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Keywords:
elasticity; advection; FEM; error estimates; saddle point problem; iterative methods
elasticity; advection; FEM; error estimates; saddle point problem; iterative methods
Summary:
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.
References:
[1] O. Axelsson, V. A. Barker: Finite Element Solution of Boundary Value Problems. Theory and Computation. Academic Press, Orlando, 1984. MR 0758437
[2] O. Axelsson, M. Neytcheva: Preconditioning methods for constrained optimization problems. Numer. Linear Algebra Appl. 10 (2003), 3–31. DOI 10.1002/nla.310 | MR 1964284
[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. DOI 10.3846/13926292.2001.9637141 | MR 1906506
[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. DOI 10.1002/(SICI)1097-0207(19990228)44:6<801::AID-NME525>3.0.CO;2-Y | MR 1672010
[5] M. Benzi, G. Golub, and J. Liesen: Numerical solution of saddle point problems. Acta Numer (to appear). MR 2168342
[6] W. Bangerth, R. Hartmann, and G. Kanschat: deal.II Differential Equations Analysis Library, Technical Reference, IWR, http://www.dealii.org</b>
[7] H. C. Elman: Preconditioning for the steady-state Navier-Stokes equations with low viscosity. SIAM J. Sci. Comput. 20 (1999), 1299–1316. DOI 10.1137/S1064827596312547 | MR 1675474 | Zbl 0935.76057
[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. DOI 10.1023/B:BITN.0000014565.86918.df | MR 2058878
[9] H. C. Elman, D. Silvester: Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations. SIAM J. Sci. Comput. 17 (1996), 33–46. DOI 10.1137/0917004 | MR 1375264
[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. DOI 10.1007/s002110100300 | MR 1888834
[11] I. Ipsen: A note on preconditioning nonsymmetric matrices. SIAM J. Sci. Comput. 23 (2001), 1050–1051. DOI 10.1137/S1064827500377435 | MR 1860977 | Zbl 0998.65049
[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. DOI 10.1137/S1064827595279575 | MR 1618832
[13] A. Klawonn, G. Starke: Block triangular preconditioners for nonsymmetric saddle point problems: Field-of-values analysis. Numer. Math. 81 (1999), 577–594. DOI 10.1007/s002110050405 | MR 1675216
[14] V. Klemann, P. Wu, and D. Wolf: Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models. Geophys. J. 153 (2003), 569–585. DOI 10.1046/j.1365-246X.2003.01920.x
[15] J. K. Kraus: Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Submitted.
[16] B. Liu, R. B. Kellogg: Discontinuous solutions of linearized steady state viscous compressible flows. J. Math. Anal. Appl. 180 (1993), 469–497. DOI 10.1006/jmaa.1993.1412 | MR 1251871
[17] D. Loghin, A. J. Wathen: Analysis of preconditioners for saddle-point problems. SIAM J. Sci. Comput. 25 (2004), 2029–2049. DOI 10.1137/S1064827502418203 | MR 2086829
[18] J. Nedoma: Numerical Modelling in Applied Geodynamics. John Wiley & Sons, New York, 2000.
[19] A. A. Ramage: A multigrid preconditioner for stabilised discretisations of advection-diffusion problems. J. Comput. Appl. Math. 110 (1999), 187–203. DOI 10.1016/S0377-0427(99)00234-4 | MR 1715555 | Zbl 0939.65135
[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.
[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
[22] P. Wu: Viscoelastic versus viscous deformation and the advection of pre-stress. Internat. J. Geophys. 108 (1992), 136–142. DOI 10.1111/j.1365-246X.1992.tb00844.x
[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. DOI 10.1111/j.1365-246X.2004.02338.x
[24] Portable, Extensible Toolkit for Scientific computation (PETSc) suite. Mathematics and Computer Science Division, Argonne Natinal Laboratory,.
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