, We proved that the coarse space of GenEO corresponds to a special case of the SPSD splitting. We discussed different types of ALS and suggested a simple method to approximate a valuable coarse space. For matrices issued from the conviction-diffusion problem, the simple method that we proposed gave very interesting results
Achdou and F. Nataf. Low frequency tangential filtering decomposition. Numerical Linear Algebra with Applications, pp.129-147, 2007. ,
Domain decomposition algorithms, Acta Numerica, vol.3, pp.61-143, 1994. ,
An introduction to domain decomposition methods, Algorithms, theory, and parallel implementation, 2015. ,
On the abstract theory of additive and multiplicative Schwarz algorithms, Numerische Mathematik, vol.70, issue.2, pp.163-180, 1995. ,
DOI : 10.1007/s002110050115
Enlarged Krylov Subspace Conjugate Gradient Methods for Reducing Communication, SIAM Journal on Matrix Analysis and Applications, vol.37, issue.2, 2014. ,
DOI : 10.1137/140989492
URL : https://hal.archives-ouvertes.fr/hal-01065985
Robust algebraic Schur complement preconditioners based on low rank corrections, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01017448
New development in freefem++, Journal of Numerical Mathematics, vol.20, issue.3-4, pp.251-265, 2012. ,
DOI : 10.1515/jnum-2012-0013
URL : https://hal.archives-ouvertes.fr/hal-01476313
Methods of conjugate gradients for solving linear systems, Journal of Research of the National Bureau of Standards, vol.49, issue.6, pp.409-436, 1952. ,
DOI : 10.6028/jres.049.044
Theory of Multilevel Methods, 1989. ,
Multilevelk-way Partitioning Scheme for Irregular Graphs, Journal of Parallel and Distributed Computing, vol.48, issue.1, pp.96-129, 1998. ,
DOI : 10.1006/jpdc.1997.1404
Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners, SIAM Journal on Matrix Analysis and Applications, vol.38, issue.3, pp.807-828, 2017. ,
DOI : 10.1137/16M110486X
A Coarse Space Construction Based on Local Dirichlet-to-Neumann Maps, SIAM Journal on Scientific Computing, vol.33, issue.4, pp.1623-1642, 2011. ,
DOI : 10.1137/100796376
URL : https://hal.archives-ouvertes.fr/hal-00491919
Mesh theorems on traces, normalizations of function traces and their inversion, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.6, issue.3, pp.1-25, 1991. ,
DOI : 10.1515/rnam.1991.6.3.223
Decomposition and fictitious domains methods for elliptic boundary value problems, 1992. ,
Modified tangential frequency filtering decomposition and its fourier analysis, Numerische Mathematik, vol.76, issue.1, pp.123-148, 2010. ,
DOI : 10.1007/978-3-642-05156-2
URL : https://hal.archives-ouvertes.fr/inria-00324378
Iterative Methods for Sparse Linear Systems Abstract robust coarse spaces for systems of pdes via generalized eigenproblems in the overlaps, Society for Industrial and Applied Mathematics Numerische Mathematik, vol.17, issue.1264, pp.741-770, 2003. ,
Automatic spectral coarse spaces for robust finite element tearing and interconnecting and balanced domain decomposition???algorithms, International Journal for Numerical Methods in Engineering, vol.54, issue.2, pp.95953-990 ,
DOI : 10.1016/j.apnum.2004.09.022
A Krylov--Schur Algorithm for Large Eigenproblems, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.3, pp.601-614, 2002. ,
DOI : 10.1137/S0895479800371529
Comparison of Two-Level Preconditioners Derived from??Deflation, Domain Decomposition and Multigrid Methods, Journal of Scientific Computing, vol.34, issue.3, pp.340-370, 2009. ,
DOI : 10.1007/b137868
URL : http://neumann.math.tufts.edu/~scott/research/defMG.pdf
Domain Decomposition Methods -Algorithms and Theory, 2005. ,
DOI : 10.1007/b137868
, Table des matières 1 Introduction 3
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, , p.11
, Algebraic local SPSD splitting of an SPD matrix 13
, 4 Algebraic stable decomposition with
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, 5 Numerical experiments 21
, Inria