Coarse mesh partitioning for tree-based AMR. (English) Zbl 1377.65126


65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
Full Text: DOI arXiv


[1] I. Babuška and W. Rheinboldt, A posteriori error estimates for the finite element method, Int. J. Numer. Methods Eng., 12 (1978), pp. 1597–1615. · Zbl 0396.65068
[2] M. Bader, Space-Filling Curves: An Introduction with Applications in Scientific Computing, Texts in Comput. Sci. Eng., Springer, 2012. · Zbl 1283.68012
[3] M. Bader and Ch. Zenger, Efficient storage and processing of adaptive triangular grids using Sierpinski curves, in Proc. International Conference on Computational Science, Lecture Notes in Comput. Sci. 3991, Springer, 2006, pp. 673–680, . · Zbl 1155.65402
[4] W. Bangerth, R. Hartmann, and G. Kanschat, deal.II—a general-purpose object-oriented finite element library, ACM Trans. Math. Software, 33 (2007), 24, . · Zbl 1365.65248
[5] M. J. Berger and P. Colella, Local adaptive mesh refinement for shock hydrodynamics, J. Comput. Phys., 82 (1989), pp. 64–84, . · Zbl 0665.76070
[6] M. J. Berger and J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53 (1984), pp. 484–512, . · Zbl 0536.65071
[7] J. Bey, Der BPX-Vorkonditionierer in drei Dimensionen: Gitterverfeinerung, Parallelisierung und Simulation, preprint, Universität Heidelberg, 1992.
[8] G. Bryan, Enzo 2.5 Documentation, Laboratory for Computational Astrophysics, University of Illinois, (accessed Oct 30, 2016).
[9] A. Burri, A. Dedner, R. Klöfkorn, and M. Ohlberger, An efficient implementation of an adaptive and parallel grid in DUNE, in Computational Science and High Performance Computing II, Springer, 2006, pp. 67–82, .
[10] C. Burstedde, p4est: Parallel AMR on Forests of Octrees, (accessed February 27, 2015).
[11] C. Burstedde, D. Calhoun, K. T. Mandli, and A. R. Terrel, Forestclaw: Hybrid forest-of-octrees AMR for hyperbolic conservation laws, in Parallel Computing: Accelerating Computational Science and Engineering (CSE), M. Bader, A. Bode, H.-J. Bungartz, M. Gerndt, G. R. Joubert, and F. Peters, eds., Advances in Parallel Computing 25, IOS Press, 2014, pp. 253–262, .
[12] C. Burstedde, O. Ghattas, M. Gurnis, T. Isaac, G. Stadler, T. Warburton, and L. C. Wilcox, Extreme-scale AMR, in SC10: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, IEEE, 2010, pp. 1–12.
[13] C. Burstedde, O. Ghattas, G. Stadler, T. Tu, and L. C. Wilcox, Towards adaptive mesh PDE simulations on petascale computers, in Proc. Teragrid ’08, 2008.
[14] C. Burstedde and J. Holke, A tetrahedral space-filling curve for nonconforming adaptive meshes, SIAM J. Sci. Comput., 38 (2016), pp. C471–C503, . · Zbl 1348.65173
[15] 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, . · Zbl 1230.65106
[16] U. Catalyurek, E. Boman, K. Devine, D. Bozdag, R. Heaphy, and L. Riesen, Hypergraph-based dynamic load balancing for adaptive scientific computations, in Proc. IEEE International Parallel and Distributed Processing Symposium (IPDPS 2007), IEEE, 2007, .
[17] C. Chevalier and F. Pellegrini, PT-Scotch: A tool for efficient parallel graph ordering, Parallel Comput., 34 (2008), pp. 318–331, .
[18] K. Devine, E. Boman, R. Heaphy, B. Hendrickson, and C. Vaughan, Zoltan data management services for parallel dynamic applications, Comput. Sci. Eng., 4 (2002), pp. 90–97.
[19] H. Digonnet, T. Coupez, and L. Silva, A massively parallel multigrid solver using PETSc for unstructured meshes on Tier0 supercomputer, Presentation at PETSc User Meeting, 2016, .
