An Adaptive Multigrid Solver for Plate Vibration and Buckling Problems
The paper describes a finite element multigrid strategy for the solution of plate vibration and buckling problems. The solution procedure combines the residual iteration scheme used in Casciaro R, Aristodemo M. International Conference on Finite Elements Nonlinear Solid and Structural Mechanics, Gel...
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| Published in | Computers & structures Vol. 69; no. 5; pp. 625 - 637 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.12.1998
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| Abstract | The paper describes a finite element multigrid strategy for the solution of plate vibration and buckling problems. The solution procedure combines the residual iteration scheme used in Casciaro R, Aristodemo M. International Conference on Finite Elements Nonlinear Solid and Structural Mechanics, Gelio, Norway, 1977, (main loop) with the adaptive multigrid scheme proposed in Lopez S, Casciaro R. International Journal of Numerical methods in Engineering 1997;40:919–96. A subspace iteration technique allows several principal eigensolutions to be obtained simultaneously. The sequence of meshes used by the multigrid process is generated through an adaptive local refinement based on the Zienkiewicz–Zhu estimate of the discretization error Zienkiewicz OC, Zhu JZ. International Journal of Numerical Methods in Engineering 1987;24:337–57. A pointer-based data structure and an HC Aristoderno M. Computers and Structures 1985;21(5):987–93, finite element discretization make the solution process highly efficient. Some numerical tests show the effectiveness of the algorithm. |
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| AbstractList | The paper describes a finite element multigrid strategy for the solution of plate vibration and buckling problems. The solution procedure combines the residual iteration scheme used by Casciaro and Aristodemo (1977) (main loop) with the adaptive multigrid scheme proposed by Lopez and Casciaro (1997). A subspace iteration technique allows several principal eigensolutions to be obtained simultaneously. The sequence of meshes used by the multigrid process is generated through an adaptive local refinement based on the Zienkiewicz-Zhu estimate of the discretization error (1987). A pointer-based data structure and a high-continuity finite element discretization (Aristodemo) make the solution process highly efficient. Numerical tests show the effectiveness of the algorithm. The paper describes a finite element multigrid strategy for the solution of plate vibration and buckling problems. The solution procedure combines the residual iteration scheme used in Casciaro R, Aristodemo M. International Conference on Finite Elements Nonlinear Solid and Structural Mechanics, Gelio, Norway, 1977, (main loop) with the adaptive multigrid scheme proposed in Lopez S, Casciaro R. International Journal of Numerical methods in Engineering 1997;40:919–96. A subspace iteration technique allows several principal eigensolutions to be obtained simultaneously. The sequence of meshes used by the multigrid process is generated through an adaptive local refinement based on the Zienkiewicz–Zhu estimate of the discretization error Zienkiewicz OC, Zhu JZ. International Journal of Numerical Methods in Engineering 1987;24:337–57. A pointer-based data structure and an HC Aristoderno M. Computers and Structures 1985;21(5):987–93, finite element discretization make the solution process highly efficient. Some numerical tests show the effectiveness of the algorithm. |
| Author | Lopez, Salvatore Casciaro, Raffaele Fortino, Stefania |
