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Volumn 111, Issue 2, 2008, Pages 293-333

Analysis of FETI methods for multiscale PDEs

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EID: 56549129453     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-008-0186-2     Document Type: Article
Times cited : (59)

References (41)
  • 1
    • 47849116645 scopus 로고    scopus 로고
    • Towards a rigorously justified algebraic preconditioner for high-contrast diffusion problems
    • 4-6
    • B. Aksoylu I.G. Graham H. Klie R. Scheichl 2008 Towards a rigorously justified algebraic preconditioner for high-contrast diffusion problems Comput. Visual. Sci. 11 4-6 319 331
    • (2008) Comput. Visual. Sci. , vol.11 , pp. 319-331
    • Aksoylu, B.1    Graham, I.G.2    Klie, H.3    Scheichl, R.4
  • 2
    • 0000014842 scopus 로고
    • The multi-grid method for the diffusion equation with strongly discontinuous coefficients
    • 4
    • R.E. Alcouffe A. Brandt J.J.E. Dendy J.W. Painter 1981 The multi-grid method for the diffusion equation with strongly discontinuous coefficients SIAM J. Sci. Comput. 2 4 430 454
    • (1981) SIAM J. Sci. Comput. , vol.2 , pp. 430-454
    • Alcouffe, R.E.1    Brandt, A.2    Dendy, J.J.E.3    Painter, J.W.4
  • 3
    • 84968495074 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, IV
    • 187
    • J.H. Bramble J.E. Pasciak A.H. Schatz 1989 The construction of preconditioners for elliptic problems by substructuring, IV Math. Comp. 53 187 1 24
    • (1989) Math. Comp. , vol.53 , pp. 1-24
    • Bramble, J.H.1    Pasciak, J.E.2    Schatz, A.H.3
  • 4
    • 3042526643 scopus 로고    scopus 로고
    • Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework
    • S.C. Brenner 2003 Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework Electron. Trans. Numer. Anal. 16 165 185
    • (2003) Electron. Trans. Numer. Anal. , vol.16 , pp. 165-185
    • Brenner, S.C.1
  • 5
    • 0242641440 scopus 로고    scopus 로고
    • Lower bounds for three-dimensional non-overlapping domain decomposition algorithms
    • 3
    • S.C. Brenner Q. He 2003 Lower bounds for three-dimensional non-overlapping domain decomposition algorithms Numer. Math. 93 3 445 470
    • (2003) Numer. Math. , vol.93 , pp. 445-470
    • Brenner, S.C.1    He, Q.2
  • 7
    • 0013079987 scopus 로고    scopus 로고
    • Parallel computation of flow in heterogeneous media modelled by mixed finite elements
    • 2
    • K.A. Cliffe I.G. Graham R. Scheichl L. Stals 2000 Parallel computation of flow in heterogeneous media modelled by mixed finite elements J. Comput. Phys. 164 2 258 282
    • (2000) J. Comput. Phys. , vol.164 , pp. 258-282
    • Cliffe, K.A.1    Graham, I.G.2    Scheichl, R.3    Stals, L.4
  • 8
    • 1842564155 scopus 로고    scopus 로고
    • A preconditioner for substructuring based on constrained energy minimization
    • 1
    • C.R. Dohrmann 2003 A preconditioner for substructuring based on constrained energy minimization SIAM J. Sci. Comput. 25 1 246 258
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 246-258
    • Dohrmann, C.R.1
  • 9
    • 55349086225 scopus 로고    scopus 로고
    • Domain decomposition for less regular subdomains: Overlapping Schwarz in two dimensions
    • 4
    • C.R. Dohrmann A. Klawonn O.B. Widlund 2008 Domain decomposition for less regular subdomains: overlapping Schwarz in two dimensions SIAM J. Numer. Anal. 46 4 2153 2168
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 2153-2168
    • Dohrmann, C.R.1    Klawonn, A.2    Widlund, O.B.3
