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Volumn 225, Issue 2, 2007, Pages 1553-1576

Controllability method for the Helmholtz equation with higher-order discretizations

Author keywords

Exact controllability; Fourth order Runge Kutta; Helmholtz equation; Mass lumping; Spectral element method

Indexed keywords

ALGEBRA; CONJUGATE GRADIENT METHOD; CONTROLLABILITY; FINITE ELEMENT METHOD; GALERKIN METHODS; HELMHOLTZ EQUATION; LEAST SQUARES APPROXIMATIONS; RUNGE KUTTA METHODS; WAVE EQUATIONS;

EID: 34547525139     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.02.003     Document Type: Article
Times cited : (32)

References (54)
  • 1
    • 28144432041 scopus 로고
    • Accurate finite difference methods for time-harmonic wave propagation
    • Harari I., and Turkel E. Accurate finite difference methods for time-harmonic wave propagation. Journal of Computational Physics 119 (1995) 252-270
    • (1995) Journal of Computational Physics , vol.119 , pp. 252-270
    • Harari, I.1    Turkel, E.2
  • 5
    • 0034345509 scopus 로고    scopus 로고
    • A review of infinite element methods for exterior Helmholtz problems
    • Gerdes K. A review of infinite element methods for exterior Helmholtz problems. Journal of Computational Acoustics 8 1 (2000) 43-62
    • (2000) Journal of Computational Acoustics , vol.8 , Issue.1 , pp. 43-62
    • Gerdes, K.1
  • 6
    • 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. Journal of the Acoustical Society of America 119 3 (2006) 1315-1330
    • (2006) Journal of the Acoustical Society of America , vol.119 , Issue.3 , pp. 1315-1330
    • Thompson, L.L.1
  • 7
    • 0031234450 scopus 로고    scopus 로고
    • A domain decomposition method for the Helmholtz equation and related optimal control problems
    • Benamou J.-D., and Desprès B. A domain decomposition method for the Helmholtz equation and related optimal control problems. Journal of Computational Physics 136 1 (1997) 68-82
    • (1997) Journal of Computational Physics , vol.136 , Issue.1 , pp. 68-82
    • Benamou, J.-D.1    Desprès, B.2
  • 8
  • 9
    • 0034405892 scopus 로고    scopus 로고
    • A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems
    • Farhat C., Macedo A., and Lesoinne M. A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems. Numerische Mathematik 85 2 (2000) 283-308
    • (2000) Numerische Mathematik , vol.85 , Issue.2 , pp. 283-308
    • Farhat, C.1    Macedo, A.2    Lesoinne, M.3
  • 10
    • 6344237441 scopus 로고    scopus 로고
    • Optimal discrete transmission conditions for a nonoverlapping domain decomposition method for the Helmholtz equation
    • Magoulès F., Roux F.-X., and Salmon S. Optimal discrete transmission conditions for a nonoverlapping domain decomposition method for the Helmholtz equation. SIAM Journal on Scientific Computing 25 5 (2004) 1497-1515
    • (2004) SIAM Journal on Scientific Computing , vol.25 , Issue.5 , pp. 1497-1515
    • Magoulès, F.1    Roux, F.-X.2    Salmon, S.3
  • 11
    • 0037199373 scopus 로고    scopus 로고
    • A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. I. Dirichlet boundary conditions
    • Farhat C., and Hetmaniuk U. A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. I. Dirichlet boundary conditions. International Journal for Numerical Methods in Engineering 54 9 (2002) 1309-1332
    • (2002) International Journal for Numerical Methods in Engineering , vol.54 , Issue.9 , pp. 1309-1332
    • Farhat, C.1    Hetmaniuk, U.2
  • 12
    • 0141795689 scopus 로고    scopus 로고
    • A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. II. Neumann boundary conditions
