메뉴 건너뛰기




Volumn 192, Issue 11-12, 2003, Pages 1389-1419

A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime

Author keywords

Discontinuous enrichment method; Discontinuous Galerkin; Finite elements; Helmholtz problems; Lagrange multipliers; Short waves

Indexed keywords

FINITE ELEMENT METHOD; GALERKIN METHODS; LAGRANGE MULTIPLIERS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS;

EID: 0037436501     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(02)00646-1     Document Type: Article
Times cited : (214)

References (29)
  • 1
    • 0029487468 scopus 로고
    • A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
    • I. Babuška, F. Ihlenburg, E.T. Paik, S.A. Sauter, A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution, Comput. Methods Appl. Mech. Engrg. 128 (1995) 325-359.
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.128 , pp. 325-359
    • Babuška, I.1    Ihlenburg, F.2    Paik, E.T.3    Sauter, S.A.4
  • 2
    • 0001254041 scopus 로고    scopus 로고
    • Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers
    • I. Babuška, S.A. Sauter, Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers, SIAM J. Numer. Anal. 34 (1997) 2392-2423.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2392-2423
    • Babuška, I.1    Sauter, S.A.2
  • 3
    • 0001721753 scopus 로고
    • Weak element approximations to elliptic differential equations
    • M.E. Rose, Weak element approximations to elliptic differential equations, Numer. Math. 24 (1975) 185-204.
    • (1975) Numer. Math. , vol.24 , pp. 185-204
    • Rose, M.E.1
  • 4
    • 0001506006 scopus 로고
    • The weak element method applied to Helmholtz type equations
    • C.I. Goldstein, The weak element method applied to Helmholtz type equations, Appl. Numer. Math. 2 (1986) 409-426.
    • (1986) Appl. Numer. Math. , vol.2 , pp. 409-426
    • Goldstein, C.I.1
  • 5
    • 0000288806 scopus 로고
    • Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains
    • I. Harari, T.J. Hughes, Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains, Comput. Methods Appl. Mech. Engrg. 98 (1992) 411-454.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.98 , pp. 411-454
    • Harari, I.1    Hughes, T.J.R.2
  • 6
    • 0030380578 scopus 로고    scopus 로고
    • The partition of unity method finite element method: Basic theory and applications
    • J.M. Melenk, I. Babuška, The partition of unity method finite element method: Basic theory and applications, Comput. Methods Appl. Mech. Engrg. 139 (1996) 289-314.
    • (1996) Comput. Methods Appl. Mech. Engrg. , vol.139 , pp. 289-314
    • Melenk, J.M.1    Babuška, I.2
  • 8
    • 0034345542 scopus 로고    scopus 로고
    • Short wave modelling using special finite elements
    • O. Laghrouche, P. Bettess, Short wave modelling using special finite elements, J. Comput. Acoust. 8 (2000) 189-210.
    • (2000) J. Comput. Acoust. , vol.8 , pp. 189-210
    • Laghrouche, O.1    Bettess, P.2
  • 10
    • 0141445578 scopus 로고    scopus 로고
    • Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem
    • O. Cessenat, B. Despres, Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem, SIAM J. Numer. Anal. 35 (1998) 255-299.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 255-299
    • Cessenat, O.1    Despres, B.2
  • 11
    • 0033157560 scopus 로고    scopus 로고
    • Subgrid modeling in a Galerkin method for the Helmholtz equation
    • J.L. Cipolla, Subgrid modeling in a Galerkin method for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg. 177 (1999) 35-49.
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.177 , pp. 35-49
    • Cipolla, J.L.1
  • 12
    • 0032637241 scopus 로고    scopus 로고
    • A least-squares method for the Helmholtz equation
    • P. Monk, Da-Qing Wang, A least-squares method for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg. 175 (1999) 121-136.
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.175 , pp. 121-136
    • Monk, P.1    Wang Da-Qing2
  • 13
    • 0034734475 scopus 로고    scopus 로고
    • A residual-based finite element method for the Helmholtz equation
    • A.A. Oberai, P.M. Pinsky, A residual-based finite element method for the Helmholtz equation, Int. J. Numer. Methods Engrg. 49 (2000) 399-419.
    • (2000) Int. J. Numer. Methods Engrg. , vol.49 , pp. 399-419