  • 10
    • 33845499690 scopus 로고    scopus 로고
    • Total FETI: An easier implementable variant of the FETI method for numerical solution of elliptic PDE
    • 12
    • Z. Dostál D. Horák R. Kučera 2006 Total FETI: an easier implementable variant of the FETI method for numerical solution of elliptic PDE Commun. Numer. Methods Eng. 22 12 1155 1162
    • (2006) Commun. Numer. Methods Eng. , vol.22 , pp. 1155-1162
    • Dostál, Z.1    Horák, D.2    Kučera, R.3
  • 12
    • 0035073391 scopus 로고    scopus 로고
    • FETI-DP: A dual-primal unified FETI method I: A faster alternative to the two-level FETI method
    • C. Farhat M. Lesoinne P. Le Tallec K. Pierson D. Rixen 2001 FETI-DP: A dual-primal unified FETI method I: a faster alternative to the two-level FETI method Int. J. Numer. Methods Eng. 50 1523 1544
    • (2001) Int. J. Numer. Methods Eng. , vol.50 , pp. 1523-1544
    • Farhat, C.1    Lesoinne, M.2    Le Tallec, P.3    Pierson, K.4    Rixen, D.5
  • 13
    • 0026239487 scopus 로고
    • A method of finite element tearing and interconnecting and its parallel solution algorithm
    • C. Farhat F.-X. Roux 1991 A method of finite element tearing and interconnecting and its parallel solution algorithm Int. J. Numer. Meth. Eng. 32 1205 1227
    • (1991) Int. J. Numer. Meth. Eng. , vol.32 , pp. 1205-1227
    • Farhat, C.1    Roux, F.-X.2
  • 14
    • 0033295349 scopus 로고    scopus 로고
    • Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients
    • 6
    • I.G. Graham M.J. Hagger 1999 Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients SIAM J. Sci. Comput. 20 6 2041 2066
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 2041-2066
    • Graham, I.G.1    Hagger, M.J.2
  • 15
  • 16
  • 17
    • 56549108512 scopus 로고    scopus 로고
    • Coefficient-explicit condition number bounds for overlapping additive Schwarz
    • Langer, U., Discacciati, M., Keyes, D.E., Widlund, O.B., Zulehner, W. (eds.) Springer, Berlin
    • Graham, I.G., Scheichl, R.: Coefficient-explicit condition number bounds for overlapping additive Schwarz. In: Langer, U., Discacciati, M., Keyes, D.E., Widlund, O.B., Zulehner, W. (eds.) Domain decomposition methods in science and engineering XVII. Lecture Notes in Computational Science and Engineering, vol. 60, pp. 365-372. Springer, Berlin (2008)
    • (2008) Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering , vol.60 , pp. 365-372
    • Graham, I.G.1    Scheichl, R.2
  • 19
    • 33751098480 scopus 로고    scopus 로고
    • Robust FETI-DP methods for heterogeneous three-dimensional elasticity problems
    • A. Klawonn O. Rheinbach 2007 Robust FETI-DP methods for heterogeneous three-dimensional elasticity problems Comput. Methods Appl. Mech. Eng. 196 1400 1414
    • (2007) Comput. Methods Appl. Mech. Eng. , vol.196 , pp. 1400-1414
    • Klawonn, A.1    Rheinbach, O.2
  • 20
    • 55349129284 scopus 로고    scopus 로고
    • An analysis of a FETI-DP algorithm on irregular subdomains in the plane
    • 5
    • A. Klawonn O. Rheinbach O.B. Widlund 2008 An analysis of a FETI-DP algorithm on irregular subdomains in the plane SIAM J. Numer. Anal. 46 5 2484 2504
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 2484-2504
    • Klawonn, A.1    Rheinbach, O.2    Widlund, O.B.3
  • 21
    • 0035526706 scopus 로고    scopus 로고
    • FETI and Neumann-Neumann iterative substructuring methods: Connections and new results
    • 1
    • A. Klawonn O.B. Widlund 2001 FETI and Neumann-Neumann iterative substructuring methods: connections and new results Comm. Pure Appl. Math. 54 1 57 90
