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Volumn 228, Issue 5, 2009, Pages 1466-1479

A damping preconditioner for time-harmonic wave equations in fluid and elastic material

Author keywords

Algebraic multigrid method; Finite element method; GMRES; Helmholtz equation; Navier equation; Preconditioning

Indexed keywords

ALGEBRA; DAMPING; ELASTIC WAVES; ELASTICITY; HELMHOLTZ EQUATION; INVERSE PROBLEMS; NUMERICAL METHODS; WAVE EQUATIONS;

EID: 58249134150     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.10.036     Document Type: Article
Times cited : (18)

References (41)
  • 1
    • 0019910925 scopus 로고
    • Structural-acoustic finite element analysis of the automobile passenger compartment: a review of current practice
    • Nefske D.J., Wolf J., and Howell L. Structural-acoustic finite element analysis of the automobile passenger compartment: a review of current practice. J. Sound Vib. 80 2 (1982) 247-266
    • (1982) J. Sound Vib. , vol.80 , Issue.2 , pp. 247-266
    • Nefske, D.J.1    Wolf, J.2    Howell, L.3
  • 2
    • 33644650994 scopus 로고    scopus 로고
    • A review of finite-element methods for time-harmonic acoustics
    • Thompson L.L. A review of finite-element methods for time-harmonic acoustics. J. Acoust. Soc. Am. 119 3 (2006) 1315-1330
    • (2006) J. Acoust. Soc. Am. , vol.119 , Issue.3 , pp. 1315-1330
    • Thompson, L.L.1
  • 3
    • 84966208271 scopus 로고
    • Absorbing boundary conditions for numerical simulation of waves
    • Engquist B., and Majda A. Absorbing boundary conditions for numerical simulation of waves. Math. Comput. 31 (1977) 629-651
    • (1977) Math. Comput. , vol.31 , pp. 629-651
    • Engquist, B.1    Majda, A.2
  • 4
    • 0003691880 scopus 로고    scopus 로고
    • Springer-Verlag, New York
    • Ihlenburg F. Finite element analysis of acoustic scattering. Applied Mathematical Sciences vol. 132 (1998), Springer-Verlag, New York
    • (1998) Applied Mathematical Sciences , vol.132
    • Ihlenburg, F.1
  • 5
    • 0000048673 scopus 로고
    • GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad Y., and Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7 3 (1986) 856-869
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , Issue.3 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 6
    • 0000005482 scopus 로고
    • Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
    • van der Vorst H.A. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 13 2 (1992) 631-644
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , Issue.2 , pp. 631-644
    • van der Vorst, H.A.1
  • 7
    • 0033901205 scopus 로고    scopus 로고
    • Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems
    • Farhat C., Macedo A., Lesoinne M., Roux F.-X., Magoulés F., and de La Bourdonnaie A. Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems. Comput. Meth. Appl. Mech. Eng. 184 2-4 (2000) 213-239
    • (2000) Comput. Meth. Appl. Mech. Eng. , vol.184 , Issue.2-4 , pp. 213-239
    • Farhat, C.1    Macedo, A.2    Lesoinne, M.3    Roux, F.-X.4    Magoulés, F.5    de La Bourdonnaie, A.6
  • 8
    • 25644456733 scopus 로고    scopus 로고
    • FETI-DPH: a dual-primal domain decomposition method for acoustic scattering
    • Farhat C., Avery P., Tezaur R., and Li J. FETI-DPH: a dual-primal domain decomposition method for acoustic scattering. J. Comput. Acoust. 13 3 (2005) 499-524