    • Hetmaniuk U., and Farhat C. A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. II. Neumann boundary conditions. International Journal for Numerical Methods in Engineering 58 1 (2003) 63-81
    • (2003) International Journal for Numerical Methods in Engineering , vol.58 , Issue.1 , pp. 63-81
    • Hetmaniuk, U.1    Farhat, C.2
  • 13
    • 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 Journal on Scientific Computing 24 5 (2003) 1567-1588
    • (2003) SIAM Journal on Scientific Computing , vol.24 , Issue.5 , pp. 1567-1588
    • Heikkola, E.1    Rossi, T.2    Toivanen, J.3
  • 14
    • 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 Journal on Scientific Computing 23 4 (2001) 1291-1315
    • (2001) SIAM Journal on Scientific Computing , vol.23 , Issue.4 , pp. 1291-1315
    • Elman, H.C.1    Ernst, O.G.2    O'Leary, D.P.3
  • 15
    • 0037245732 scopus 로고    scopus 로고
    • Multigrid simulation for high-frequency solutions of the Helmholtz problem in heterogeneous media
    • Kim S., and Kim S. Multigrid simulation for high-frequency solutions of the Helmholtz problem in heterogeneous media. SIAM Journal on Scientific Computing 24 2 (2002) 684-701
    • (2002) SIAM Journal on Scientific Computing , vol.24 , Issue.2 , pp. 684-701
    • Kim, S.1    Kim, S.2
  • 17
    • 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. Applied Numerical Mathematics 50 3-4 (2004) 409-425
    • (2004) Applied Numerical Mathematics , vol.50 , Issue.3-4 , pp. 409-425
    • Erlangga, Y.A.1    Vuik, C.2    Oosterlee, C.W.3
  • 18
    • 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 Journal on Scientific Computing 27 4 (2006) 1471-1492
    • (2006) SIAM Journal on Scientific Computing , vol.27 , Issue.4 , pp. 1471-1492
    • Erlangga, Y.A.1    Oosterlee, C.W.2    Vuik, C.3
  • 20
    • 0001299857 scopus 로고    scopus 로고
    • Finite element solution of the Helmholtz equation with high wave number part II: The h-p-version of the FEM
    • Ihlenburg F., and Babuska I. Finite element solution of the Helmholtz equation with high wave number part II: The h-p-version of the FEM. SIAM Journal on Numerical Analysis 34 1 (1997) 315-358
    • (1997) SIAM Journal on Numerical Analysis , vol.34 , Issue.1 , pp. 315-358
    • Ihlenburg, F.1    Babuska, I.2
  • 21
    • 0001254041 scopus 로고    scopus 로고
    • Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?
    • Babuska I.M., and Sauter S.A. Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?. SIAM Journal on Numerical Analysis 34 6 (1997) 2392-2423
    • (1997) SIAM Journal on Numerical Analysis , vol.34 , Issue.6 , pp. 2392-2423
    • Babuska, I.M.1    Sauter, S.A.2
  • 24
    • 1642369052 scopus 로고    scopus 로고
    • A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes
    • Farhat C., Wiedemann-Goiran P., and Tezaur R. A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes. Wave Motion 39 4 (2004) 307-317
    • (2004) Wave Motion , vol.39 , Issue.4 , pp. 307-317
    • Farhat, C.1    Wiedemann-Goiran, P.2    Tezaur, R.3
  • 26
    • 0037436501 scopus 로고    scopus 로고
    • A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime
    • Farhat C., Harari I., and Hetmaniuk U. A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime. Computer Methods in Applied Mechanics and Engineering 192 11-12 (2003) 1389-1419
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.192 , Issue.11-12 , pp. 1389-1419
    • Farhat, C.1    Harari, I.2    Hetmaniuk, U.3
  • 27
    • 0042859901 scopus 로고    scopus 로고
