메뉴 건너뛰기




Volumn 46, Issue 5, 2012, Pages 1175-1199

Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms

Author keywords

Brinkman's problem; Domain decomposition; High contrast; Multiscale problems; Robust additive Schwarz preconditioner; Spectral coarse spaces

Indexed keywords

ADDITIVES; DOMAIN DECOMPOSITION METHODS; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; MESH GENERATION; NUMBER THEORY; POROUS MATERIALS;

EID: 84861912028     PISSN: 28227840     EISSN: 28047214     Source Type: Journal    
DOI: 10.1051/m2an/2011073     Document Type: Article
Times cited : (129)

References (32)
  • 1
    • 84861909902 scopus 로고
    • Sobolev spaces 1st edition
    • Academic Press, Inc.
    • R.A. Adams, Sobolev Spaces, 1st edition. Pure Appl. Math. Academic Press, Inc. (1978).
    • (1978) Pure Appl. Math.
    • Adams, R.A.1
  • 2
    • 34548277425 scopus 로고    scopus 로고
    • Deal.II-a general purpose object oriented finite element library
    • W. Bangerth, R. Hartmann and G. Kanschat, deal.II-a general purpose object oriented finite element library. ACM Trans. Math. Softw. 33 (2007) 241-2427.
    • (2007) ACM Trans. Math. Softw. , vol.33 , pp. 241-2427
    • Bangerth, W.1    Hartmann, R.2    Kanschat, G.3
  • 3
    • 0004219794 scopus 로고
    • 1st edition. Longman Scientific & Technical Essex
    • J.H. Bramble, Multigrid Methods, 1st edition. Longman Scientific & Technical, Essex (1993).
    • (1993) Multigrid Methods
    • Bramble, J.H.1
  • 5
    • 34250582623 scopus 로고
    • A calculation of the viscouse force exerted by a flowing fluid on a dense swarm of particles
    • H.C. Brinkman, A calculation of the viscouse force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1 (1947) 27-34.
    • (1947) Appl. Sci. Res. , vol.A1 , pp. 27-34
    • Brinkman, H.C.1
  • 7
    • 0030556926 scopus 로고    scopus 로고
    • Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions
    • M. Dryja, M.V. Sarkis and O.B. Widlund, Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions. Numer. Math. 72 (1996) 313-348.
    • (1996) Numer. Math. , vol.72 , pp. 313-348
    • Dryja, M.1    Sarkis, M.V.2    Widlund, O.B.3
  • 8
    • 79251479900 scopus 로고    scopus 로고
    • Multiscale finite element methods, Theory and applications. Surveys and Tutorials
    • Springer New York
    • Y. Efendiev and T.Y. Hou, Multiscale finite element methods, Theory and applications. Surveys and Tutorials. in Appl. Math. Sci. Springer, New York 4 (2009).
    • (2009) Appl. Math. Sci. , pp. 4
    • Efendiev, Y.1    Hou, T.Y.2
  • 9
    • 68149100382 scopus 로고    scopus 로고
    • A simplified method for upscaling composite materials with high contrast of the conductivity
    • R.E. Ewing, O. Iliev, R.D. Lazarov, I. Rybak and J. Willems, A simplified method for upscaling composite materials with high contrast of the conductivity. SIAM J. Sci. Comput. 31 (2009) 2568-2586.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 2568-2586
    • Ewing, R.E.1    Iliev, O.2    Lazarov, R.D.3    Rybak, I.4    Willems, J.5
  • 10
    • 77956746765 scopus 로고    scopus 로고
    • Domain decomposition preconditioners for multiscale flows in high-contrast media
    • J. Galvis and Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high-contrast media. Multiscale Model. Simul. 8 (2010) 1461-1483.
    • (2010) Multiscale Model. Simul. , vol.8 , pp. 1461-1483
    • Galvis, J.1    Efendiev, Y.2
  • 11
    • 78650578559 scopus 로고    scopus 로고
    • Domain decomposition preconditioners for multiscale flows in high contrast media : reduced dimension coarse spaces
    • J. Galvis and Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high contrast media : reduced dimension coarse spaces. Multiscale Model. Simul. 8 (2010) 1621-1644.
    • (2010) Multiscale Model. Simul. , vol.8 , pp. 1621-1644
    • Galvis, J.1    Efendiev, Y.2
  • 12
  • 13
    • 34249880401 scopus 로고    scopus 로고
    • Domain decomposition for multiscale PDEs
    • I.G. Graham, P.O. Lechner and R. Scheichl, Domain decomposition for multiscale PDEs. Numer. Math. 106 (2007) 589-626.
    • (2007) Numer. Math. , vol.106 , pp. 589-626
    • Graham, I.G.1    Lechner, P.O.2    Scheichl, R.3
  • 14
    • 0041010250 scopus 로고
    • Elliptic problems in nonsmooth domains, monographs and studies in mathematics
    • Boston, MA
