메뉴 건너뛰기




Volumn 69, Issue 2, 2007, Pages 284-307

Inexact FETI-DP methods

Author keywords

Algebraic multigrid; Domain decomposition; Elasticity; Elliptic systems; FETI; Finite elements; Inexact; Lagrange multipliers; Multilevel methods; Parallel computing; Preconditioners

Indexed keywords

ALGEBRA; ALGORITHMS; ELASTICITY; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; PARALLEL PROCESSING SYSTEMS;

EID: 33846047406     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1758     Document Type: Article
Times cited : (70)

References (53)
  • 3
    • 20044366501 scopus 로고    scopus 로고
    • Dual-primal FETI methods for linear elasticity
    • Technical Report 2004-855, Courant Institute of Mathematical Sciences, New York University, New York, U.S.A., September
    • Klawonn A, Widlund OB. Dual-primal FETI methods for linear elasticity. Technical Report 2004-855, Courant Institute of Mathematical Sciences, New York University, New York, U.S.A., September 2004.
    • (2004)
    • Klawonn, A.1    Widlund, O.B.2
  • 4
    • 85140870437 scopus 로고    scopus 로고
    • A parallel implementation of dual-primal FETI methods for three dimensional linear elasticity using a transformation of basis
    • in press
    • Klawonn A, Rheinbach O. A parallel implementation of dual-primal FETI methods for three dimensional linear elasticity using a transformation of basis. SIAM Journal on Scientific Computing, in press.
    • SIAM Journal on Scientific Computing
    • Klawonn, A.1    Rheinbach, O.2
  • 5
    • 0026239487 scopus 로고
    • A method of Finite Element Tearing and Interconnecting and its parallel solution algorithm
    • Farhat C, Roux F-X. A method of Finite Element Tearing and Interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering 1991; 32:1205-1227.
    • (1991) International Journal for Numerical Methods in Engineering , vol.32 , pp. 1205-1227
    • Farhat, C.1    Roux, F.-X.2
  • 6
    • 0028449824 scopus 로고
    • Implicit parallel processing in structural mechanics
    • In Tinsley Oden J (ed.). North-Holland: Amsterdam
    • Farhat C, Roux F-X. Implicit parallel processing in structural mechanics. In Computational Mechanics Advances, Tinsley Oden J (ed.). vol. 2(1). North-Holland: Amsterdam, 1994; 1-124.
    • (1994) Computational Mechanics Advances , vol.2 , Issue.1 , pp. 1-124
    • Farhat, C.1    Roux, F.-X.2
  • 8
    • 0032022379 scopus 로고    scopus 로고
    • The two-level FETI method for static and dynamic plate problems - Part I: An optimal iterative solver for biharmonic systems
    • Farhat C, Mandel J. The two-level FETI method for static and dynamic plate problems - Part I: An optimal iterative solver for biharmonic systems. Computer Methods in Applied Mechanics and Engineering 1998; 155:129-152.
    • (1998) Computer Methods in Applied Mechanics and Engineering , vol.155 , pp. 129-152
    • Farhat, C.1    Mandel, J.2
  • 9
    • 0033878506 scopus 로고    scopus 로고
    • The second generation of FETI methods and their application to the parallel solution of large-scale linear and geometrically nonlinear structural analysis problems
    • Farhat C, Pierson KH, Lesoinne M. The second generation of FETI methods and their application to the parallel solution of large-scale linear and geometrically nonlinear structural analysis problems. Computer Methods in Applied Mechanics and Engineering 2000; 184:333-374.
    • (2000) Computer Methods in Applied Mechanics and Engineering , vol.184 , pp. 333-374
    • Farhat, C.1    Pierson, K.H.2    Lesoinne, M.3
  • 10
    • 33846119232 scopus 로고    scopus 로고
    • A matrix description for the domain decomposition methods of the FETI family
    • In Bathe K-J (ed.). Elsevier: Amsterdam
    • Rixen D, Tallec PL, Klawonn A. A matrix description for the domain decomposition methods of the FETI family. In First MIT Conference on Computational Fluid and Solid Mechanics, Bathe K-J (ed.). Elsevier: Amsterdam, 2001: 1636-1639.
