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A generic finite element framework on parallel tree-based adaptive meshes. (English) Zbl 07328656
MSC:
65Y05 Parallel numerical computation
65Y20 Complexity and performance of numerical algorithms
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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[1] J. Holke, Scalable Algorithms for Parallel Tree-based Adaptive Mesh Refinement with General Element Types, Ph.D. thesis, Bonn University, Bonn, Germany, 2018.
[2] 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), pp. 1103-1133, https://doi.org/10.1137/100791634. · Zbl 1230.65106
[3] T. Isaac, C. Burstedde, L. C. Wilcox, and O. Ghattas, Recursive algorithms for distributed forests of octrees, SIAM J. Sci. Comput., 37 (2015), pp. C497-C531, https://doi.org/10.1137/140970963. · Zbl 1323.65105
[4] H. Sundar, R. S. Sampath, and G. Biros, Bottom-up construction and 2:1 balance refinement of linear octrees in parallel, SIAM J. Sci. Comput., 30 (2008), pp. 2675-2708, https://doi.org/10.1137/070681727. · Zbl 1186.68554
[5] C. Burstedde and J. Holke, A tetrahedral space-filling curve for nonconforming adaptive meshes, SIAM J. Sci. Comput., 38 (2016), pp. C471-C503, https://doi.org/10.1137/15M1040049. · Zbl 1348.65173
[6] L. C. Wilcox, G. Stadler, C. Burstedde, and O. Ghattas, A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media, J. Comput. Phys., 229 (2010), pp. 9373-9396, https://doi.org/10.1016/J.JCP.2010.09.008. · Zbl 1427.74071
[7] J. Rudi, O. Ghattas, A. C. I. Malossi, T. Isaac, G. Stadler, M. Gurnis, P. W. J. Staar, Y. Ineichen, C. Bekas, and A. Curioni, An extreme-scale implicit solver for complex PDEs: Highly heterogeneous flow in earth’s mantle, in Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis - SC ’15, ACM, New York, 2015, pp. 1-12, https://doi.org/10.1145/2807591.2807675.
[8] M. Olm, S. Badia, and A. F. Martín, Simulation of high temperature superconductors and experimental validation, Comput. Phys. Commun., 237 (2018), pp. 154-167, https://doi.org/10.1016/J.CPC.2018.11.021.
[9] E. Neiva, S. Badia, A. F. Martín, and M. Chiumenti, A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing, Internat. J. Numer. Methods Engrg., 119 (2019), pp. 1098-1125.
[10] S. Badia, A. F. Martín, and F. Verdugo, Mixed aggregated finite element methods for the unfitted discretization of the Stokes problem, SIAM J. Sci. Comput., 40 (2018), pp. B1541-B1576, https://doi.org/10.1137/18M1185624. · Zbl 1412.65184
[11] S. Badia, F. Verdugo, and A. F. Martín, The aggregated unfitted finite element method for elliptic problems, Comput. Methods Appl. Mech. Engrg., 336 (2018), pp. 533-553, https://doi.org/10.1016/j.cma.2018.03.022. · Zbl 1440.65175
[12] W. C. Rheinboldt and C. K. Mesztenyi, On a data structure for adaptive finite element mesh refinements, ACM Trans. Math. Software, 6 (1980), pp. 166-187, https://doi.org/10.1145/355887.355891. · Zbl 0437.65081
[13] M. S. Shephard, Linear multipoint constraints applied via transformation as part of a direct stiffness assembly process, Internat. J. Numer. Methods Engrg., 20 (1984), pp. 2107-2112, https://doi.org/10.1002/nme.1620201112. · Zbl 0547.73069
[14] W. Bangerth, C. Burstedde, T. Heister, and M. Kronbichler, Algorithms and data structures for massively parallel generic adaptive finite element codes, ACM Trans. Math. Software, 38 (2012), 14, https://doi.org/10.1145/2049673.2049678. · Zbl 1365.65247
[15] W. Bangerth, R. Hartmann, and G. Kanschat, DEAL.\(II\)—A general-purpose object-oriented finite element library, ACM Trans. Math. Software, 33 (2007), https://doi.org/10.1145/1268776.1268779. · Zbl 1365.65248
[16] S. Badia, A. F. Martín, and J. Principe, A highly scalable parallel implementation of balancing domain decomposition by constraints, SIAM J. Sci. Comput., 36 (2014), pp. C190-C218, https://doi.org/10.1137/130931989. · Zbl 1296.65177
[17] S. Badia, A. F. Martín, and J. Principe, Multilevel balancing domain decomposition at extreme scales, SIAM J. Sci. Comput., 38 (2016), pp. C22-C52, https://doi.org/10.1137/15M1013511. · Zbl 1334.65217
[18] S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, K. Rupp, B. F. Smith, S. Zampini, H. Zhang, and H. Zhang, PETSc Users Manual, Technical Report ANL-95/11 - Revision 3.7, Argonne National Laboratory, Argonne, IL, 2016.
[19] 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. Software, 31 (2005), pp. 397-423, https://doi.org/10.1145/1089014.1089021. · Zbl 1136.65354
[20] S. Badia, A. F. Martín, and J. Principe, FEMPAR: An object-oriented parallel finite element framework, Arch. Comput. Methods Eng., 25 (2018), 195-271, https://doi.org/10.1007/s11831-017-9244-1. · Zbl 1392.65005
[21] T. Isaac, C. Burstedde, and O. Ghattas, Low-cost parallel algorithms for \(2{:}1\) octree balance, in Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IEEE, Piscataway, NJ, 2012, pp. 426-437, https://doi.org/10.1109/IPDPS.2012.47.
[22] M. Olm, S. Badia, and A. F. Martín, On a general implementation of \(h\)- and \(p\)-adaptive curl-conforming finite elements, Adv. Eng. Software, 132 (2019), pp. 74-91, https://doi.org/10.1016/J.ADVENGSOFT.2019.03.006.
[23] J. Cervený, V. Dobrev, and T. Kolev, Nonconforming mesh refinement for high-order finite elements, SIAM J. Sci. Comput., 41 (2019), pp. C367-C392, https://doi.org/10.1137/18M1193992. · Zbl 07105497
[24] D. W. Kelly, J. P. De S. R. Gago, O. C. Zienkiewicz, and I. Babuska, A posteriori error analysis and adaptive processes in the finite element method: Part I: Error analysis, Internat. J. Numer. Methods Engrg., 19 (1983), https://doi.org/10.1002/nme.1620191103. · Zbl 0534.65068
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