[20] J. Dreher and R. Grauer, Racoon: A parallel mesh-adaptive framework for hyperbolic conservation laws, Parallel Comput., 31 (2005), pp. 913–932.
[21] D. Feng, C. Tsolakis, A. N. Chernikov, and N. P. Chrisochoides, Scalable \(3\)d hybrid parallel Delaunay image-to-mesh conversion algorithm for distributed shared memory architectures, Computer-Aided Design, 85 (2017), pp. 10–19.
[22] 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 Methods Engrg., 79 (2009), pp. 1309–1331, . · Zbl 1176.74181
[23] M. Griebel and G. Zumbusch, Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves, Parallel Comput., 25 (1999), pp. 827–843. · Zbl 0945.65138
[24] M. Griebel and G. Zumbusch, Hash based adaptive parallel multilevel methods with space-filling curves, in Proc. NIC Symposium 2001, H. Rollnik and D. Wolf, eds., NIC Ser. 9, Forschungszentrum Jülich, 2002, pp. 479–492.
[25] D. Hilbert, Über die stetige Abbildung einer Linie auf ein Flächenstück, Math. Ann., 38 (1891), pp. 459–460. · JFM 23.0422.01
[26] D. A. Ibanez, E. S. Seol, C. W. Smith, and M. S. Shephard, Pumi: Parallel unstructured mesh infrastructure, ACM Trans. Math. Software, 42 (2016), 17, . · Zbl 1369.65155
[27] 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, . · Zbl 1323.65105
[28] Y. Ito, A. M. Shih, A. K. Erukala, B. K. Soni, A. Chernikov, N. P. Chrisochoides, and K. Nakahashi, Parallel unstructured mesh generation by an advancing front method, Math. Comput. Simul., 75 (2007), pp. 200–209. · Zbl 1124.65025
[29] Jülich Supercomputing Centre, JUQUEEN: IBM Blue Gene/Q supercomputer system at the Jülich supercomputing centre, J. Large-Scale Res. Facilities, 1 (2015), A1, .
[30] G. Karypis and V. Kumar, A parallel algorithm for multilevel graph partitioning and sparse matrix ordering, J. Parallel Distrib. Comput., 48 (1998), pp. 71–95.
[31] R. Maxwell, S. Kollet, S. Smith, C. Woodward, R. Falgout, I. Ferguson, N. Engdahl, L. Condon, B. Hector, S. Lopez, J. Gilbert, L. Bearup, J. Jefferson, C. Collins, I. de Graaf, C. Prubilick, C. Baldwin, W. Bosl, R. Hornung, and S. Ashby, ParFlow User’s Manual, Report GWMI 2016-01, Integrated Ground Water Modeling Center, 2016.
[32] O. Meister, K. Rahnema, and M. Bader, Parallel memory-efficient adaptive mesh refinement on structured triangular meshes with billions of grid cells, ACM Trans. Math. Software, 43 (2017), 19, . · Zbl 1396.65122
[33] M. Mirzadeh, A. Guittet, C. Burstedde, and F. Gibou, Parallel level-set methods on adaptive tree-based grids, J. Comput. Phys., 322 (2016), pp. 345–364. · Zbl 1352.65253
[34] W. F. Mitchell, A refinement-tree based partitioning method for dynamic load balancing with adaptively refined grids, J. Parallel Distrib. Comput., 67 (2007), pp. 417–429, . · Zbl 1115.68020
[35] G. M. Morton, A Computer Oriented Geodetic Data Base, and a New Technique in File Sequencing, Tech. report, IBM Ltd., 1966.
[36] C. D. Norton, G. Lyzenga, J. Parker, and R. E. Tisdale, Developing Parallel GeoFEST(P) Using the PYRAMID AMR Library, Tech. report, Jet Propulsion Laboratory, National Aeronautics and Space Administration, 2004.