    • (2001) First MIT Conference on Computational Fluid and Solid Mechanics , pp. 1636-1639
    • Rixen, D.1    Tallec, P.L.2    Klawonn, A.3
  • 11
    • 0034890938 scopus 로고    scopus 로고
    • A domain decomposition method with Lagrange multipliers and inexact solvers for linear elasticity
    • Klawonn A, Widlund OB. A domain decomposition method with Lagrange multipliers and inexact solvers for linear elasticity. SIAM Journal on Scientific Computing 2000; 22(4):1199-1219.
    • (2000) SIAM Journal on Scientific Computing , vol.22 , Issue.4 , pp. 1199-1219
    • Klawonn, A.1    Widlund, O.B.2
  • 12
    • 84966214346 scopus 로고
    • A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems
    • Bramble JH, Pasciak JE. A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems. Mathematics of Computation 1988; 50(181):1-17.
    • (1988) Mathematics of Computation , vol.50 , Issue.181 , pp. 1-17
    • Bramble, J.H.1    Pasciak, J.E.2
  • 13
    • 11744250187 scopus 로고    scopus 로고
    • Block-triangular preconditioners for saddle point problems with a penalty term
    • Klawonn A. Block-triangular preconditioners for saddle point problems with a penalty term. SIAM Journal on Scientific Computing 1998; 19(1):172-184.
    • (1998) SIAM Journal on Scientific Computing , vol.19 , Issue.1 , pp. 172-184
    • Klawonn, A.1
  • 14
    • 20044366132 scopus 로고    scopus 로고
    • A primal based penalty preconditioner for elliptic saddle point systems
    • Technical Report SAND 2004-5964J, Sandia National Laboratories
    • Dohrmann CR, Lehoucq RB. A primal based penalty preconditioner for elliptic saddle point systems. Technical Report SAND 2004-5964J, Sandia National Laboratories, 2004.
    • (2004)
    • Dohrmann, C.R.1    Lehoucq, R.B.2
  • 15
    • 33645471089 scopus 로고    scopus 로고
    • A preconditioner for the Schur complement domain decomposition method
    • In Widlund O, Herrera I, Keyes D, Yates R (eds), Proceedings of the 14th International Conference on Domain Decomposition Methods in Science and Engineering. National Autonomous University of Mexico (UNAM): Mexico City, Mexico, ISBN 970-32-0859-2
    • Cros J-N. A preconditioner for the Schur complement domain decomposition method. In Domain Decomposition Methods in Science and Engineering, Widlund O, Herrera I, Keyes D, Yates R (eds), Proceedings of the 14th International Conference on Domain Decomposition Methods in Science and Engineering. National Autonomous University of Mexico (UNAM): Mexico City, Mexico, ISBN 970-32-0859-2, 2003; 373-380. http://www.ddm.org/DD14
    • (2003) Domain Decomposition Methods in Science and Engineering , pp. 373-380
    • Cros, J.-N.1
  • 16
    • 1842564155 scopus 로고    scopus 로고
    • A preconditioner for substructuring based on constrained energy minimization
    • Dohrmann CR. A preconditioner for substructuring based on constrained energy minimization. SIAM Journal on Scientific Computing 2003; 25(1):246-258.
    • (2003) SIAM Journal on Scientific Computing , vol.25 , Issue.1 , pp. 246-258
    • Dohrmann, C.R.1
  • 17
    • 0242287760 scopus 로고    scopus 로고
    • Convergence of a balancing domain decomposition by constraints and energy minimization
    • Mandel J, Dohrmann CR. Convergence of a balancing domain decomposition by constraints and energy minimization. Numerical Linear in Algebra with Applications 2003; 10:639-659.