    • (2005) J. Comput. Acoust. , vol.13 , Issue.3 , pp. 499-524
    • Farhat, C.1    Avery, P.2    Tezaur, R.3    Li, J.4
  • 9
    • 0037246084 scopus 로고    scopus 로고
    • Optimized Schwarz methods without overlap for the Helmholtz equation
    • Gander M.J., Magoulès F., and Nataf F. Optimized Schwarz methods without overlap for the Helmholtz equation. SIAM J. Sci. Comput. 24 1 (2002) 38-60
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.1 , pp. 38-60
    • Gander, M.J.1    Magoulès, F.2    Nataf, F.3
  • 10
    • 34147136264 scopus 로고    scopus 로고
    • A fast iterative solver for scattering by elastic objects in layered media
    • Ito K., and Toivanen J. A fast iterative solver for scattering by elastic objects in layered media. Appl. Numer. Math. 57 5-7 (2007) 811-820
    • (2007) Appl. Numer. Math. , vol.57 , Issue.5-7 , pp. 811-820
    • Ito, K.1    Toivanen, J.2
  • 11
    • 49349109475 scopus 로고    scopus 로고
    • A domain decomposition solver for acoustic scattering by elastic objects in layered media
    • Ito K., Qiao Z., and Toivanen J. A domain decomposition solver for acoustic scattering by elastic objects in layered media. J. Comput. Phys. 227 19 (2008) 8685-8698
    • (2008) J. Comput. Phys. , vol.227 , Issue.19 , pp. 8685-8698
    • Ito, K.1    Qiao, Z.2    Toivanen, J.3
  • 12
    • 0033233449 scopus 로고    scopus 로고
    • Iterative solution of the Helmholtz equation by a second-order method
    • Otto K., and Larsson E. Iterative solution of the Helmholtz equation by a second-order method. SIAM J. Matrix Anal. Appl. 21 1 (1999) 209-229
    • (1999) SIAM J. Matrix Anal. Appl. , vol.21 , Issue.1 , pp. 209-229
    • Otto, K.1    Larsson, E.2
  • 13
    • 0040571329 scopus 로고    scopus 로고
    • A domain decomposition method for solving a Helmholtz-like problem in elasticity based on the Wilson nonconforming element
    • Bennethum L.S., and Feng X. A domain decomposition method for solving a Helmholtz-like problem in elasticity based on the Wilson nonconforming element. RAIRO Model. Math. Anal. Numer. 31 1 (1997) 1-25
    • (1997) RAIRO Model. Math. Anal. Numer. , vol.31 , Issue.1 , pp. 1-25
    • Bennethum, L.S.1    Feng, X.2
  • 14
    • 19044383720 scopus 로고    scopus 로고
    • An iterative domain decomposition method for the solution of a class of indefinite problems in computational structural dynamics
    • Farhat C., and Li J. An iterative domain decomposition method for the solution of a class of indefinite problems in computational structural dynamics. Appl. Numer. Math. 54 2 (2005) 150-166
    • (2005) Appl. Numer. Math. , vol.54 , Issue.2 , pp. 150-166
    • Farhat, C.1    Li, J.2
  • 15
    • 0034646784 scopus 로고    scopus 로고
    • Domain decomposition method for harmonic wave propagation: a general presentation
    • vistas in domain decomposition and parallel processing in computational mechanics
    • Collino F., Ghanemi S., and Joly P. Domain decomposition method for harmonic wave propagation: a general presentation. Comput. Meth. Appl. Mech. Eng. 184 2-4 (2000) 171-211 vistas in domain decomposition and parallel processing in computational mechanics
    • (2000) Comput. Meth. Appl. Mech. Eng. , vol.184 , Issue.2-4 , pp. 171-211