    • Using plane waves as base functions for solving time harmonic equations with the ultra weak variational formulation
    • Cessenat O., and Després B. Using plane waves as base functions for solving time harmonic equations with the ultra weak variational formulation. Journal of Computational Acoustics 11 2 (2003) 227-238
    • (2003) Journal of Computational Acoustics , vol.11 , Issue.2 , pp. 227-238
    • Cessenat, O.1    Després, B.2
  • 28
    • 6344289260 scopus 로고    scopus 로고
    • The perfectly matched layer for the ultra weak variational formulation of the 3D Helmholtz equation
    • Huttunen T., Kaipio J.P., and Monk P. The perfectly matched layer for the ultra weak variational formulation of the 3D Helmholtz equation. International Journal for Numerical Methods in Engineering 61 7 (2004) 1072-1092
    • (2004) International Journal for Numerical Methods in Engineering , vol.61 , Issue.7 , pp. 1072-1092
    • Huttunen, T.1    Kaipio, J.P.2    Monk, P.3
  • 30
    • 0035919547 scopus 로고    scopus 로고
    • Preconditioners for spectral discretizations of Helmholtz's equation with Sommerfeld boundary conditions
    • Pavarino L.F., and Zampieri E. Preconditioners for spectral discretizations of Helmholtz's equation with Sommerfeld boundary conditions. Computer Methods in Applied Mechanics and Engineering 190 40-41 (2001) 5341-5356
    • (2001) Computer Methods in Applied Mechanics and Engineering , vol.190 , Issue.40-41 , pp. 5341-5356
    • Pavarino, L.F.1    Zampieri, E.2
  • 31
    • 0039631248 scopus 로고
    • Using exact controllability to solve the Helmholtz equation at high wave numbers
    • Kleinman R., Angell T., Colton D., Santosa F., and Stakgold I. (Eds), SIAM, Philadelphia, Pennsylvania
    • Bristeau M.O., Glowinski R., and Périaux J. Using exact controllability to solve the Helmholtz equation at high wave numbers. In: Kleinman R., Angell T., Colton D., Santosa F., and Stakgold I. (Eds). Mathematical and Numerical Aspects of Wave Propagation (1993), SIAM, Philadelphia, Pennsylvania 113-127
    • (1993) Mathematical and Numerical Aspects of Wave Propagation , pp. 113-127
    • Bristeau, M.O.1    Glowinski, R.2    Périaux, J.3
  • 32
    • 34547530065 scopus 로고
    • On the numerical solution of the Helmholtz equation at large wave numbers using exact controllability methods. Application to scattering
    • Bristeau M.O., Glowinski R., and Périaux J. On the numerical solution of the Helmholtz equation at large wave numbers using exact controllability methods. Application to scattering. Contemporary Mathematics 157 (1994) 399-419
    • (1994) Contemporary Mathematics , vol.157 , pp. 399-419
    • Bristeau, M.O.1    Glowinski, R.2    Périaux, J.3
  • 33
    • 0039631241 scopus 로고
    • Exact controllability to solve the Helmholtz equation with absorbing boundary conditions
    • Křížek M., Neittaanmäki P., and Stenberg R. (Eds), Marcel Dekker, New York, NY
    • Bristeau M.O., Glowinski R., and Périaux J. Exact controllability to solve the Helmholtz equation with absorbing boundary conditions. In: Křížek M., Neittaanmäki P., and Stenberg R. (Eds). Finite Element Methods: Fifty Years of the Courant Elements (1994), Marcel Dekker, New York, NY 75-93
    • (1994) Finite Element Methods: Fifty Years of the Courant Elements , pp. 75-93
    • Bristeau, M.O.1    Glowinski, R.2    Périaux, J.3
  • 34
    • 84959656664 scopus 로고    scopus 로고
    • Exact and approximate controllability for distributed parameter systems (II)
    • Glowinski R., and Lions J.L. Exact and approximate controllability for distributed parameter systems (II). Acta Numerica (1996) 159-333
