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Volumn 197, Issue 17-18, 2008, Pages 1466-1478

A modified wavelet approximation for multi-resolution AWCM in simulating nonlinear vibration of MDOF systems

Author keywords

Adaptive wavelet collocation method; Boundary first order time derivative; Initial value problem; MDOF systems; Multi resolution; Nonlinear vibration

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; INITIAL VALUE PROBLEMS; MULTIRESOLUTION ANALYSIS; VIBRATIONS (MECHANICAL);

EID: 39149085991     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.11.017     Document Type: Article
Times cited : (27)

References (46)
  • 1
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element methods
    • Babuska I., and Rheinboldt W.C. Error estimates for adaptive finite element methods. SIAM J. Numer. Anal. 15 (1978) 736-754
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babuska, I.1    Rheinboldt, W.C.2
  • 2
    • 39149118093 scopus 로고
    • A posteriori error estimation and adaptive mesh-refinement techniques
    • Verfurth R. A posteriori error estimation and adaptive mesh-refinement techniques. J. Comput. Appl. Math. 44 (1994) 283-301
    • (1994) J. Comput. Appl. Math. , vol.44 , pp. 283-301
    • Verfurth, R.1
  • 3
    • 0029485184 scopus 로고
    • Adaptive error control for multigrid finite element methods
    • Becker R., Johnson C., and Rannacher R. Adaptive error control for multigrid finite element methods. Computing 55 (1995) 271-288
    • (1995) Computing , vol.55 , pp. 271-288
    • Becker, R.1    Johnson, C.2    Rannacher, R.3
  • 4
    • 0001701058 scopus 로고    scopus 로고
    • A posteriori error estimates for elliptic problems in two and three space dimensions
    • Bornemann F.A., Erdmann B., and Kornhuber R. A posteriori error estimates for elliptic problems in two and three space dimensions. SIAM J. Numer. Anal. 33 (1996) 1188-1204
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1188-1204
    • Bornemann, F.A.1    Erdmann, B.2    Kornhuber, R.3
  • 5
    • 39149140066 scopus 로고    scopus 로고
    • S. Bertoluzza, G. Naldi, An adaptive wavelet collocation method, Technical Report 932, Pubbl I.A.N., 1994.
    • S. Bertoluzza, G. Naldi, An adaptive wavelet collocation method, Technical Report 932, Pubbl I.A.N., 1994.
  • 7
    • 0002228719 scopus 로고    scopus 로고
    • A wavelet collocation method for the numerical solution of partial differential equations
    • Bertoluzza S., and Naldi G. A wavelet collocation method for the numerical solution of partial differential equations. Appl. Comput. Harm. Anal. 3 (1996) 1-9
    • (1996) Appl. Comput. Harm. Anal. , vol.3 , pp. 1-9
    • Bertoluzza, S.1    Naldi, G.2
  • 8
    • 0032217559 scopus 로고    scopus 로고
    • Application of wavelet Galerin FEM to bending of beam and plate structures
    • Zhou Y.-H., Wang J.-Z., and Zheng X.-J. Application of wavelet Galerin FEM to bending of beam and plate structures. Appl. Math. Mech. 19 8 (1998) 745-755
    • (1998) Appl. Math. Mech. , vol.19 , Issue.8 , pp. 745-755
    • Zhou, Y.-H.1    Wang, J.-Z.2    Zheng, X.-J.3
  • 9
    • 0033293883 scopus 로고    scopus 로고
    • Solving hyperbolic PDEs using interpolating wavelet
    • Holmströn M. Solving hyperbolic PDEs using interpolating wavelet. SIAM J. Sci. Comput. 21 (1999) 405-420
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 405-420
    • Holmströn, M.1
  • 10
    • 0033448969 scopus 로고    scopus 로고
    • Applications of wavelet Galerkin FEM to bending of plate structure
    • Zhou Y.-H., Wang J.-Z., and Zheng X.-J. Applications of wavelet Galerkin FEM to bending of plate structure. Acta Mechanica Solida Sinica 12 2 (1999) 136-143