    • (2003) Numerical Linear in Algebra With Applications , vol.10 , pp. 639-659
    • Mandel, J.1    Dohrmann, C.R.2
  • 18
    • 19044366698 scopus 로고    scopus 로고
    • An algebraic theory for primal and dual substructuring methods by constraints
    • Mandel J, Dohrmann CR, Tezaur R. An algebraic theory for primal and dual substructuring methods by constraints. Applied Numerical Mathematics 2005; 54(2):167-193.
    • (2005) Applied Numerical Mathematics , vol.54 , Issue.2 , pp. 167-193
    • Mandel, J.1    Dohrmann, C.R.2    Tezaur, R.3
  • 20
    • 33645466916 scopus 로고    scopus 로고
    • Three-level BDDC in two dimensions
    • Technical Report TR2004-856, Department of Computer Science, Courant Institute, New York University
    • Tu X. Three-level BDDC in two dimensions. Technical Report TR2004-856, Department of Computer Science, Courant Institute, New York University, 2004.
    • (2004)
    • Tu, X.1
  • 21
    • 33645471014 scopus 로고    scopus 로고
    • Three-level BDDC in three dimensions
    • Technical Report TR2005-862, Department of Computer Science, Courant Institute, New York University
    • Tu X. Three-level BDDC in three dimensions. Technical Report TR2005-862, Department of Computer Science, Courant Institute, New York University, 2005.
    • (2005)
    • Tu, X.1
  • 22
    • 33645466676 scopus 로고    scopus 로고
    • On the use of inexact subdomain solvers for BDDC algorithms
    • Technical Report TR2005-871, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, July
    • Li J, Widlund OB. On the use of inexact subdomain solvers for BDDC algorithms. Technical Report TR2005-871, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, July 2005.
    • (2005)
    • Li, J.1    Widlund, O.B.2
  • 23
    • 33846050004 scopus 로고    scopus 로고
    • Méthodes de décomposition de domaine et méthodes d'accéleration pour les problèmes multichamps en non-linéaire
    • Ph.D. Thesis, Université Paris 6
    • Gosselet P. Méthodes de décomposition de domaine et méthodes d'accéleration pour les problèmes multichamps en non-linéaire. Ph.D. Thesis, Université Paris 6, 2003.
    • (2003)
    • Gosselet, P.1
  • 26
    • 0035609885 scopus 로고    scopus 로고
    • On the convergence of a dual-primal substructuring method
    • Mandel J, Tezaur R. On the convergence of a dual-primal substructuring method. Numerische Mathematik 2001; 88:543-558.
    • (2001) Numerische Mathematik , vol.88 , pp. 543-558
    • Mandel, J.1    Tezaur, R.2
  • 27
    • 0036556595 scopus 로고    scopus 로고
    • Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients
    • Klawonn A, Widlund OB, Dryja M. Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. SIAM Journal on Numerical Analysis 2002; 40:159-179.
    • (2002) SIAM Journal on Numerical Analysis , vol.40 , pp. 159-179
    • Klawonn, A.1    Widlund, O.B.2    Dryja, M.3
  • 28
    • 33749361043 scopus 로고    scopus 로고
    • Some computational results for dual-primal FETI methods for three dimensional elliptic problems
    • In Kornhuber R, Hoppe RHW, Périaux J, Pironneau O, Widlund OB, Xu J (eds). Lecture Notes in Computational Science and Engineering. Springer: Berlin, 2004; Proceedings of the 15th International Conference on Domain Decomposition Methods, Berlin, July 21-25
    • Klawonn A, Rheinbach O, Widlund OB. Some computational results for dual-primal FETI methods for three dimensional elliptic problems. In Domain Decomposition Methods in Science and Engineering, Kornhuber R, Hoppe RHW, Périaux J, Pironneau O, Widlund OB, Xu J (eds). Lecture Notes in Computational Science and Engineering. Springer: Berlin, 2004; Proceedings of the 15th International Conference on Domain Decomposition Methods, Berlin, July 21-25, 2003.