| Author_xml | – sequence: 1 givenname: Salvatore surname: Lopez fullname: Lopez, Salvatore organization: Istituto di Scienza delle Costruzioni, Universitàdi Bologna, 40136, Bologna, Italy – sequence: 2 givenname: Stefania surname: Fortino fullname: Fortino, Stefania organization: Dipartimento di Strutture, Universitàdella Calabria, 87030, Rende (CS), Italy – sequence: 3 givenname: Raffaele surname: Casciaro fullname: Casciaro, Raffaele organization: Dipartimento di Strutture, Universitàdella Calabria, 87030, Rende (CS), Italy |
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| Cites_doi | 10.1007/978-3-663-14245-4_3 10.1002/nme.1620281209 10.1016/0045-7825(91)90113-K 10.1137/0719064 10.1002/nme.1620381403 10.1145/1271.1274 10.1002/(SICI)1097-0207(19960915)39:17<3007::AID-NME991>3.0.CO;2-S 10.1007/BF00370092 10.1007/BFb0069928 10.1002/nme.1620240206 10.1090/S0025-5718-1977-0431719-X 10.1002/(SICI)1097-0207(19970315)40:5<919::AID-NME95>3.0.CO;2-U 10.1016/0021-9991(74)90114-4 10.1002/nme.1620240710 10.1016/0045-7949(85)90211-1 |
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| References | Zienkiewicz, Zhu (BIB13) 1989; 28 Lopez S, Fortino S. Soluzione adattativa multigrid di problemi bidimensionali elastici (in italian). Report No. 164. Dip. Strutture, Unical, Cosenza, Italy, 1995 Rivara (BIB16) 1987; 28 Aristodemo M, Casciaro R, Vencia G. Analysis of two-dimensional elastoplastic continua by high-continuity finite elements. In: Taylor et al., eds. Numerical methods for nonlinear problems. Pineridge Press, Swansea, 1982 Lopez S. Aspetti algoritmici dei metodi multigrid in problemi di meccanica computazionale’ (in italian). Ph.D. Thesis. Unical, Cosenza, Italy, 1994 Lopez S, Fortino S, Casciaro R. Multigrid analysis of two-dimensional eigenvalue problems. Report no. 169. Dip. Strutture, Unical, Cosenza, Italy, 1995 Rivara (BIB15) 1984; 10 Lanzo, Garcea, Casciaro (BIB1) 1995; 38 Bank (BIB7) 1982; 19 Thompson, Thames, Waine (BIB21) 1974; 15 Lopez S, Fortino S, Casciaro S. Analisi multigrid di piastre alla Kirchhoff (in italian). Proceedings of XII Congresso AIMETA, Napoli, Italy, 1995 Storti, Nigro, Idelsohn (BIB17) 1991; 93 Stüben K, Trottenberg U. Multigrid methods: fundamental algorithms, model problem analysis and applications. In: Hackbusch W, Trottenberg U, editors. Multigrid Methods. Springer, Berlin, 1982:1–176 Hwang, Parsons (BIB8) 1992; 10 Lopez S, Fortino S, Lanzo AD. Post-buckling analysis of plates by multigrid FEM approach. In: ECCOMAS ‘96 Conference. Wiley, Parigi, 1996 Casciaro R, Aristodemo M. Perturbation analysis of geometrically nonlinear structures. International Conference on Finite elements nonlinear solid and structural mechanics, Gelio, Norway, 1977 Aristodemo (BIB20) 1985; 21 Zienkiewicz, Zhu (BIB12) 1987; 24 Hackbusch W. Multi-grid eigenvalue problem. In: Advances in multi-grid methods. Proceedings Conference. Oberwolfach, Friedr. Vieweg-Sohn, 1984 Lanzo, Garcea (BIB2) 1996; 39 Brandt (BIB4) 1977; 31 Lopez, Casciaro (BIB9) 1997; 40 10.1016/S0045-7949(98)80097-7_BIB19 10.1016/S0045-7949(98)80097-7_BIB5 Lanzo (10.1016/S0045-7949(98)80097-7_BIB1) 1995; 38 10.1016/S0045-7949(98)80097-7_BIB3 10.1016/S0045-7949(98)80097-7_BIB18 Rivara (10.1016/S0045-7949(98)80097-7_BIB15) 1984; 10 10.1016/S0045-7949(98)80097-7_BIB14 Rivara (10.1016/S0045-7949(98)80097-7_BIB16) 1987; 28 Thompson (10.1016/S0045-7949(98)80097-7_BIB21) 1974; 15 Brandt (10.1016/S0045-7949(98)80097-7_BIB4) 1977; 31 Lopez (10.1016/S0045-7949(98)80097-7_BIB9) 1997; 40 Lanzo (10.1016/S0045-7949(98)80097-7_BIB2) 1996; 39 10.1016/S0045-7949(98)80097-7_BIB6 Bank (10.1016/S0045-7949(98)80097-7_BIB7) 1982; 19 Zienkiewicz (10.1016/S0045-7949(98)80097-7_BIB13) 1989; 28 Storti (10.1016/S0045-7949(98)80097-7_BIB17) 1991; 93 Hwang (10.1016/S0045-7949(98)80097-7_BIB8) 1992; 10 Aristodemo (10.1016/S0045-7949(98)80097-7_BIB20) 1985; 21 10.1016/S0045-7949(98)80097-7_BIB11 10.1016/S0045-7949(98)80097-7_BIB22 10.1016/S0045-7949(98)80097-7_BIB10 Zienkiewicz (10.1016/S0045-7949(98)80097-7_BIB12) 1987; 24 |
