319-0_3 + 101 + 158 + + + + + + DemkowiczLeszek + OdenJ. T. + RachowiczW. + + Toward a universal hp adaptive finite element strategy. Part 1: Constrained approximation and data structure + Computer Methods in Applied Mechanics and Engineering + 1989 + 77 + 10.1016/0045-7825(89)90129-1 + 79 + 112 + + + + + + OdenJ. T. + DemkowiczLeszek + RachowiczR. + WestermannT. A. + + Toward a universal hp adaptive finite element strategy. Part 2: A posteriori error estimation + Computer Methods in Applied Mechanics and Engineering + 1989 + 77 + 10.1016/0045-7825(89)90130-8 + 113 + 180 + + + + + + RachowiczW. + OdenJ. T. + DemkowiczLeszek + + Toward a universal hp adaptive finite element strategy. Part 3: Design of hp meshes + Computer Methods in Applied Mechanics and Engineering + 1989 + 77 + 10.1016/0045-7825(89)90131-X + 181 + 212 + + + + + + DemkowiczLeszek + GopalakrishnanJay + + Discontinuous Petrov–Galerkin (DPG) method + Encyclopedia of Computational Mechanics Second Edition + John Wiley & Sons + 2017 + 10.1002/9781119176817.ecm2105 + 1 + 15 + + + + + + FuentesFederico + DemkowiczLeszek + WilderAleta + + Using a DPG method to validate DMA experimental calibration of viscoelastic materials + Computers & Mathematics with Applications + Elsevier + 2017 + 325 + 10.1016/j.cma.2017.07.012 + 748 + 765 + + + + + + BangerthWolfgang + HartmannRalf + KanschatGuido + + Deal.II–general-purpose object-oriented finite element library + ACM Transactions on Mathematical Software + ACM New York, NY, USA + 2007 + 33 + 4 + 10.1145/1268776.1268779 + 24 + es + + + + + + AndersonRobert + AndrejJulian + BarkerAndrew + BramwellJamie + CamierJean-Sylvain + CervenyJakub + DobrevVeselin + DudouitYohann + FisherAaron + KolevTzanio + others + + MFEM: A modular finite element methods library + Computers & Mathematics with Applications + Elsevier + 2021 + 81 + 10.1016/j.camwa.2020.06.009 + 42 + 74 + + + + + + DevineK. + BomanE. + HeaphyR. + HendricksonB. + VaughanC. + + Zoltan data management services for parallel dynamic applications + Computing in Science and Engineering + 2002 + 4 + 2 + 10.1109/5992.988653 + 90 + 97 + + + + + + AhrensJ. + GeveciB. + LawC. + + Paraview: An end-user tool for large data visualization + The visualization handbook + Elsevier + 2005 + 10.1016/b978-012387582-2/50038-1 + + + + + + FuentesFederico + KeithBrendan + DemkowiczLeszek + NagarajSriram + + Orientation embedded high order shape functions for the exact sequence elements of all shapes + Computers & Mathematics with Applications + Elsevier + 2015 + 70 + 4 + 10.1016/j.camwa.2015.04.027 + 353 + 458 + + + + + + PetridesSocratis + + Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems + The University of Texas at Austin + 2019 + 10.26153/tsw/2153 + + + + + + KimKyungjoo + + Finite element modeling of electromagnetic radiation and induced heat transfer in the human body + The University of Texas at Austin + 2013 + https://hdl.handle.net/2152/21292 + + + + + + GattoPaolo + + Modeling bone conduction of sound in the human head using hp-finite elements + The University of Texas at Austin + 2012 + https://hdl.handle.net/2152/19517 + + + + + + NagarajSriram + GrosekJacob + PetridesSocratis + DemkowiczLeszek + MoraJaime David + + A 3D DPG Maxwell approach to nonlinear Raman gain in fiber laser amplifiers + Journal of Computational Physics + Elsevier + 2019 + 2 + 10.1016/j.jcpx.2019.100002 + 100002 + + + + + + +

The + + hp2D + FE library for two-dimensional problems is conceptually equivalent + to + + hp3D + but has not yet been released publicly.

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