Title:
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Numerical simulations of glacial rebound using preconditioned iterative solution methods (English) |
Author:
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Bängtsson, Erik |
Author:
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Neytcheva, Maya |
Language:
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English |
Journal:
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Applications of Mathematics |
ISSN:
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0862-7940 (print) |
ISSN:
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1572-9109 (online) |
Volume:
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50 |
Issue:
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3 |
Year:
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2005 |
Pages:
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183-201 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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This paper discusses finite element discretization and preconditioning strategies for the iterative solution of nonsymmetric indefinite linear algebraic systems of equations arising in modelling of glacial rebound processes. Some numerical experiments for the purely elastic model setting are provided. Comparisons of the performance of the iterative solution method with a direct solution method are included as well. (English) |
Keyword:
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elasticity |
Keyword:
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advection |
Keyword:
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FEM |
Keyword:
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error estimates |
Keyword:
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saddle point problem |
Keyword:
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iterative methods |
MSC:
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65F10 |
MSC:
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86-08 |
MSC:
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86A40 |
idZBL:
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Zbl 1099.65030 |
idMR:
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MR2133726 |
DOI:
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10.1007/s10492-005-0013-3 |
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Date available:
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2009-09-22T18:21:53Z |
Last updated:
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2020-07-02 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/134602 |
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Reference:
|
[1] O. Axelsson, V. A. Barker: Finite Element Solution of Boundary Value Problems. Theory and Computation.Academic Press, Orlando, 1984. MR 0758437 |
Reference:
|
[2] O. Axelsson, M. Neytcheva: Preconditioning methods for constrained optimization problems.Numer. Linear Algebra Appl. 10 (2003), 3–31. MR 1964284, 10.1002/nla.310 |
Reference:
|
[3] O. Axelsson, V. A. Barker, M. Neytcheva, and B. Polman: Solving the Stokes problem on a massively parallel computer.Math. Model. Anal. 6 (2001), 7–27. MR 1906506, 10.3846/13926292.2001.9637141 |
Reference:
|
[4] O. Axelsson, A. Padiy: On a robust and scalable linear elasticity solver based on a saddle point formulation.Int. J. Numer. Methods Eng. 44 (1999), 801–818. MR 1672010, 10.1002/(SICI)1097-0207(19990228)44:6<801::AID-NME525>3.0.CO;2-Y |
Reference:
|
[5] M. Benzi, G. Golub, and J. Liesen: Numerical solution of saddle point problems.Acta Numer (to appear). MR 2168342 |
Reference:
|
[6] W. Bangerth, R. Hartmann, and G. Kanschat: deal.II Differential Equations Analysis Library, Technical Reference, IWR, http://www.dealii.org.. |
Reference:
|
[7] H. C. Elman: Preconditioning for the steady-state Navier-Stokes equations with low viscosity.SIAM J. Sci. Comput. 20 (1999), 1299–1316. Zbl 0935.76057, MR 1675474, 10.1137/S1064827596312547 |
Reference:
|
[8] H. C. Elman, D. Loghin, A. J. Wathen: Preconditioning techniques for Newton’s method for the incompressible Navier-Stokes equations.BIT 43 (2003), 961–974. MR 2058878, 10.1023/B:BITN.0000014565.86918.df |
Reference:
|
[9] H. C. Elman, D. Silvester: Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations.SIAM J. Sci. Comput. 17 (1996), 33–46. MR 1375264, 10.1137/0917004 |
Reference:
|
[10] H. Elman, D. Silvester, A. J. Wathen: Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations.Numer. Math. 90 (2002), 665–688. MR 1888834, 10.1007/s002110100300 |
Reference:
|
[11] I. Ipsen: A note on preconditioning nonsymmetric matrices.SIAM J. Sci. Comput. 23 (2001), 1050–1051. Zbl 0998.65049, MR 1860977, 10.1137/S1064827500377435 |
Reference:
|
[12] A. Klawonn: An optimal preconditioners for a class of saddle point problems with a penalty term.SIAM J. Sci. Comput 19 (1998), 540–552. MR 1618832, 10.1137/S1064827595279575 |
Reference:
|
[13] A. Klawonn, G. Starke: Block triangular preconditioners for nonsymmetric saddle point problems: Field-of-values analysis.Numer. Math. 81 (1999), 577–594. MR 1675216, 10.1007/s002110050405 |
Reference:
|
[14] V. Klemann, P. Wu, and D. Wolf: Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models.Geophys. J. 153 (2003), 569–585. 10.1046/j.1365-246X.2003.01920.x |
Reference:
|
[15] J. K. Kraus: Algebraic multilevel preconditioning of finite element matrices using local Schur complements.Submitted. |
Reference:
|
[16] B. Liu, R. B. Kellogg: Discontinuous solutions of linearized steady state viscous compressible flows.J. Math. Anal. Appl. 180 (1993), 469–497. MR 1251871, 10.1006/jmaa.1993.1412 |
Reference:
|
[17] D. Loghin, A. J. Wathen: Analysis of preconditioners for saddle-point problems.SIAM J. Sci. Comput. 25 (2004), 2029–2049. MR 2086829, 10.1137/S1064827502418203 |
Reference:
|
[18] J. Nedoma: Numerical Modelling in Applied Geodynamics.John Wiley & Sons, New York, 2000. |
Reference:
|
[19] A. A. Ramage: A multigrid preconditioner for stabilised discretisations of advection-diffusion problems.J. Comput. Appl. Math. 110 (1999), 187–203. Zbl 0939.65135, MR 1715555, 10.1016/S0377-0427(99)00234-4 |
Reference:
|
[20] Y. Saad: SPARSKIT: A basic tool-kit for sparse matrix computations.Technical Documentation, http://www-users.cs.umn.edu/$\sim $saad/software/SPARSKIT/sparskit.html. |
Reference:
|
[21] S. Shaw, M. K. Warby, J. R. Whiteman, C. Dawson, and M. F. Wheeler: Numerical techniques for the treatment of quasistatic viscoelastic stress problems in linear isotropic solids.Comput. Methods Appl. Mech. Eng. 118 (1994), 211–237. MR 1298954 |
Reference:
|
[22] P. Wu: Viscoelastic versus viscous deformation and the advection of pre-stress.Internat. J. Geophys. 108 (1992), 136–142. 10.1111/j.1365-246X.1992.tb00844.x |
Reference:
|
[23] P. Wu: Using commercial finite element packages for the study of earth deformations, sea levels and the state of stress.Internat. J. Geophys. 158 (2004), 401–408. 10.1111/j.1365-246X.2004.02338.x |
Reference:
|
[24] : Portable, Extensible Toolkit for Scientific computation (PETSc) suite.Mathematics and Computer Science Division, Argonne Natinal Laboratory,. |
. |