| References_xml | – volume: 10 start-page: 247 year: 1992 end-page: 262 ident: BIB8 article-title: Multigrid solution procedures for structural dynamics eigenvalue problems publication-title: Comput Mech contributor: fullname: Parsons – volume: 93 start-page: 13 year: 1991 end-page: 30 ident: BIB17 article-title: Multigrid methods and adaptive refinement techniques in elliptic problems by finite element methods publication-title: Comp Meth Appl Mech Engng contributor: fullname: Idelsohn – volume: 38 start-page: 2325 year: 1995 end-page: 2345 ident: BIB1 article-title: Asymptotic post-buckling analysis of rectangular plates by HC finite elements publication-title: Int J Numer Meth Engng contributor: fullname: Casciaro – volume: 15 start-page: 299 year: 1974 ident: BIB21 article-title: Automatic numerical generation of body-fitted curvilinear coordinate system for fiels containing any number of arbitrary two-dimensional bodies publication-title: J Comp Phys contributor: fullname: Waine – volume: 28 start-page: 1343 year: 1987 end-page: 1354 ident: BIB16 article-title: A grid generator based on 4-triangles conforming mesh-refinement algorithms publication-title: Int J Numer Meth Engng contributor: fullname: Rivara – volume: 28 start-page: 2839 year: 1989 end-page: 2853 ident: BIB13 article-title: Error estimates and adaptive refinement for plate bending problems publication-title: Int J Numer Meth Engng contributor: fullname: Zhu – volume: 39 start-page: 3007 year: 1996 end-page: 3031 ident: BIB2 article-title: Koiter's post-buckling analysis of thin-walled structures by a finite element approach publication-title: Int J Numer Meth Engng contributor: fullname: Garcea – volume: 24 start-page: 337 year: 1987 end-page: 357 ident: BIB12 article-title: A simple error estimator and adaptive procedure for pratical engineering analysis publication-title: Int J Numer Meth Engng contributor: fullname: Zhu – volume: 31 start-page: 333 year: 1977 end-page: 390 ident: BIB4 article-title: Multi-level adaptive solutions to boundary value problems publication-title: Math Comp contributor: fullname: Brandt – volume: 40 start-page: 919 year: 1997 end-page: 936 ident: BIB9 article-title: Algorithmic aspects of adaptive multigrid finite element analysis publication-title: Int J Num Meth Engng contributor: fullname: Casciaro – volume: 19 start-page: 886 year: 1982 end-page: 893 ident: BIB7 article-title: Analysis of a multilevel inverse iteration procedure for eigenvalue problems publication-title: SIAM J Numer Anal contributor: fullname: Bank – volume: 10 start-page: 242 year: 1984 end-page: 264 ident: BIB15 article-title: Design and data structure of fully adaptive, multigrid, finite element software publication-title: ACM Trans Math Soft contributor: fullname: Rivara – volume: 21 start-page: 987 year: 1985 end-page: 993 ident: BIB20 article-title: A high-continuity finite element model for two-dimensional elastic problems publication-title: Comput Struct contributor: fullname: Aristodemo – ident: 10.1016/S0045-7949(98)80097-7_BIB11 – ident: 10.1016/S0045-7949(98)80097-7_BIB14 – ident: 10.1016/S0045-7949(98)80097-7_BIB6 doi: 10.1007/978-3-663-14245-4_3 – volume: 28 start-page: 2839 year: 1989 ident: 10.1016/S0045-7949(98)80097-7_BIB13 article-title: Error estimates and adaptive refinement for plate bending problems publication-title: Int J Numer Meth Engng doi: 10.1002/nme.1620281209 contributor: fullname: Zienkiewicz – volume: 93 start-page: 13 year: 1991 ident: 10.1016/S0045-7949(98)80097-7_BIB17 article-title: Multigrid methods and adaptive