    • Collino, F.1    Ghanemi, S.2    Joly, P.3
  • 16
    • 0030186069 scopus 로고    scopus 로고
    • Spectral-domain decomposition methods for the solution of acoustic and elastic wave equations
    • Faccioli E., Maggio F., Quarteroni A., and Tagliani A. Spectral-domain decomposition methods for the solution of acoustic and elastic wave equations. Geophysics 61 4 (1996) 1160-1174
    • (1996) Geophysics , vol.61 , Issue.4 , pp. 1160-1174
    • Faccioli, E.1    Maggio, F.2    Quarteroni, A.3    Tagliani, A.4
  • 17
    • 34547525139 scopus 로고    scopus 로고
    • Controllability method for the Helmholtz equation with higher-order discretizations
    • Heikkola E., Mönkölä S., Pennanen A., and Rossi T. Controllability method for the Helmholtz equation with higher-order discretizations. J. Comput. Phys. 225 2 (2007) 1553-1576
    • (2007) J. Comput. Phys. , vol.225 , Issue.2 , pp. 1553-1576
    • Heikkola, E.1    Mönkölä, S.2    Pennanen, A.3    Rossi, T.4
  • 18
    • 42649085363 scopus 로고    scopus 로고
    • Time-harmonic elasticity with controllability and higher-order discretization methods
    • Mönkölä S., Heikkola E., Pennanen A., and Rossi T. Time-harmonic elasticity with controllability and higher-order discretization methods. J. Comput. Phys. 227 11 (2008) 5513-5534
    • (2008) J. Comput. Phys. , vol.227 , Issue.11 , pp. 5513-5534
    • Mönkölä, S.1    Heikkola, E.2    Pennanen, A.3    Rossi, T.4
  • 19
    • 0000657234 scopus 로고    scopus 로고
    • Wave-ray multigrid method for standing wave equations
    • Brandt A., and Livshits I. Wave-ray multigrid method for standing wave equations. Electron. Trans. Numer. Anal. 6 (1997) 162-181
    • (1997) Electron. Trans. Numer. Anal. , vol.6 , pp. 162-181
    • Brandt, A.1    Livshits, I.2
  • 20
    • 0036344991 scopus 로고    scopus 로고
    • A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations
    • Elman H.C., Ernst O.G., and O'Leary D.P. A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations. SIAM J. Sci. Comput. 23 4 (2001) 1291-1315
    • (2001) SIAM J. Sci. Comput. , vol.23 , Issue.4 , pp. 1291-1315
    • Elman, H.C.1    Ernst, O.G.2    O'Leary, D.P.3
  • 21
    • 33746033769 scopus 로고    scopus 로고
    • A novel multigrid based preconditioner for heterogeneous Helmholtz problems
    • Erlangga Y.A., Oosterlee C.W., and Vuik C. A novel multigrid based preconditioner for heterogeneous Helmholtz problems. SIAM J. Sci. Comput. 27 4 (2006) 1471-1492
    • (2006) SIAM J. Sci. Comput. , vol.27 , Issue.4 , pp. 1471-1492
    • Erlangga, Y.A.1    Oosterlee, C.W.2    Vuik, C.3
  • 22
    • 2342579516 scopus 로고    scopus 로고
    • An algebraic multigrid method for linear elasticity
    • Griebel M., Oeltz D., and Schweitzer M.A. An algebraic multigrid method for linear elasticity. SIAM J. Sci. Comput. 25 2 (2003) 385-407
    • (2003) SIAM J. Sci. Comput. , vol.25 , Issue.2 , pp. 385-407
    • Griebel, M.1    Oeltz, D.2    Schweitzer, M.A.3
  • 23
    • 0030369255 scopus 로고    scopus 로고
    • A finite-element capacitance matrix method for exterior Helmholtz problems
    • Ernst O.G. A finite-element capacitance matrix method for exterior Helmholtz problems. Numer. Math. 75 2 (1996) 175-204
    • (1996) Numer. Math. , vol.75 , Issue.2 , pp. 175-204