    • (1996) Acta Numerica , pp. 159-333
    • Glowinski, R.1    Lions, J.L.2
  • 35
    • 0039243984 scopus 로고    scopus 로고
    • Controllability methods for the computation of time-periodic solutions; application to scattering
    • Bristeau M.O., Glowinski R., and Périaux J. Controllability methods for the computation of time-periodic solutions; application to scattering. Journal of Computational Physics 147 2 (1998) 265-292
    • (1998) Journal of Computational Physics , vol.147 , Issue.2 , pp. 265-292
    • Bristeau, M.O.1    Glowinski, R.2    Périaux, J.3
  • 36
    • 0023966723 scopus 로고
    • Exact controllability, stabilization and perturbations for distributed systems
    • Lions J.L. Exact controllability, stabilization and perturbations for distributed systems. SIAM Review 30 1 (1988) 1-68
    • (1988) SIAM Review , vol.30 , Issue.1 , pp. 1-68
    • Lions, J.L.1
  • 37
    • 34247183852 scopus 로고    scopus 로고
    • Time-periodic solutions of wave equation via controllability and fictitious domain methods
    • Cohen G., Heikkola E., Joly P., and Neittaanmäki P. (Eds), Springer, Jyväskylä, Finland
    • Glowinski R., Périaux J., and Toivanen J. Time-periodic solutions of wave equation via controllability and fictitious domain methods. In: Cohen G., Heikkola E., Joly P., and Neittaanmäki P. (Eds). Mathematical and Numerical Aspects of Wave Propagation, Proceedings of WAVES 2003 (2003), Springer, Jyväskylä, Finland 805-810
    • (2003) Mathematical and Numerical Aspects of Wave Propagation, Proceedings of WAVES 2003 , pp. 805-810
    • Glowinski, R.1    Périaux, J.2    Toivanen, J.3
  • 38
    • 85189845751 scopus 로고    scopus 로고
    • E. Heikkola, S. Mönkölä, A. Pennanen, T. Rossi, Controllability method for acoustic scattering with spectral elements, Journal of Computational and Applied Mathematics, in press.
  • 39
    • 84980151986 scopus 로고
    • Radiation boundary conditions for acoustic and elastic wave calculations
    • Engquist B., and Majda A. Radiation boundary conditions for acoustic and elastic wave calculations. Communications on Pure and Applied Mathematics 32 (1979) 313-357
    • (1979) Communications on Pure and Applied Mathematics , vol.32 , pp. 313-357
    • Engquist, B.1    Majda, A.2
  • 41
    • 48549109395 scopus 로고
    • Spectral element method for fluid dynamics: laminar flow in a channel expansion
    • Patera A.T. Spectral element method for fluid dynamics: laminar flow in a channel expansion. Journal of Computational Physics 15 (1984) 468-488
    • (1984) Journal of Computational Physics , vol.15 , pp. 468-488
    • Patera, A.T.1
  • 42
    • 0024917277 scopus 로고
    • Spectral element methods for the incompressible Navier-Stokes equations
    • Noor A.K., and Oden J.T. (Eds), American Society of Mechanical Engineering, New York
    • Maday Y., and Patera A.T. Spectral element methods for the incompressible Navier-Stokes equations. In: Noor A.K., and Oden J.T. (Eds). State-of-the-art Surveys on Computational Mechanics (1989), American Society of Mechanical Engineering, New York 71-143
    • (1989) State-of-the-art Surveys on Computational Mechanics , pp. 71-143
    • Maday, Y.1    Patera, A.T.2
  • 43
    • 0034190273 scopus 로고    scopus 로고
    • A generalized diagonal mass matrix spectral element method for non-quadrilateral elements
    • Taylor M.A., and Wingate B.A. A generalized diagonal mass matrix spectral element method for non-quadrilateral elements. Applied Numerical Mathematics 33 (2000) 259-265