refinement techniques in elliptic problems by finite element methods publication-title: Comp Meth Appl Mech Engng doi: 10.1016/0045-7825(91)90113-K contributor: fullname: Storti – volume: 19 start-page: 886 year: 1982 ident: 10.1016/S0045-7949(98)80097-7_BIB7 article-title: Analysis of a multilevel inverse iteration procedure for eigenvalue problems publication-title: SIAM J Numer Anal doi: 10.1137/0719064 contributor: fullname: Bank – ident: 10.1016/S0045-7949(98)80097-7_BIB18 – volume: 38 start-page: 2325 year: 1995 ident: 10.1016/S0045-7949(98)80097-7_BIB1 article-title: Asymptotic post-buckling analysis of rectangular plates by HC finite elements publication-title: Int J Numer Meth Engng doi: 10.1002/nme.1620381403 contributor: fullname: Lanzo – ident: 10.1016/S0045-7949(98)80097-7_BIB3 – ident: 10.1016/S0045-7949(98)80097-7_BIB10 – volume: 10 start-page: 242 year: 1984 ident: 10.1016/S0045-7949(98)80097-7_BIB15 article-title: Design and data structure of fully adaptive, multigrid, finite element software publication-title: ACM Trans Math Soft doi: 10.1145/1271.1274 contributor: fullname: Rivara – volume: 39 start-page: 3007 year: 1996 ident: 10.1016/S0045-7949(98)80097-7_BIB2 article-title: Koiter's post-buckling analysis of thin-walled structures by a finite element approach publication-title: Int J Numer Meth Engng doi: 10.1002/(SICI)1097-0207(19960915)39:17<3007::AID-NME991>3.0.CO;2-S contributor: fullname: Lanzo – volume: 10 start-page: 247 year: 1992 ident: 10.1016/S0045-7949(98)80097-7_BIB8 article-title: Multigrid solution procedures for structural dynamics eigenvalue problems publication-title: Comput Mech doi: 10.1007/BF00370092 contributor: fullname: Hwang – ident: 10.1016/S0045-7949(98)80097-7_BIB5 doi: 10.1007/BFb0069928 – volume: 24 start-page: 337 year: 1987 ident: 10.1016/S0045-7949(98)80097-7_BIB12 article-title: A simple error estimator and adaptive procedure for pratical engineering analysis publication-title: Int J Numer Meth Engng doi: 10.1002/nme.1620240206 contributor: fullname: Zienkiewicz – ident: 10.1016/S0045-7949(98)80097-7_BIB22 – volume: 31 start-page: 333 year: 1977 ident: 10.1016/S0045-7949(98)80097-7_BIB4 article-title: Multi-level adaptive solutions to boundary value problems publication-title: Math Comp doi: 10.1090/S0025-5718-1977-0431719-X contributor: fullname: Brandt – volume: 40 start-page: 919 year: 1997 ident: 10.1016/S0045-7949(98)80097-7_BIB9 article-title: Algorithmic aspects of adaptive multigrid finite element analysis publication-title: Int J Num Meth Engng doi: 10.1002/(SICI)1097-0207(19970315)40:5<919::AID-NME95>3.0.CO;2-U contributor: fullname: Lopez – ident: 10.1016/S0045-7949(98)80097-7_BIB19 – volume: 15 start-page: 299 year: 1974 ident: 10.1016/S0045-7949(98)80097-7_BIB21 article-title: Automatic numerical generation of body-fitted curvilinear coordinate system for fiels containing any number of arbitrary two-dimensional bodies publication-title: J Comp Phys doi: 10.1016/0021-9991(74)90114-4 contributor: fullname: Thompson – volume: 28 start-page: 1343 year: 1987 ident: 10.1016/S0045-7949(98)80097-7_BIB16 article-title: A grid generator based on 4-triangles conforming mesh-refinement algorithms publication-title: Int J Numer Meth Engng doi: 10.1002/nme.1620240710 contributor: fullname: Rivara – volume: 21 start-page: 987 issue: 5 year: 1985 ident: 10.1016/S0045-7949(98)80097-7_BIB20 article-title: A high-continuity finite element model for two-dimensional elastic problems publication-title: Comput Struct doi: 10.1016/0045-7949(85)90211-1 contributor: fullname: Aristodemo |
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| Title | An Adaptive Multigrid Solver for Plate Vibration and Buckling Problems |
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