    • Ernst, O.G.1
  • 24
    • 0003070124 scopus 로고    scopus 로고
    • Fictitious domain methods for the numerical solution of two-dimensional scattering problems
    • Heikkola E., Kuznetsov Y.A., Neittaanmäki P., and Toivanen J. Fictitious domain methods for the numerical solution of two-dimensional scattering problems. J. Comput. Phys. 145 1 (1998) 89-109
    • (1998) J. Comput. Phys. , vol.145 , Issue.1 , pp. 89-109
    • Heikkola, E.1    Kuznetsov, Y.A.2    Neittaanmäki, P.3    Toivanen, J.4
  • 25
    • 0042100716 scopus 로고    scopus 로고
    • A parallel fictitious domain method for the three-dimensional Helmholtz equation
    • Heikkola E., Rossi T., and Toivanen J. A parallel fictitious domain method for the three-dimensional Helmholtz equation. SIAM J. Sci. Comput. 24 5 (2003) 1567-1588
    • (2003) SIAM J. Sci. Comput. , vol.24 , Issue.5 , pp. 1567-1588
    • Heikkola, E.1    Rossi, T.2    Toivanen, J.3
  • 26
    • 0035604025 scopus 로고    scopus 로고
    • Fictitious domains, mixed finite elements and perfectly matched layers for 2D elastic wave propagation
    • ultrasonic field synthesis and modeling (Trieste, 1999
    • Bécache E., Joly P., and Tsogka C. Fictitious domains, mixed finite elements and perfectly matched layers for 2D elastic wave propagation. J. Comput. Acoust. 9 3 (2001) 1175-1201 ultrasonic field synthesis and modeling (Trieste, 1999
    • (2001) J. Comput. Acoust. , vol.9 , Issue.3 , pp. 1175-1201
    • Bécache, E.1    Joly, P.2    Tsogka, C.3
  • 27
    • 0035916190 scopus 로고    scopus 로고
    • Incomplete factorization-based preconditionings for solving the Helmholtz equation
    • Magolu monga Made M. Incomplete factorization-based preconditionings for solving the Helmholtz equation. Int. J. Numer. Meth. Eng. 50 (2001) 1077-1101
    • (2001) Int. J. Numer. Meth. Eng. , vol.50 , pp. 1077-1101
    • Magolu monga Made, M.1
  • 28
    • 0037296994 scopus 로고    scopus 로고
    • Separation-of-variables as a preconditioner for an iterative Helmholtz solver
    • Plessix R.E., and Mulder W.A. Separation-of-variables as a preconditioner for an iterative Helmholtz solver. Appl. Numer. Math. 44 3 (2003) 385-400
    • (2003) Appl. Numer. Math. , vol.44 , Issue.3 , pp. 385-400
    • Plessix, R.E.1    Mulder, W.A.2
  • 29
    • 33747879159 scopus 로고    scopus 로고
    • Numerical methods and nature
    • Turkel E. Numerical methods and nature. J. Sci. Comput. 28 2-3 (2006) 549-570
    • (2006) J. Sci. Comput. , vol.28 , Issue.2-3 , pp. 549-570
    • Turkel, E.1
  • 30
    • 3142611583 scopus 로고    scopus 로고
    • On a class of preconditioners for solving the Helmholtz equation
    • Erlangga Y.A., Vuik C., and Oosterlee C.W. On a class of preconditioners for solving the Helmholtz equation. Appl. Numer. Math. 50 3-4 (2004) 409-425
    • (2004) Appl. Numer. Math. , vol.50 , Issue.3-4 , pp. 409-425
    • Erlangga, Y.A.1    Vuik, C.2    Oosterlee, C.W.3
  • 31
    • 85189837830 scopus 로고    scopus 로고
    • A.L. Laird, M.B. Giles, Preconditioned iterative solution of the 2D Helmholtz equation, Technical Report 02/12, Oxford Computer Laboratory, Oxford, UK, 2002.
    • A.L. Laird, M.B. Giles, Preconditioned iterative solution of the 2D Helmholtz equation, Technical Report 02/12, Oxford Computer Laboratory, Oxford, UK, 2002.