    • (1999) Acta Mechanica Solida Sinica , vol.12 , Issue.2 , pp. 136-143
    • Zhou, Y.-H.1    Wang, J.-Z.2    Zheng, X.-J.3
  • 11
    • 0034295945 scopus 로고    scopus 로고
    • Vibration control of variable thickness plates with piezoelectric sensors and actuators based on wavelet theory
    • Zhou Y.-H., Wang J.-Z., Zheng X.-J., and Jiang Q. Vibration control of variable thickness plates with piezoelectric sensors and actuators based on wavelet theory. J. Sound Vib. 237 3 (2000) 395-410
    • (2000) J. Sound Vib. , vol.237 , Issue.3 , pp. 395-410
    • Zhou, Y.-H.1    Wang, J.-Z.2    Zheng, X.-J.3    Jiang, Q.4
  • 13
    • 39149117124 scopus 로고    scopus 로고
    • N. Kevlahan, O.V. Vasilyev, D. Goldstein, A. Jay, A three-dimensional adaptive wavelet method for fluid-structure interaction, in: B.J. Geurts, R. Friedrich, O. Metais (Eds.), Direct and Large-Eddy Simulation V, 2004, pp. 147-154.
    • N. Kevlahan, O.V. Vasilyev, D. Goldstein, A. Jay, A three-dimensional adaptive wavelet method for fluid-structure interaction, in: B.J. Geurts, R. Friedrich, O. Metais (Eds.), Direct and Large-Eddy Simulation V, 2004, pp. 147-154.
  • 14
    • 18144367270 scopus 로고    scopus 로고
    • An adaptive multilevel wavelet collocation method for elliptic problems
    • Vasilyev O.V., and Kevlahan N.-R. An adaptive multilevel wavelet collocation method for elliptic problems. J. Comp. Phys. 206 (2005) 412-431
    • (2005) J. Comp. Phys. , vol.206 , pp. 412-431
    • Vasilyev, O.V.1    Kevlahan, N.-R.2
  • 15
    • 27844490293 scopus 로고    scopus 로고
    • An adaptive wavelet collocation method for fluid-structure interaction at high Reynolds numbers
    • Kevlahan N.K.-R., and Vasilyev O.V. An adaptive wavelet collocation method for fluid-structure interaction at high Reynolds numbers. SIAM J. Sci. Comput. 26 6 (2005) 1894-1915
    • (2005) SIAM J. Sci. Comput. , vol.26 , Issue.6 , pp. 1894-1915
    • Kevlahan, N.K.-R.1    Vasilyev, O.V.2
  • 16
    • 33644948810 scopus 로고    scopus 로고
    • Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations
    • Alam J.M., Kevlahan N.K.-R., and Vasilyev O.V. Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations. J. Comp. Phys. 214 (2006) 829-857
    • (2006) J. Comp. Phys. , vol.214 , pp. 829-857
    • Alam, J.M.1    Kevlahan, N.K.-R.2    Vasilyev, O.V.3
  • 17
    • 33744905590 scopus 로고    scopus 로고
    • 'les fleurs du mal' II: A dynamically adaptive wavelet method of arbitrary lines for nonlinear evolutionary problems capturing steep moving fronts
    • July
    • Ren X., and Xanthis L.S. 'les fleurs du mal' II: A dynamically adaptive wavelet method of arbitrary lines for nonlinear evolutionary problems capturing steep moving fronts. Comput. Meth. Appl. Mech. Engrg. 195 (2006) 4962-4970 July
    • (2006) Comput. Meth. Appl. Mech. Engrg. , vol.195 , pp. 4962-4970
    • Ren, X.1    Xanthis, L.S.2
  • 18
    • 0028496320 scopus 로고
    • An overview of wavelet based multi-resolution analysis
    • Jawerth B., and Sweldens W. An overview of wavelet based multi-resolution analysis. SIAM Rev. 36 (1994) 377-412
    • (1994) SIAM Rev. , vol.36 , pp. 377-412
    • Jawerth, B.1    Sweldens, W.2
  • 19
    • 0035280516 scopus 로고    scopus 로고
    • Wavelet methods for PDEs - some recent developments
    • Dahmen W. Wavelet methods for PDEs - some recent developments. J. Comp. Appl. Math. 128 (2001) 133-185
    • (2001) J. Comp. Appl. Math. , vol.128 , pp. 133-185
    • Dahmen, W.1
  • 21
    • 84953600891 scopus 로고    scopus 로고