    • Oberai, A.A.1    Pinsky, P.M.2
  • 17
    • 0005311960 scopus 로고    scopus 로고
    • The mortar element method for three-dimensional finite elements
    • F. Ben Belgacem, Y. Maday, The mortar element method for three-dimensional finite elements, RAIRO Modél. Math. Anal. Numér. 31 (1997) 289-302.
    • (1997) RAIRO Modél. Math. Anal. Numér. , vol.31 , pp. 289-302
    • Ben Belgacem, F.1    Maday, Y.2
  • 18
    • 0041800397 scopus 로고    scopus 로고
    • The mortar finite element method with Lagrange multipliers
    • F. Ben Belgacem, Y. Maday, The mortar finite element method with Lagrange multipliers, Numer. Math. 84 (1999) 173-197.
    • (1999) Numer. Math. , vol.84 , pp. 173-197
    • Ben Belgacem, F.1    Maday, Y.2
  • 19
    • 0001237820 scopus 로고
    • A Lagrange multiplier based divide and conquer finite element algorithm
    • C. Farhat, A Lagrange multiplier based divide and conquer finite element algorithm, J. Comput. Syst. Engrg. 2 (1991) 149-156.
    • (1991) J. Comput. Syst. Engrg. , vol.2 , pp. 149-156
    • Farhat, C.1
  • 20
    • 0028762823 scopus 로고
    • On a component mode synthesis method and its application to incompatible substructures
    • C. Farhat, M. Géradin, On a component mode synthesis method and its application to incompatible substructures, Comput. Struct. 51 (1994) 459-473.
    • (1994) Comput. Struct. , vol.51 , pp. 459-473
    • Farhat, C.1    Géradin, M.2
  • 21
    • 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
    • C. Farhat, K. Pierson, M. Lesoinne, The second generation of FETI methods and their application to the parallel solution of large-scale linear and geometrically nonlinear structural analysis problems, Comput. Methods Appl. Mech. Engrg. 184 (2000) 333-374.
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.184 , pp. 333-374
    • Farhat, C.1    Pierson, K.2    Lesoinne, M.3
  • 22
    • 0034405892 scopus 로고    scopus 로고
    • A two-level domain decomposition method for the iterative solution of high frequency exterior helmholtz problems
    • C. Farhat, A.P. Macedo, M. Lesoinne, A two-level domain decomposition method for the iterative solution of high frequency exterior helmholtz problems, Numer. Math. 85 (2000) 283-308.
    • (2000) Numer. Math. , vol.85 , pp. 283-308
    • Farhat, C.1    Macedo, A.P.2    Lesoinne, M.3
  • 23
  • 24
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
    • T.J. Hughes, Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Comput. Methods Appl. Mech. Engrg. 127 (1995) 387-401.
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.127 , pp. 387-401
    • Hughes, T.J.R.1
  • 25
    • 34250459417 scopus 로고
    • The finite element method with Lagrange multipliers
    • I. Babuška, The finite element method with Lagrange multipliers, Numer. Math. 20 (1973) 179-192.
    • (1973) Numer. Math. , vol.20 , pp. 179-192
    • Babuška, I.1
  • 26
    • 0016093926 scopus 로고
    • On the existence, uniqueness, and approximation of saddle-point problems arising from Lagrange multipliers
    • F. Brezzi, On the existence, uniqueness, and approximation of saddle-point problems arising from Lagrange multipliers, Rev. Francaise d'Automat. Inform. Rech. Opér., vol. 8-R2 (1974), pp. 129-151.
    • (1974) Rev. Francaise d'Automat. Inform. Rech. Opér , vol.2-8 R , pp. 129-151
    • Brezzi, F.1
  • 27
    • 0035073391 scopus 로고    scopus 로고
    • FETI-DP: A dual-primal unified FETI method - part I: A faster alternative to the two-level FETI method
    • C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson, D. Rixen, FETI-DP: a dual-primal unified FETI method-part I: a faster alternative to the two-level FETI method, Int. J. Numer. Methods Engrg. 50 (2001) 1523-1544.
    • (2001) Int. J. Numer. Methods Engrg. , vol.50 , pp. 1523-1544
    • Farhat, C.1    Lesoinne, M.2    LeTallec, P.3    Pierson, K.4    Rixen, D.5
  • 29
    • 0003881705 scopus 로고
    • Springer Series in Computational Mathematics, Springer-Verlag, New York
    • F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods, volume 15 of Springer Series in Computational Mathematics, Springer-Verlag, New York, 1991.
    • (1991) Mixed and Hybrid Finite Element Methods , vol.15
    • Brezzi, F.1    Fortin, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.