    • (2001) Comm. Pure Appl. Math. , vol.54 , pp. 57-90
    • Klawonn, A.1    Widlund, O.B.2
  • 22
    • 0036556595 scopus 로고    scopus 로고
    • Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients
    • 1
    • A. Klawonn O.B. Widlund M. Dryja 2002 Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients SIAM J. Numer. Anal. 40 1 159 179
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 159-179
    • Klawonn, A.1    Widlund, O.B.2    Dryja, M.3
  • 23
    • 33845717162 scopus 로고    scopus 로고
    • Coupled finite and boundary element tearing and interconnecting solvers for non-linear potential problems
    • 12
    • U. Langer C. Pechstein 2006 Coupled finite and boundary element tearing and interconnecting solvers for non-linear potential problems ZAMM Z. Angew. Math. Mech. 86 12 915 931
    • (2006) ZAMM Z. Angew. Math. Mech. , vol.86 , pp. 915-931
    • Langer, U.1    Pechstein, C.2
  • 24
    • 0242287760 scopus 로고    scopus 로고
    • Convergence of a balancing domain decomposition by constraints and energy minimization
    • J. Mandel C.R. Dohrmann 2003 Convergence of a balancing domain decomposition by constraints and energy minimization Numer. Lin. Alg. Appl. 10 639 659
    • (2003) Numer. Lin. Alg. Appl. , vol.10 , pp. 639-659
    • Mandel, J.1    Dohrmann, C.R.2
  • 25
    • 19044366698 scopus 로고    scopus 로고
    • An algebraic theory for primal and dual substructuring methods by constraints
    • J. Mandel C.R. Dohrmann R. Tezaur 2005 An algebraic theory for primal and dual substructuring methods by constraints Appl. Numer. Math. 54 167 193
    • (2005) Appl. Numer. Math. , vol.54 , pp. 167-193
    • Mandel, J.1    Dohrmann, C.R.2    Tezaur, R.3
  • 26
    • 0030559707 scopus 로고    scopus 로고
    • Convergence of a substrucuring method with Lagrange multipliers
    • J. Mandel R. Tezaur 1996 Convergence of a substrucuring method with Lagrange multipliers Numer. Math. 73 473 487
    • (1996) Numer. Math. , vol.73 , pp. 473-487
    • Mandel, J.1    Tezaur, R.2
  • 27
    • 0035609885 scopus 로고    scopus 로고
    • On the convergence of a dual-primal substructuring method
    • J. Mandel R. Tezaur 2001 On the convergence of a dual-primal substructuring method Numer. Math. 88 543 558
    • (2001) Numer. Math. , vol.88 , pp. 543-558
    • Mandel, J.1    Tezaur, R.2
  • 29
    • 47849107946 scopus 로고    scopus 로고
    • Analysis of dual and dual-primal tearing and interconnecting methods in unbounded domains
    • SFB-Report 2007-15, SFB F013, Johannes Kepler University of Linz, August
    • Pechstein, C.: Analysis of dual and dual-primal tearing and interconnecting methods in unbounded domains. SFB-Report 2007-15, SFB. Numerical and Symbolic Scientific Computing. F013, Johannes Kepler University of Linz, August 2007. http://www.sfb013.uni-linz.ac.at/~sfb/reports/2007/pdf-files/ rep_07-15_pechstein.pdf
    • (2007) Numerical and Symbolic Scientific Computing
    • Pechstein, C.1
  • 30
    • 56549098399 scopus 로고    scopus 로고
    • Boundary element tearing and interconnecting methods in unbounded domains
    • (to appear)
    • Pechstein, C.: Boundary element tearing and interconnecting methods in unbounded domains. Appl. Num. Math. (2008, to appear)
    • (2008) Appl. Num. Math
    • Pechstein, C.1
  • 32
    • 0004334289 scopus 로고    scopus 로고
    • Preconditioning the FETI method for problems with intra- and inter-subdomain coefficientjumps
    • Bjørstad, P.E., Espedal, M., Keyes, D. (eds.)