  • 32
    • 0027001298 scopus 로고
    • Eliminating interior resonances in finite element - boundary integral methods for scattering
    • Collins J.D., Jin J.M., and Volakis J.L. Eliminating interior resonances in finite element - boundary integral methods for scattering. IEEE Trans. Antennas Propag. 40 12 (1992) 1583-1585
    • (1992) IEEE Trans. Antennas Propag. , vol.40 , Issue.12 , pp. 1583-1585
    • Collins, J.D.1    Jin, J.M.2    Volakis, J.L.3
  • 33
    • 0001011514 scopus 로고
    • Solving electromagnetic scattering problems at resonance frequencies
    • Murphy W.D., Rokhlin V., and Vassiliou M.S. Solving electromagnetic scattering problems at resonance frequencies. J. Appl. Phys. 67 10 (1990) 6061-6065
    • (1990) J. Appl. Phys. , vol.67 , Issue.10 , pp. 6061-6065
    • Murphy, W.D.1    Rokhlin, V.2    Vassiliou, M.S.3
  • 34
    • 34548405076 scopus 로고    scopus 로고
    • An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation
    • Airaksinen T., Heikkola E., Pennanen A., and Toivanen J. An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation. J. Comput. Phys. 226 1 (2007) 1196-1210
    • (2007) J. Comput. Phys. , vol.226 , Issue.1 , pp. 1196-1210
    • Airaksinen, T.1    Heikkola, E.2    Pennanen, A.3    Toivanen, J.4
  • 35
    • 85189837594 scopus 로고    scopus 로고
    • T. Airaksinen, S. Mönkölä, Comparison between shifted-laplacian preconditioning and controllability method for computational acoustics, J. Comput. Appl. Math. (2008), accepted for publication.
    • T. Airaksinen, S. Mönkölä, Comparison between shifted-laplacian preconditioning and controllability method for computational acoustics, J. Comput. Appl. Math. (2008), accepted for publication.
  • 36
    • 46349085492 scopus 로고    scopus 로고
    • Spectral analysis of the discrete Helmholtz operator preconditioned with a shifted Laplacian
    • van Gijzen M., Erlangga Y., and Vuik C. Spectral analysis of the discrete Helmholtz operator preconditioned with a shifted Laplacian. SIAM J. Sci. Comput. 29 5 (2007) 1942-1958
    • (2007) SIAM J. Sci. Comput. , vol.29 , Issue.5 , pp. 1942-1958
    • van Gijzen, M.1    Erlangga, Y.2    Vuik, C.3
  • 38
    • 85189838306 scopus 로고    scopus 로고
    • E. Turkel, Y. Erlangga, Preconditioning a finite element solver of the exterior Helmholtz equation, in: P. Wesseling, E. Oñate, J. Périaux (Eds.), ECCOMAS CFD, ECCOMAS, 2006.
    • E. Turkel, Y. Erlangga, Preconditioning a finite element solver of the exterior Helmholtz equation, in: P. Wesseling, E. Oñate, J. Périaux (Eds.), ECCOMAS CFD, ECCOMAS, 2006.
  • 39
    • 0000266939 scopus 로고    scopus 로고
    • Algebraic multi-grid for discrete elliptic second-order problems
    • Springer, Berlin
    • Kickinger F. Algebraic multi-grid for discrete elliptic second-order problems. Multigrid Methods V (Stuttgart, 1996) (1998), Springer, Berlin 157-172
    • (1998) Multigrid Methods V (Stuttgart, 1996) , pp. 157-172
    • Kickinger, F.1
  • 40
    • 85189842729 scopus 로고    scopus 로고
    • I. Gustafsson, Modified incomplete Cholesky (MIC) methods, Preconditioning methods: analysis and applications, Top. Comput. Math., vol. 1, Gordon & Breach, New York, 1983, pp. 265-293.
    • I. Gustafsson, Modified incomplete Cholesky (MIC) methods, Preconditioning methods: analysis and applications, Top. Comput. Math., vol. 1, Gordon & Breach, New York, 1983, pp. 265-293.
  • 41
    • 85189842076 scopus 로고    scopus 로고
    • C. Vuik, Y. Erlangga, C. Oosterlee, M. van Gijzen, Complex shifted-Laplace preconditioners for the Helmholtz equation, in: C. Vuik (Ed.), Proceedings of the Ninth Copper Mountain Conference on Iterative Methods, April 2-7, Copper Mountain, CO, USA, 2006.
    • C. Vuik, Y. Erlangga, C. Oosterlee, M. van Gijzen, Complex shifted-Laplace preconditioners for the Helmholtz equation, in: C. Vuik (Ed.), Proceedings of the Ninth Copper Mountain Conference on Iterative Methods, April 2-7, Copper Mountain, CO, USA, 2006.


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