    • P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics. Pitman Advanced Publishing Program, Boston, MA 24 (1985).
    • (1985) Pitman Advanced Publishing Program , pp. 24
    • Grisvard, P.1
  • 15
    • 0003815501 scopus 로고    scopus 로고
    • Multi-grid methods and applications
    • 2nd edition Springer Series Berlin
    • W. Hackbusch, Multi-Grid Methods and Applications, 2nd edition. Springer Series in Comput. Math. Springer, Berlin (2003).
    • (2003) Comput. Math. Springer
    • Hackbusch, W.1
  • 16
    • 0039982148 scopus 로고    scopus 로고
    • Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
    • T.Y. Hou, X.-H. Wu and Z. Cai, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comp. 68 (1999) 913-943.
    • (1999) Math. Comp. , vol.68 , pp. 913-943
    • Hou, T.Y.1    Wu, X.-H.2    Cai, Z.3
  • 17
    • 0036556595 scopus 로고    scopus 로고
    • Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients
    • SIAM J electronic
    • A. Klawonn, O.B. Widlund and M. Dryja, Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. SIAM J. Numer. Anal. 40 (2002) 159-179 (electronic).
    • (2002) Numer. Anal. , vol.40 , pp. 159-179
    • Klawonn, A.1    Widlund, O.B.2    Dryja, M.3
  • 18
    • 0030518529 scopus 로고    scopus 로고
    • Balancing domain decomposition for problems with large jumps in coefficients
    • J. Mandel and M. Brezina, Balancing domain decomposition for problems with large jumps in coefficients. Math. Comp. 65 (1996) 1387-1401.
    • (1996) Math. Comp. , vol.65 , pp. 1387-1401
    • Mandel, J.1    Brezina, M.2
  • 19
    • 78651555398 scopus 로고    scopus 로고
    • Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
    • Springer Berlin Heidelberg
    • T.P.A. Mathew, Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations. Lect. Notes Comput. Sci. Eng. Springer, Berlin Heidelberg (2008).
    • (2008) Lect. Notes Comput. Sci. Eng.
    • Mathew, T.P.A.1
  • 20
    • 84861731976 scopus 로고
    • Mesh theorems on traces, normalizations of function traces and their inversion
    • S.V. Nepomnyaschikh, Mesh theorems on traces, normalizations of function traces and their inversion. Sov. J. Numer. Anal. Math. Modelling 6 (1991) 151-168.
    • (1991) Sov. J. Numer. Anal. Math. Modelling , vol.6 , pp. 151-168
    • Nepomnyaschikh, S.V.1
  • 21
    • 56549129453 scopus 로고    scopus 로고
    • Analysis of FETI methods for multiscale PDEs
    • C. Pechstein and R. Scheichl, Analysis of FETI methods for multiscale PDEs. Numer. Math. 111 (2008) 293-333.
    • (2008) Numer. Math. , vol.111 , pp. 293-333
    • Pechstein, C.1    Scheichl, R.2
  • 22
    • 79958288607 scopus 로고    scopus 로고
    • Analysis of FETI methods for multiscale PDEs-Part II : interface variation
    • C. Pechstein and R. Scheichl, Analysis of FETI methods for multiscale PDEs-Part II : interface variation. To appear in Numer. Math.
    • Numer. Math
    • Pechstein, C.1    Scheichl, R.2
  • 25
    • 0031519837 scopus 로고    scopus 로고
    • Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements
    • M.V. Sarkis, Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements. Numer. Math. 77 (1997) 383-406.
    • (1997) Numer. Math. , vol.77 , pp. 383-406
    • Sarkis, M.V.1
  • 28
    • 70349608544 scopus 로고    scopus 로고
    • Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs
    • J. Van Lent, R. Scheichl and I.G. Graham, Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs. Numer. Linear Algebra Appl. 16 (2009) 775-799.
    • (2009) Numer. Linear Algebra Appl. , vol.16 , pp. 775-799
    • Van Lent, J.1    Scheichl, R.2    Graham, I.G.3
  • 30
    • 46949090921 scopus 로고    scopus 로고
    • New finite element methods in computational fluid dynamics by H(div) elements
    • J. Wang and X. Ye, New finite element methods in computational fluid dynamics by H(div) elements. SIAM J. Numer. Anal. 45 (2007) 1269-1286.
    • (2007) SIAM J. Numer. Anal. , vol.45 , pp. 1269-1286
    • Wang, J.1    Ye, X.2
  • 32
    • 33750160340 scopus 로고    scopus 로고
    • On an energy minimizing basis for algebraic multigrid methods
    • J. Xu and L.T. Zikatanov, On an energy minimizing basis for algebraic multigrid methods. Comput. Visualisation Sci. 7 (2004) 121-127.
    • (2004) Comput. Visualisation Sci. , vol.7 , pp. 121-127
    • Xu, J.1    Zikatanov, L.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.