    • J. Crank, P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, in: Proceedings of the Cambustion Philosophical Society 43 (1947) 50-67. (Reprinted in Adv. Comput. Math. 6 (1996) 207-226).
    • J. Crank, P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, in: Proceedings of the Cambustion Philosophical Society 43 (1947) 50-67. (Reprinted in Adv. Comput. Math. 6 (1996) 207-226).
  • 22
    • 0002689020 scopus 로고
    • A method of computation for structural dynamics
    • Newmark N.A. A method of computation for structural dynamics. J. Engrg. Mech. Div. ASCE 85 EM3 (1959) 67-94
    • (1959) J. Engrg. Mech. Div. ASCE , vol.85 , Issue.EM3 , pp. 67-94
    • Newmark, N.A.1
  • 24
    • 0009268083 scopus 로고
    • Huazhong University of Science and Technology Press (Chinese edition)
    • Li Q.-Y., Wang N.-C., and Yi D.-Y. Numerical Analysis (1982), Huazhong University of Science and Technology Press (Chinese edition)
    • (1982) Numerical Analysis
    • Li, Q.-Y.1    Wang, N.-C.2    Yi, D.-Y.3
  • 25
    • 10844264668 scopus 로고    scopus 로고
    • A FETI-based multi-time-step coupling method for Newmark schemes in structural dynamics
    • Prakash A., and Hjelmstad K.D. A FETI-based multi-time-step coupling method for Newmark schemes in structural dynamics. Int. J. Numer. Meth. Engrg. 61 13 (2005) 2183-2204
    • (2005) Int. J. Numer. Meth. Engrg. , vol.61 , Issue.13 , pp. 2183-2204
    • Prakash, A.1    Hjelmstad, K.D.2
  • 26
    • 0031210701 scopus 로고    scopus 로고
    • Mechanical integrators derived from a discrete variational principle
    • Wendlandt J.M., and Marsden J.E. Mechanical integrators derived from a discrete variational principle. Physica D 106 (1997) 223-246
    • (1997) Physica D , vol.106 , pp. 223-246
    • Wendlandt, J.M.1    Marsden, J.E.2
  • 27
    • 0034516803 scopus 로고    scopus 로고
    • Variational integrators and the Newmark algorithm for conservative and dissipative mechanical system
    • Kane C., Marsden J.E., Ortiz M., and West M. Variational integrators and the Newmark algorithm for conservative and dissipative mechanical system. Int. J. Numer. Math. Engrg. 49 (1999) 1295-1325
    • (1999) Int. J. Numer. Math. Engrg. , vol.49 , pp. 1295-1325
    • Kane, C.1    Marsden, J.E.2    Ortiz, M.3    West, M.4
  • 28
    • 84959193128 scopus 로고    scopus 로고
    • Discrete mechanics and variational integrators
    • Marsden J.E., and West M. Discrete mechanics and variational integrators. Acta Numer. (2001) 357-514
    • (2001) Acta Numer. , pp. 357-514
    • Marsden, J.E.1    West, M.2
  • 29
    • 0037243629 scopus 로고    scopus 로고
    • The anisotropic Lagrangian averaged euler and Navier-Stokes equations
    • Marsden J.E., and Shkoller S. The anisotropic Lagrangian averaged euler and Navier-Stokes equations. Arch. Rat. Mech. Anal. 166 (2003) 27-46
    • (2003) Arch. Rat. Mech. Anal. , vol.166 , pp. 27-46
    • Marsden, J.E.1    Shkoller, S.2
  • 31
    • 0032678575 scopus 로고    scopus 로고
    • A fast wavelet collocation method for highspeed VLSI circuit simulation
    • Zhou D., and Cai W. A fast wavelet collocation method for highspeed VLSI circuit simulation. IEEE Trans. Circ. Syst-I: Fund. Theory Appl. 46 8 (1999) 20-930
    • (1999) IEEE Trans. Circ. Syst-I: Fund. Theory Appl. , vol.46 , Issue.8 , pp. 20-930
    • Zhou, D.1    Cai, W.2
  • 32
    • 0032690786 scopus 로고    scopus 로고
    • An adaptive wavelet method for nonlinear circuit simulation
    • Zhou D., and Cai W. An adaptive wavelet method for nonlinear circuit simulation. IEEE Trans. Circ. Syst-I: Fund. Theory Appl. 46 8 (1999) 931-938
    • (1999) IEEE Trans. Circ. Syst-I: Fund. Theory Appl. , vol.46 , Issue.8 , pp. 931-938
    • Zhou, D.1    Cai, W.2
  • 34
