Time-harmonic elasticity with controllability and higher-order discretization methods

Journal of Computational Physics

Volumn 227, Issue 11, 2008, Pages 5513-5534

  Mönkölä, Sanna ^a   Heikkola, Erkki ^b   Pennanen, Anssi ^a   Rossi, Tuomo ^a  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

^b Numerola Oy   (Finland)

Author keywords

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

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DISCRETE EVENT SIMULATION; ELASTIC WAVES; HARMONIC ANALYSIS; LINEAR SYSTEMS; RUNGE KUTTA METHODS; WAVE EQUATIONS;

DISCRETIZATION METHOD; ELASTIC WAVE EQUATIONS; EXACT CONTROLLABILITY; FOURTH-ORDER RUNGE-KUTTA; HIGHER ORDER DISCRETIZATION; INITIAL CONDITIONS; MASS-LUMPING; NAVIER EQUATIONS; SPECTRAL ELEMENT METHOD; TIME-HARMONIC;

CONTROLLABILITY;

EID: 42649085363     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.01.054     Document Type: Article

References (35)

1. L.D. Landau E.M. Lifshitz Theory of Elasticity 1975 Pergamon Press Oxford
2. L.S. Bennethum X. Feng A domain decomposition method for solving a Helmholtz-like problem in elasticity based on the Wilson nonconforming element RAIRO Modélisation Mathématique et Analyse Numérique 31 1997 1 25
3. C. Farhat J. Li An iterative domain decomposition method for the solution of a class of indefinite problems in computational structural dynamics Applied Numerical Mathematics 54 2005 150 166
4. S. Collino F. Ghanemi P. Joly Domain decomposition method for harmonic wave propagation: a general presentation Computer Methods in Applied Mechanics and Engineering 184 2–4 2000 171 211
5. E. Faccioli F. Maggio A. Quarteroni A. Tagliani Spectral domain decomposition methods for the solution of acoustic and elastic wave propagation Geophysics 61 1996 1160 1174
6. E. Bécache P. Joly C. Tsogka Application of the fictitious domain method to 2D linear elastodynamic problems Journal of Computational Acoustics 9 3 2001 1175 1202
7. W. Hackbusch Multigrid Methods and Applications 1985 Springer-Verlag Berlin, Germany
8. U. Trottenberg C.W. Oosterlee A. Schüller Multigrid 2001 Academic Press London
9. D.S. Bindel S. Govindjee Elastic PMLs for resonator anchor loss simulation International Journal for Numerical Methods in Engineering 64 6 2005 789 818
10. G.K. Gächter M.J. Grote Dirichlet-to-Neumann map for three-dimensional elastic waves Wave Motion 37 3 2003 293 311
11. I. Harari U. Albocher Studies of FE/PML for exterior problems of time-harmonic elastic waves Computer Methods in Applied Mechanics and Engineering 195 29–32 2006 3854 3879
12. O. Cessenat B. Després 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
13. T. Huttunen P. Monk F. Collino J. Kaipio The ultra-weak variational formulation for elastic wave problems SIAM Journal on Scientific Computing 25 5 2004 1717 1742
14. I. Harari S. Haham Improved finite element methods for elastic waves Computer Methods in Applied Mechanics and Engineering 166 1–2 1998 143 164
15. L. Zhang R. Tezaur C. Farhat The discontinuous enrichment method for elastic wave propagation in the medium-frequency regime International Journal for Numerical Methods in Engineering 66 13 2006 2086 2114
16. M. Käser M. Dumbser An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes I: the two-dimensional isotropic case with external source terms Geophysical Journal International 166 2 2006 855 877
17. B. Cockburn G.E. Karniadakis C.-W. Shu Discontinuous Galerkin Methods: Theory Computation and Applications 2000 Springer-Verlag Berlin
18. A. Cividini A. Quarteroni E. Zampieri Numerical solution of linear elastic problems by spectral collocation methods Computer Methods in Applied Mechanics and Engineering 104 1 1993 49 76
19. R. Glowinski J.L. Lions Exact and approximate controllability for distributed parameter systems (II) Acta Numerica 1995 159 333
20. M.O. Bristeau R. Glowinski J. Périaux Controllability methods for the computation of time-periodic solutions; application to scattering Journal of Computational Physics 147 2 1998 265 292
21. E. Heikkola S. Mönkölä A. Pennanen T. Rossi Controllability method for acoustic scattering with spectral elements Journal of Computational and Applied Mathematics 204 2 2007 344 355
22. E. Heikkola S. Mönkölä A. Pennanen T. Rossi Controllability method for the Helmholtz equation with higher-order discretizations Journal of Computational Physics 225 2 2007 1553 1576
23. G. Cohen Higher-Order Numerical Methods for Transient Wave Equations 2001 Springer-Verlag Berlin
24. D. Komatitsch J.P. Vilotte R. Vai J.M. Castillo-Covarrubias F.J. Sánchez-Sesma The spectral element method for elastic wave equations: application to 2D and 3D seismic problems International Journal for Numerical Methods in Engineering 45 1999 1139 1164
25. M.O. Bristeau R. Glowinski J. Périaux Using exact controllability to solve the Helmholtz equation at high wave numbers R. Kleinman T. Angell D. Colton F. Santosa I. Stakgold Mathematical and Numerical Aspects of Wave Propagation 1993 SIAM Philadelphia, Pennsylvania 113 127
26. J. Martikainen, A. Pennanen, T. Rossi, Application of an algebraic multigrid method to incompressible flow problems, Reports of the Department of Mathematical Information Technology, Series B. Scientific Computing, B 2/2006, Department of Mathematical Information Technology, University of Jyväskylä, 2006.
27. T. Airaksinen E. Heikkola A. Pennanen J. Toivanen An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation Journal of Computational Physics 226 2007 1196 1210
28. C.P.A. Wapenaar A.J. Berkhout Elastic Wave Field Extrapolation: Redatuming of Single and Multi-Component Seismic Data 1989 Elsevier Amsterdam
29. B. Engquist A. Majda Radiation boundary conditions for acoustic and elastic wave calculations Communications on Pure and Applied Mathematics 32 1979 313 357
30. A. Quarteroni T. Tagliani E. Zampieri Generalized Galerkin approximations of elastic waves with absorbing boundary conditions Computer Methods in Applied Mechanics and Engineering 163 1998 323 341
31. D. Komatitsch R. Martin J. Tromp M.A. Taylor B.A. Wingate Wave propagation in 2-D elastic media using a spectral element method with triangles and quadrangles Journal of Computational Acoustics 9 2 2001 703 718
32. G. Mur 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
33. F. Kickinger Algebraic multigrid for discrete elliptic second-order problems Multigrid Methods V (Stuttgart, 1996) 1998 Springer-Verlag Berlin 157 172
34. J. Heys T. Manteuffel S. McCormick L. Olson Algebraic multigrid for higher-order finite elements Journal of Computational Physics 204 2 2005 520 532
35. Y. Saad Iterative Methods for Sparse Linear Systems second ed. 2003 SIAM Philadelphia