    • (2003) Domain Decomposition Methods in Science and Engineering
    • Klawonn, A.1    Rheinbach, O.2    Widlund, O.B.3
  • 29
    • 0043144674 scopus 로고    scopus 로고
    • A family of domain decomposition methods for the massively parallel solution of computational mechanics problems
    • Ph.D. Thesis, University of Colorado at Boulder, Aerospace Engineering
    • Pierson KH. A family of domain decomposition methods for the massively parallel solution of computational mechanics problems. Ph.D. Thesis, University of Colorado at Boulder, Aerospace Engineering, 2000.
    • (2000)
    • Pierson, K.H.1
  • 31
    • 33846119231 scopus 로고    scopus 로고
    • FETI-DP and BDDC domain decomposition methods for spectral elements in 2D
    • Technical Report, in preparation
    • Klawonn A, Pavarino LF, Rheinbach O. FETI-DP and BDDC domain decomposition methods for spectral elements in 2D. Technical Report, 2006, in preparation.
    • (2006)
    • Klawonn, A.1    Pavarino, L.F.2    Rheinbach, O.3
  • 32
    • 1542379947 scopus 로고    scopus 로고
    • Block triangular preconditioners for symmetric saddle-point problems
    • Simoncini V. Block triangular preconditioners for symmetric saddle-point problems. Applied Numerical Mathematics 2004; 49:63-80.
    • (2004) Applied Numerical Mathematics , vol.49 , pp. 63-80
    • Simoncini, V.1
  • 33
    • 0004173267 scopus 로고
    • Preconditioners for indefinite problems
    • Ph.D. Thesis, Westfälische Wilhelms-Universität Münster, November
    • Klawonn A. Preconditioners for indefinite problems. Ph.D. Thesis, Westfälische Wilhelms-Universität Münster, November 1995.
    • (1995)
    • Klawonn, A.1
  • 34
    • 0035526706 scopus 로고    scopus 로고
    • FETI and Neumann-Neumann iterative substructuring methods: Connections and new results
    • Klawonn A, Widlund OB. FETI and Neumann-Neumann iterative substructuring methods: connections and new results. Communications in Pure and Applied Mathematics 2001; 54:57-90.
    • (2001) Communications in Pure and Applied Mathematics , vol.54 , pp. 57-90
    • Klawonn, A.1    Widlund, O.B.2
  • 36
    • 0035282142 scopus 로고    scopus 로고
    • A review of algebraic multigrid
    • Also available as GMD Report 69, November 1999
    • Stüben K. A review of algebraic multigrid. Journal of Computational and Applied Mathematics 2001; 128:281-309. Also available as GMD Report 69, November 1999.
    • (2001) Journal of Computational and Applied Mathematics , vol.128 , pp. 281-309
    • Stüben, K.1
  • 37
    • 33645387258 scopus 로고    scopus 로고
    • An introduction to algebraic multigrid
    • [38]. Also available as GMD Report 70, November
    • Stüben K. An introduction to algebraic multigrid. Multigrid [38]. Also available as GMD Report 70, November 1999; 413-532.
    • (1999) Multigrid , pp. 413-532
    • Stüben, K.1
  • 39
    • 0003798972 scopus 로고    scopus 로고
    • ParMetis - Parallel graph partitioning and sparse matrix ordering, version 3.1
    • Technical Report, Department of Computer Science and Engineering, University of Minnesota, August
    • Karypis G, Schloegel K, Kumar V. ParMetis - parallel graph partitioning and sparse matrix ordering, version 3.1. Technical Report, Department of Computer Science and Engineering, University of Minnesota, August 2003.
