zbMATH — the first resource for mathematics

An asynchronous incomplete block LU preconditioner for computational fluid dynamics on unstructured grids. (English) Zbl 07303435
65F08 Preconditioners for iterative methods
65Y05 Parallel numerical computation
Full Text: DOI
[1] E. Lindholm, J. Nickolls, S. Oberman, and J. Montrym, NVIDIA Tesla: A unified graphics and computing architecture, IEEE Micro, 28 (2008), pp. 39-55.
[2] A. Sodani, R. Gramunt, J. Corbal, H.-S. Kim, K. Vined, S. Chinthamani, S. Hutsell, R. Agarwal, and Y.-C. Liu, Knights Landing: Second-generation Intel Xeon Phi product, IEEE Micro, 36 (2016).
[3] F. D. Witherden, A. M. Farrington, and P. E. Vincent, PyFR: An open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach, Comput. Phys. Commun., 185 (2014), pp. 3028-3040. · Zbl 1348.65005
[4] Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, Philadelphia, 2003. · Zbl 1031.65046
[5] B. F. Smith, P. E. Bjørstad, and W. D. Gropp, Domain Decomposition - Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, Cambridge, 1996. · Zbl 0857.65126
[6] S. Fujino and S. Doi, Optimizing multicolor ICCG methods on some vector computers, in Iterative Methods in Linear Algebra, R. Beauwens and P. de Groen, eds., North-Holland, Amsterdam, 1992, pp. 349-358. · Zbl 0785.65028
[7] M. Benzi, W. Joubert, and G. Mateescu, Numerical experiments with parallel orderings for ILU preconditioners, Electron. Trans. Numer. Anal., 8 (1999), pp. 88-114. · Zbl 0923.65012
[8] M. T. Nguyen, P. Castonguay, and E. Laurendeau, GPU parallelization of multigrid RANS solver for three-dimensional aerodynamic simulations on multiblock grids, J. Supercomput., 75 (2019), pp. 2562-2583.
[9] M. Naumov, Parallel Sparse Triangular Systems in the Preconditioned Iterative Methods on the GPU, Technical report NVR-2011-001, NVIDIA, 2011.
[10] M. Naumov, Parallel Incomplete-LU and Cholesky Factorization in the Preconditioned Iterative Methods on the GPU, Technical report NVR-2012-003, NVIDIA, 2012.
[11] L. Luo, J.R. Edwards, H. Luo, and F. Mueller, A fine-grained block ILU scheme on regular structures for GPGPUs, Comput. & Fluids, 119 (2015), pp. 149-161. · Zbl 1390.65139
[12] B. Suchoski, C. Severn, M. Shantharam, and P. Raghavan, Adapting sparse triangular solution to GPUs, in 41st International Conference on Parallel Processing, Workshops, IEEE, Piscataway, NJ, 2012, pp. 140-148.
[13] F. L. Alvarado and R. Schreiber, Optimal parallel solution of sparse triangular systems, SIAM J. Sci. Comput., 14 (1993), pp. 446-460. · Zbl 0774.65011
[14] D. Chazan and W. Miranker, Chaotic relaxation, Linear Algebra Appl., 2 (1969), pp. 199-222. · Zbl 0225.65043
[15] A. Frommer and D. B. Szyld, On asynchronous iterations, J. Comput. Appl. Math., 123 (2000), pp. 201-216. · Zbl 0967.65066
[16] E. Chow and A. Patel, Fine-grained parallel incomplete LU factorization, SIAM J. Sci. Comput., 37 (2015), pp. C169-C193. · Zbl 1320.65048
[17] M. N. Anwar and M. N. El Tarazi, Asynchronous algorithms for Poisson’s equation with nonlinear boundary conditions, Computing, 34 (1985), pp. 155-168. · Zbl 0555.65074
[18] J. N. Hawkes, S. R. Turnock, G. Vaz, A. B. Phillips, and S. J. Cox, Chaotic linear-system solvers for unsteady CFD, in VI International Conference on Computational Methods in Marine Engineering MARINE, F. Salvatore, R. Broglia, and R. Muscari, eds., CIMNE, Barcelona, 2015, pp. 955-962.