    • (2000) Applied Numerical Mathematics , vol.33 , pp. 259-265
    • Taylor, M.A.1    Wingate, B.A.2
  • 44
    • 3042777494 scopus 로고    scopus 로고
    • Spectral element methods on triangles and quadrilaterals: comparisons and applications
    • Pasquetti R., and Rapetti F. Spectral element methods on triangles and quadrilaterals: comparisons and applications. Journal of Computational Physics 198 1 (2004) 349-362
    • (2004) Journal of Computational Physics , vol.198 , Issue.1 , pp. 349-362
    • Pasquetti, R.1    Rapetti, F.2
  • 45
    • 34547542773 scopus 로고    scopus 로고
    • A cardinal function algorithm for computing multivariate quadrature points
    • Taylor M.A., Wingate B.A., and Bos L.P. A cardinal function algorithm for computing multivariate quadrature points. SIAM Journal on Numerical Analysis 45 1 (2007) 193-205
    • (2007) SIAM Journal on Numerical Analysis , vol.45 , Issue.1 , pp. 193-205
    • Taylor, M.A.1    Wingate, B.A.2    Bos, L.P.3
  • 47
    • 0027635106 scopus 로고
    • The finite-element modeling of three-dimensional electromagnetic fields using edge and nodal elements
    • Mur G. The finite-element modeling of three-dimensional electromagnetic fields using edge and nodal elements. IEEE Transactions on Antennas and Propagation 41 7 (1993) 948-953
    • (1993) IEEE Transactions on Antennas and Propagation , vol.41 , Issue.7 , pp. 948-953
    • Mur, G.1
  • 49
    • 0001885411 scopus 로고
    • Algebraic multigrid (AMG)
    • McCormick S.F. (Ed), SIAM, Philadelphia, Pennsylvania
    • Ruge J.W., and Stüben K. Algebraic multigrid (AMG). In: McCormick S.F. (Ed). Multigrid Methods Frontiers in Applied Mathematics (1987), SIAM, Philadelphia, Pennsylvania 73-130
    • (1987) Multigrid Methods Frontiers in Applied Mathematics , pp. 73-130
    • Ruge, J.W.1    Stüben, K.2
  • 50
    • 0000266939 scopus 로고    scopus 로고
    • Algebraic multigrid for discrete elliptic second-order problems
    • Springer, Berlin
    • Kickinger F. Algebraic multigrid 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
  • 52
    • 10444290190 scopus 로고    scopus 로고
    • Discrete dispersion relation for hp-version finite element approximation at high wave number
    • Ainsworth M. Discrete dispersion relation for hp-version finite element approximation at high wave number. SIAM Journal on Numerical Analysis 42 2 (2004) 553-575
    • (2004) SIAM Journal on Numerical Analysis , vol.42 , Issue.2 , pp. 553-575
    • Ainsworth, M.1
  • 53
    • 17144423944 scopus 로고    scopus 로고
    • Simulation and experimental measurement of side-aspect target strength of Atlantic salmon (Salmo salar) at high frequency
    • Lilja J., Marjomäki T., Jurvelius J., Rossi T., and Heikkola E. Simulation and experimental measurement of side-aspect target strength of Atlantic salmon (Salmo salar) at high frequency. Canadian Journal of Fisheries and Aquatic Sciences 61 (2004) 2227-2236
    • (2004) Canadian Journal of Fisheries and Aquatic Sciences , vol.61 , pp. 2227-2236
    • Lilja, J.1    Marjomäki, T.2    Jurvelius, J.3    Rossi, T.4    Heikkola, E.5
  • 54
    • 0042233328 scopus 로고    scopus 로고
    • The adaptive computation of far-field patterns by a posteriori error estimation of linear functionals
    • Monk P., and Suli E. The adaptive computation of far-field patterns by a posteriori error estimation of linear functionals. SIAM Journal on Numerical Analysis 36 (1998) 251-274
    • (1998) SIAM Journal on Numerical Analysis , vol.36 , pp. 251-274
    • Monk, P.1    Suli, E.2


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