    • (2003)
    • Karypis, G.1    Schloegel, K.2    Kumar, V.3
  • 40
    • 2942655475 scopus 로고    scopus 로고
    • A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
    • Davis TA. A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Transactions on Mathematical Software 2004; 30(2):165-195.
    • (2004) ACM Transactions on Mathematical Software , vol.30 , Issue.2 , pp. 165-195
    • Davis, T.A.1
  • 41
    • 0030818949 scopus 로고    scopus 로고
    • A high-performance MPI implementation on a shared-memory vector supercomputer
    • Gropp W, Lusk E. A high-performance MPI implementation on a shared-memory vector supercomputer. Parallel Computing 1997; 22(11):1513-1526.
    • (1997) Parallel Computing , vol.22 , Issue.11 , pp. 1513-1526
    • Gropp, W.1    Lusk, E.2
  • 43
    • 0030243005 scopus 로고    scopus 로고
    • A high-performance, portable implementation of the MPI message passing interface standard
    • Gropp W, Lusk E, Doss N, Skjellum A. A high-performance, portable implementation of the MPI message passing interface standard. Parallel Computing 1996; 22(6):789-828.
    • (1996) Parallel Computing , vol.22 , Issue.6 , pp. 789-828
    • Gropp, W.1    Lusk, E.2    Doss, N.3    Skjellum, A.4
  • 46
    • 0002515487 scopus 로고    scopus 로고
    • Efficient management of parallelism in object oriented numerical software libraries
    • In Arge E, Bruaset AM, Langtangen HP (eds). Birkhäuser: Basel
    • Balay S, Eijkhout V, Gropp WD, McInnes LC, Smith BF. Efficient management of parallelism in object oriented numerical software libraries. In Modern Software Tools in Scientific Computing, Arge E, Bruaset AM, Langtangen HP (eds). Birkhäuser: Basel, 1997; 163-202.
    • (1997) Modern Software Tools in Scientific Computing , pp. 163-202
    • Balay, S.1    Eijkhout, V.2    Gropp, W.D.3    McInnes, L.C.4    Smith, B.F.5
  • 47
    • 2942653250 scopus 로고    scopus 로고
    • Algorithm 832: UMFPACK - An unsymmetric - Pattern multifrontal method with a column pre-ordering strategy
    • Davis TA. Algorithm 832: UMFPACK - an unsymmetric - pattern multifrontal method with a column pre-ordering strategy. ACM Transactions on Mathematical Software 2004; 30:(2):196-199.
    • (2004) ACM Transactions on Mathematical Software , vol.30 , Issue.2 , pp. 196-199
    • Davis, T.A.1
  • 48
    • 0036532956 scopus 로고    scopus 로고
    • Boomeramg: A parallel algebraic multigrid solver and preconditioner
    • Henson VE, Yang UM. Boomeramg: a parallel algebraic multigrid solver and preconditioner. Applied Numerical Mathematics 2002; 41:155-177.
    • (2002) Applied Numerical Mathematics , vol.41 , pp. 155-177
    • Henson, V.E.1    Yang, U.M.2
  • 49
    • 84880490288 scopus 로고    scopus 로고
    • The design and implementation of hypre, a library of parallel high performance preconditioners
    • In Chapter in Numerical Solution of Partial Differential Equations on Parallel Computers, Bruaset AM, Bjorstad P, Tveito A (eds), Springer: Berlin
    • Falgout RD, Jones JE, Yang UM. The design and implementation of hypre, a library of parallel high performance preconditioners. In Chapter in Numerical Solution of Partial Differential Equations on Parallel Computers, Bruaset AM, Bjorstad P, Tveito A (eds), Lecture Notes in Computational Science and Engineering, vol. 51. Springer: Berlin, 2005; 267-294.
    • (2005) Lecture Notes in Computational Science and Engineering , vol.51 , pp. 267-294
    • Falgout, R.D.1    Jones, J.E.2    Yang, U.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.