[37] G. Peano, Sur une courbe, qui remplit toute une aire plane, Math. Ann., 36 (1890), pp. 157–160. · JFM 22.0405.01
[38] A. Pinar and C. Aykanat, Fast optimal load balancing algorithms for 1D partitioning, J. Parallel Distrib. Comput., 64 (2004), pp. 974–996, . · Zbl 1068.68038
[39] A. Rahimian, I. Lashuk, S. Veerapaneni, A. Chandramowlishwaran, D. Malhotra, L. Moon, R. Sampath, A. Shringarpure, J. Vetter, R. Vuduc, et al., Petascale direct numerical simulation of blood flow on 200k cores and heterogeneous architectures, in Proc. 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis, IEEE, 2010, pp. 1–11.
[40] M. Rasquin, C. Smith, K. Chitale, E. S. Seol, B. A. Matthews, J. L. Martin, O. Sahni, R. M. Loy, M. S. Shephard, and K. E. Jansen, Scalable implicit flow solver for realistic wing simulations with flow control, Comput. Sci. Eng., 16 (2014), pp. 13–21, .
[41] 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, . · Zbl 0437.65081
[42] H.-Y. Schive, Y.-C. Tsai, and T. Chiueh, Gamer: A graphic processing unit accelerated adaptive-mesh-refinement code for astrophysics, Astrophys. J. Suppl. Ser., 186 (2010), pp. 457–484.
[43] P. M. Selwood and M. Berzins, Parallel unstructured tetrahedral mesh adaptation: Algorithms, implementation and scalability, Concurrency Practice Experience, 11 (1999), pp. 863–884, .
[44] J. R. Shewchuk, Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator, in Applied Computational Geometry: Towards Geometric Engineering, M. C. Lin and D. Manocha, eds., Lecture Notes in Comput. Sci. 1148, Springer, 1996, pp. 203–222.
[45] H. Si, TetGen—A Quality Tetrahedral Mesh Generator and Three-Dimensional Delaunay Triangulator, Weierstraß Institute for Applied Analysis and Stochastics, Berlin, 2006.
[46] W. Sierpiński, Sur une nouvelle courbe continue qui remplit toute une aire plane, Bull. Acad. Sci. Cracovie Sér. A, 1912, pp. 462–478.
[47] W. Skamarock, J. Oliger, and R. L. Street, Adaptive grid refinement for numerical weather prediction, J. Comput. Phys., 80 (1989), pp. 27–60, . · Zbl 0661.76021
[48] C. W. Smith, M. Rasquin, D. Ibanez, K. E. Jansen, and M. S. Shephard, Application Specific Mesh Partition Improvement, Tech. report 2015-3, Rensselaer Polytechnic Institute, 2015, .
[49] D. A. Steinman, J. S. Milner, C. J. Norley, S. P. Lownie, and D. W. Holdsworth, Image-based computational simulation of flow dynamics in a giant intracranial aneurysm, Amer. J. Neuroradiology, 24 (2003), pp. 559–566.
[50] J. R. Stewart and H. C. Edwards, A framework approach for developing parallel adaptive multiphysics applications, Finite Elements Anal. Design, 40 (2004), pp. 1599–1617, .
[51] 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, . · Zbl 1186.68554
[52] T. Tu, D. R. O’Hallaron, and O. Ghattas, Scalable parallel octree meshing for TeraScale applications, in SC ’05: Proceedings of the 2005 ACM/IEEE Conference on Supercomputing, ACM/IEEE, 2005, .
[53] T. Weinzierl and M. Mehl, Peano—a traversal and storage scheme for octree-like adaptive Cartesian multiscale grids, SIAM J. Sci. Comput., 33 (2011), pp. 2732–2760, . · Zbl 1245.65169
[54] Y. Y\ilmaz, C. Özturan, O. Tosun, A. H. Özer, and S. Soner, Parallel Mesh Generation, Migration and Partitioning for the Elmer Application, Tech. report, PREMA-Partnership for Advanced Computing in Europe, 2010.
[55] M. Zhou, O. Sahni, K. D. Devine, M. S. Shephard, and K. E. Jansen, Controlling unstructured mesh partitions for massively parallel simulations, SIAM J. Sci. Comput., 32 (2010), pp. 3201–3227, . · Zbl 1221.65358
[56] G. Zumbusch, Parallel Multilevel Methods. Adaptive Mesh Refinement and Load Balancing, Vieweg+Teubner Verlag, 2003. · Zbl 1089.65127
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.