Ultrascalable 619 Implicit Finite Element Analyses in Solid Mechanics with over a Half a Billion Degrees of 620 ,
, Proceedings of the 2004 ACM/IEEE Conference on Supercomputing, SC '04, vol.621, 2004.
Parallel Multigrid Solver for 3D Unstructured Finite El-623 ement Problems, Proceedings of the 1999 ACM/IEEE Conference on Supercomputing, 624 SC '99, ACM, 1999. ,
A class of efficient locally constructed preconditioners based on 626 coarse spaces, SIAM Journal on Matrix Analysis and Applications, vol.40, pp.66-91, 2019. ,
Multilevel balancing domain decomposition at extreme 628 scales, SIAM Journal on Scientific Computing, vol.38, pp.22-52, 2016. ,
, Does SHEM for Additive, p.630
, Schwarz Work Better than Predicted by Its Condition Number Estimate?, International 631 Conference on Domain Decomposition Methods, pp.129-137, 2017.
Parallel algebraic multilevel Schwarz precon-633 ditioners for a class of elliptic PDE systems, Computing and Visualization in Science, vol.16, pp.1-14, 2013. ,
Algebraic Multigrid Based on Element Interpolation (AMGe), SIAM Journal 637 on Scientific Computing, vol.22, pp.1570-1592, 2001. ,
A restricted additive Schwarz preconditioner for general sparse 639 linear systems, SIAM Journal on Scientific Computing, vol.21, pp.792-797, 1999. ,
Domain decomposition algorithms, Acta Numerica, vol.3, pp.61-143, 1994. ,
, , p.643
, Spectral AMGe (?AMGe), vol.25, pp.1-26, 2003.
PT-SCOTCH: A tool for efficient parallel graph ordering, p.646 ,
URL : https://hal.archives-ouvertes.fr/hal-00410427
, Parallel Matrix Algorithms and Applications, vol.34, pp.318-331, 2008.
An introduction to domain decomposition methods, Algorithms, theory, and parallel 649 implementation, 2015. ,
URL : https://hal.archives-ouvertes.fr/cel-01100932
On the abstract theory of additive and multiplicative Schwarz 651 algorithms, Numerische Mathematik, vol.70, pp.163-180, 1995. ,
New development in FreeFem++, Journal of Numerical Mathematics, vol.20, pp.251-266, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-01476313
A Three-Level Extension of the 655 GDSW Overlapping Schwarz Preconditioner in Three Dimensions, technical report, Uni-656 versität zu Köln, 2018. ,
BoomerAMG: A parallel algebraic multigrid solver and pre-658 conditioner, Developments and 659 Trends in Iterative Methods for Large Systems of Equations, vol.41, pp.155-177, 2002. ,
, , 2019.
Application to high-performance computing, the-662 ses, 2014. ,
Scalable domain decomposition pre-664 conditioners for heterogeneous elliptic problems, Proceedings of the International Con-665 ference on High Performance Computing, Networking, Storage and Analysis, SC13, ACM, vol.666, 2013. ,
AMGe Based on Element Agglomeration, SIAM Journal on 668 Scientific Computing, vol.23, pp.109-133, 2001. ,
Upscaling of mixed finite 670 element discretization problems by the spectral AMGe method, SIAM Journal on Scientific 671 Computing, vol.38, pp.2912-2933, 2016. ,
Multilevel k-way partitioning scheme for irregular graphs, Journal 673 of Parallel and Distributed Computing, vol.48, pp.96-129, 1998. ,
A highly scalable multilevel Schwarz method with boundary geometry 675 preserving coarse spaces for 3D elasticity problems on domains with complex geometry, 676 SIAM Journal on Scientific Computing, vol.38, pp.73-95, 2016. ,
ARPACK users' guide: solution of large-scale 678 eigenvalue problems with implicitly restarted Arnoldi methods, Society for Industrial 679 and Applied Mathematics, vol.6, 1998. ,
Multispace and multilevel BDDC, Comput-681 ing, vol.83, pp.55-85, 2008. ,
DOI : 10.1007/s00607-008-0014-7
URL : http://arxiv.org/pdf/0712.3977
Tuning 683 the coarse space construction in a spectral AMG solver, International Conference on Computational Science, vol.80, pp.6-8, 2016. ,
DOI : 10.1016/j.procs.2016.05.311
URL : https://doi.org/10.1016/j.procs.2016.05.311
Mesh theorems of traces, normalizations of function traces and their 687 inversions, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.6, pp.688-689, 1991. ,
An aggregation-based algebraic multigrid method, Electronic Transactions on Nu-692 merical Analysis, vol.37, pp.123-146, 2010. ,
A Flexible Inner-Outer Preconditioned GMRES Algorithm, SIAM Journal on Sci-694 entific Computing, vol.14, pp.461-469, 1993. ,
DOI : 10.1137/0914028
, Iterative Methods for Sparse Linear Systems, Society for Industrial and Applied 696 Mathematics, 2003.
DOI : 10.1137/1.9780898718003
Abstract 698 robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps, p.699 ,
, Numerische Mathematik, vol.126, pp.741-770, 2014.
, Domain Decomposition Methods -Algorithms and Theory, p.701
DOI : 10.1007/b137868
, Springer Series in Computational Mathematics, p.702, 2005.
, Theory of Multilevel Methods, p.703, 1989.
PCBDDC: A class of robust dual-primal methods in PETSc, SIAM Journal on 704 Scientific Computing, vol.38, pp.282-306, 2016. ,