    • Rixen, D., Farhat, C.: Preconditioning the FETI method for problems with intra- and inter-subdomain coefficient jumps. In: Bjørstad, P.E., Espedal, M., Keyes, D. (eds.) Ninth International Conference on Domain Decomposition Methods, pp. 472-479 (1997). http://www.ddm.org/DD9/Rixen.pdf
    • (1997) Ninth International Conference on Domain Decomposition Methods , pp. 472-479
    • Rixen, D.1    Farhat, C.2
  • 33
    • 0033079432 scopus 로고    scopus 로고
    • A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems
    • D. Rixen C. Farhat 1999 A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems Int. J. Numer. Methods Eng. 44 489 516
    • (1999) Int. J. Numer. Methods Eng. , vol.44 , pp. 489-516
    • Rixen, D.1    Farhat, C.2
  • 34
    • 0001326593 scopus 로고
    • Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG)
    • Paddon, D.J., Holstein, H. (eds.) Clarendon Press, Oxford
    • Ruge, J., Stüben, K.: Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG). In: Paddon, D.J., Holstein, H. (eds.) Multigrid Methods for integral and differential equations. IMA Conference Series, pp. 169-212. Clarendon Press, Oxford (1985)
    • (1985) Multigrid Methods for Integral and Differential Equations. IMA Conference Series , pp. 169-212
    • Ruge, J.1    Stüben, K.2
  • 35
    • 0031519837 scopus 로고    scopus 로고
    • Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements
    • 3
    • M. Sarkis 1997 Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements Numer. Math. 77 3 383 406
    • (1997) Numer. Math. , vol.77 , pp. 383-406
    • Sarkis, M.1
  • 36
    • 34548454586 scopus 로고    scopus 로고
    • Additive Schwarz and aggregation-based coarsening for elliptic problems with highly variable coefficients
    • 4
    • R. Scheichl E. Vainikko 2007 Additive Schwarz and aggregation-based coarsening for elliptic problems with highly variable coefficients Computing 80 4 319 343
    • (2007) Computing , vol.80 , pp. 319-343
    • Scheichl, R.1    Vainikko, E.2
  • 37
    • 84966200902 scopus 로고
    • Finite element interpolation of non-smooth functions satisfying boundary conditions
    • L.R. Scott S. Zhang 1990 Finite element interpolation of non-smooth functions satisfying boundary conditions Math. Comp. 54 483 493
    • (1990) Math. Comp. , vol.54 , pp. 483-493
    • Scott, L.R.1    Zhang, S.2
  • 39
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid by smoothed aggregation for 2nd and 4th order elliptic problems
    • 3
    • P. Vanek J. Mandel M. Brezina 1996 Algebraic multigrid by smoothed aggregation for 2nd and 4th order elliptic problems Computing 56 3 179 196
    • (1996) Computing , vol.56 , pp. 179-196
    • Vanek, P.1    Mandel, J.2    Brezina, M.3
  • 40
    • 47849119733 scopus 로고    scopus 로고
    • Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients
    • Technical Report AM311. Department of Mathematics, Pennsylvania (to appear)
    • Xu, J., Zhu, Y.: Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients. Math. Mod. Meth. Appl. Sci. Technical Report AM311. Department of Mathematics, Pennsylvania (2007, to appear)
    • (2007) Math. Mod. Meth. Appl. Sci
    • Xu, J.1    Zhu, Y.2
  • 41
    • 14844322265 scopus 로고    scopus 로고
    • On Friedrichs-Poincaré-type inequalities
    • W. Zheng H. Qi 2005 On Friedrichs-Poincaré-type inequalities J. Math. Anal. Appl 304 542 551
    • (2005) J. Math. Anal. Appl , vol.304 , pp. 542-551
    • Zheng, W.1    Qi, H.2


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