[19] A. Kashi, S. Vangara, S. Nadarajah, and P. Castonguay, Asynchronous fine-grain parallel implicit smoother in multigrid solvers for compressible flow, Comput. & Fluids, 198 (2019), 104255. · Zbl 07157282
[20] E. Chow, H. Anzt, J. Scott, and J. Dongarra, Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning, J. Parallel Distrib. Comput., 119 (2018), pp. 219-230.
[21] Y. Saad, A flexible inner-outer preconditioned GMRES algorithm, SIAM J. Sci. Comput., 14 (1993), pp. 461-469. · Zbl 0780.65022
[22] J. Blazek, Computational Fluid Dynamics - Principles and Applications, 3rd ed., Elsevier, Amsterdam, 2015. · Zbl 1308.76001
[23] J. C. Strikwerda, A convergence theorem for chaotic asynchronous relaxation, Linear Algebra Appl., 253 (1997), pp. 15-24. · Zbl 0872.65029
[24] G. M. Baudet, Asynchronous iterative methods for multiprocessors, J. ACM, 25 (1978), pp. 226-244. · Zbl 0372.68015
[25] H. Anzt, E. Chow, and J. Dongarra, Iterative Sparse Triangular Solves for Preconditioning, in Euro-Par 2015: Parallel Processing, Springer, Berlin, 2015, pp. 650-661.
[26] OpenMP Architecture Review Board, OpenMP Application Programming Interface, 4.5 ed., 2015.
[27] H. Anzt, S. Tomov, J. Dongarra, and V. Heuveline, A block-asynchronous relaxation method for graphics processing units, J. Parallel Distrib. Comput., 73 (2013), pp. 1613-1626.
[28] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970. · Zbl 0241.65046
[29] E. Cuthill and J. McKee, Reducing the bandwidth of sparse symmetric matrices, in Proceedings of the 24th National Conference, New York, 1969, Association for Computing Machinery, New York, pp. 157-172.
[30] A. George and J. W. Liu, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981. · Zbl 0516.65010
[31] A. George, An automatic one-way dissection algorithm for irregular finite element problems, SIAM J. Numer. Anal., 17 (1980), pp. 740-751. · Zbl 0467.65057
[32] 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, D. A. May, L. Curfman McInnes, K. Rupp, B. F. Smith, S. Zampini, H. Zhang, and H. Zhang, PETSc, http://www.mcs.anl.gov/petsc (2017).
[33] M. J. Wright, G. V. Candler, and D. Bose, Data-parallel line relaxation method for the Navier-Stokes equations, AIAA Journal, 36 (1998), pp. 1603-1609.
[34] R. Ramamurti and R. Löhner, A parallel implicit incompressible flow solver using unstructured meshes, Computers & Fluids, 25 (1996), pp. 119-132. · Zbl 0866.76046
[35] D. J. Mavriplis, Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes, J. Comput. Phys., 145 (1998), pp. 141-165. · Zbl 0926.76066
[36] 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, D. A. May, L. Curfman McInnes, K. Rupp, P. Sanan, B. F. Smith, S. Zampini, H. Zhang, and H.g Zhang, PETSc Users Manual, Technical report ANL-95/11 - Revision 3.8, Argonne National Laboratory, Argonne, IL, 2017.
[37] Eigen v3, http://eigen.tuxfamily.org, 2010.
[38] A. Kashi, Asynchronous Fine-grain Parallel Iterative Solvers for Computational Fluid Dynamics, Ph.D. thesis, McGill University, Montreal, 2020.
[39] J. D. McCalpin, Memory bandwidth and machine balance in current high performance computers, in IEEE Comput. Soc. Tech. Committee in Comput. Archit. (TCCA) Newsletter, (1995), pp. 19-25.
[40] T. D. Economon, F. Palacios, S. R. Copeland, T. W. Lukaczyk, and J. J. Alonso, SU2: An open-source suite for multiphysics simulation and design, AIAA Journal, 54 (2016), pp. 828-846.
[41] SU2 Test Cases Repository, https://github.com/su2code/TestCases.git.
[42] H. Anzt, E. Chow, and J. Dongarra, ParILUT-a new parallel threshold ILU factorization, SIAM J. Sci. Comput., 40 (2018), pp. C503-C519. · Zbl 1391.65055
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.