    • 0035689713 scopus 로고    scopus 로고
    • Comparison of wavelet- and time-marching-based microwave circuit transient analyses
    • Christoffersen C.E., and Steer M.B. Comparison of wavelet- and time-marching-based microwave circuit transient analyses. IEEE Microwave Guided Wave Lett. (2001)
    • (2001) IEEE Microwave Guided Wave Lett.
    • Christoffersen, C.E.1    Steer, M.B.2
  • 35
    • 39149141644 scopus 로고    scopus 로고
    • Ji-Zeng Wang, Generalized theory and arithmetic of orthogonal wavelets and applications to researches of mechanics including piezoelectric smart structures, PhD Thesis, Department of Mechanics, Lanzhou University, 2001. (Chinese edition).
    • Ji-Zeng Wang, Generalized theory and arithmetic of orthogonal wavelets and applications to researches of mechanics including piezoelectric smart structures, PhD Thesis, Department of Mechanics, Lanzhou University, 2001. (Chinese edition).
  • 36
    • 84990575058 scopus 로고
    • Orthonormal bases of compactly supported wavelets
    • Daubechies I. Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41 (1988) 909-996
    • (1988) Commun. Pure Appl. Math. , vol.41 , pp. 909-996
    • Daubechies, I.1
  • 38
    • 39149117777 scopus 로고    scopus 로고
    • I. Daubechies, Ten lectures on wavelets, CBMS-NSF regional conference series in applied mathematics. Soc. Ind. Appl. Math., 1992.
    • I. Daubechies, Ten lectures on wavelets, CBMS-NSF regional conference series in applied mathematics. Soc. Ind. Appl. Math., 1992.
  • 39
    • 39149131133 scopus 로고    scopus 로고
    • D.L. Donoho, Interpolating wavelet transforms, Technical Report 408, Department of Statistics, Stanford University, 1992 (November).
    • D.L. Donoho, Interpolating wavelet transforms, Technical Report 408, Department of Statistics, Stanford University, 1992 (November).
  • 40
    • 0002372605 scopus 로고
    • Some remarks on wavelet interpolation
    • Bertoluzza S., and Naldi G. Some remarks on wavelet interpolation. Comp. Appl. Math. 14 1 (1994)
    • (1994) Comp. Appl. Math. , vol.14 , Issue.1
    • Bertoluzza, S.1    Naldi, G.2
  • 41
    • 0034190369 scopus 로고    scopus 로고
    • A wavelet-based method for numerical solution of nonlinear evolution equations
    • Comincioli V., Naldi G., and Scapolla T. A wavelet-based method for numerical solution of nonlinear evolution equations. Appl. Numer. Math. 33 (2000) 197-291
    • (2000) Appl. Numer. Math. , vol.33 , pp. 197-291
    • Comincioli, V.1    Naldi, G.2    Scapolla, T.3
  • 42
    • 0342470964 scopus 로고    scopus 로고
    • The wavelet-collocation method for transient problems with steep gradients
    • Liu Y., Cameron I.T., and Wang F.Y. The wavelet-collocation method for transient problems with steep gradients. Chem. Engrg. Sci. 55 (2000) 1729-1734
    • (2000) Chem. Engrg. Sci. , vol.55 , pp. 1729-1734
    • Liu, Y.1    Cameron, I.T.2    Wang, F.Y.3
  • 43
    • 0035890830 scopus 로고    scopus 로고
    • A wavelet-based adaptive technique for adsorption problems involving steep gradient
    • Liu Y., Camerson I.T., and Bhatia S.K. A wavelet-based adaptive technique for adsorption problems involving steep gradient. Comput. Chem. Engrg. 25 (2001) 1611-1619
    • (2001) Comput. Chem. Engrg. , vol.25 , pp. 1611-1619
    • Liu, Y.1    Camerson, I.T.2    Bhatia, S.K.3
  • 44
    • 0000288810 scopus 로고
    • Un méthode de resolution d'une categorie d'equations transcendantes
    • Lahaye E. Un méthode de resolution d'une categorie d'equations transcendantes. C.R. Acad. Sci. 198 (1934) 1840-1844
    • (1934) C.R. Acad. Sci. , vol.198 , pp. 1840-1844
    • Lahaye, E.1


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