Numerical simulations of glacial rebound using preconditioned iterative solution methods

Erik Bängtsson; Maya Neytcheva

Applications of Mathematics (2005)

  • Volume: 50, Issue: 3, page 183-201
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Bängtsson, Erik, and Neytcheva, Maya. "Numerical simulations of glacial rebound using preconditioned iterative solution methods." Applications of Mathematics 50.3 (2005): 183-201. <http://eudml.org/doc/33217>.

@article{Bängtsson2005,
abstract = {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.},
author = {Bängtsson, Erik, Neytcheva, Maya},
journal = {Applications of Mathematics},
keywords = {elasticity; advection; FEM; error estimates; saddle point problem; iterative methods; elasticity; advection; FEM; error estimates; saddle point problem; iterative methods},
language = {eng},
number = {3},
pages = {183-201},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical simulations of glacial rebound using preconditioned iterative solution methods},
url = {http://eudml.org/doc/33217},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Bängtsson, Erik
AU - Neytcheva, Maya
TI - Numerical simulations of glacial rebound using preconditioned iterative solution methods
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 3
SP - 183
EP - 201
AB - 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.
LA - eng
KW - elasticity; advection; FEM; error estimates; saddle point problem; iterative methods; elasticity; advection; FEM; error estimates; saddle point problem; iterative methods
UR - http://eudml.org/doc/33217
ER -

References

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  1. Finite Element Solution of Boundary Value Problems. Theory and Computation, Academic Press, Orlando, 1984. (1984) MR0758437
  2. 10.1002/nla.310, Numer. Linear Algebra Appl. 10 (2003), 3–31. (2003) MR1964284DOI10.1002/nla.310
  3. 10.3846/13926292.2001.9637141, Math. Model. Anal. 6 (2001), 7–27. (2001) MR1906506DOI10.3846/13926292.2001.9637141
  4. 10.1002/(SICI)1097-0207(19990228)44:6<801::AID-NME525>3.0.CO;2-Y, Int. J.  Numer. Methods Eng. 44 (1999), 801–818. (1999) MR1672010DOI10.1002/(SICI)1097-0207(19990228)44:6<801::AID-NME525>3.0.CO;2-Y
  5. Numerical solution of saddle point problems, Acta Numer (to appear). (to appear) MR2168342
  6. deal.II Differential Equations Analysis Library, Technical Reference, IWR, http://www.dealii.org, . 
  7. 10.1137/S1064827596312547, SIAM J.  Sci. Comput. 20 (1999), 1299–1316. (1999) Zbl0935.76057MR1675474DOI10.1137/S1064827596312547
  8. 10.1023/B:BITN.0000014565.86918.df, BIT 43 (2003), 961–974. (2003) MR2058878DOI10.1023/B:BITN.0000014565.86918.df
  9. 10.1137/0917004, SIAM J.  Sci. Comput. 17 (1996), 33–46. (1996) MR1375264DOI10.1137/0917004
  10. 10.1007/s002110100300, Numer. Math. 90 (2002), 665–688. (2002) MR1888834DOI10.1007/s002110100300
  11. 10.1137/S1064827500377435, SIAM J.  Sci. Comput. 23 (2001), 1050–1051. (2001) Zbl0998.65049MR1860977DOI10.1137/S1064827500377435
  12. 10.1137/S1064827595279575, SIAM J.  Sci. Comput 19 (1998), 540–552. (1998) MR1618832DOI10.1137/S1064827595279575
  13. 10.1007/s002110050405, Numer. Math. 81 (1999), 577–594. (1999) MR1675216DOI10.1007/s002110050405
  14. 10.1046/j.1365-246X.2003.01920.x, Geophys. J. 153 (2003), 569–585. (2003) DOI10.1046/j.1365-246X.2003.01920.x
  15. Algebraic multilevel preconditioning of finite element matrices using local Schur complements, Submitted. 
  16. 10.1006/jmaa.1993.1412, J.  Math. Anal. Appl. 180 (1993), 469–497. (1993) MR1251871DOI10.1006/jmaa.1993.1412
  17. 10.1137/S1064827502418203, SIAM J.  Sci. Comput. 25 (2004), 2029–2049. (2004) MR2086829DOI10.1137/S1064827502418203
  18. Numerical Modelling in Applied Geodynamics, John Wiley & Sons, New York, 2000. (2000) 
  19. 10.1016/S0377-0427(99)00234-4, J.  Comput. Appl. Math. 110 (1999), 187–203. (1999) Zbl0939.65135MR1715555DOI10.1016/S0377-0427(99)00234-4
  20. SPARSKIT: A basic tool-kit for sparse matrix computations, Technical Documentation, http://www-users.cs.umn.edu/saad/software/SPARSKIT/sparskit.html. 
  21. Numerical techniques for the treatment of quasistatic viscoelastic stress problems in linear isotropic solids, Comput. Methods Appl. Mech. Eng. 118 (1994), 211–237. (1994) MR1298954
  22. 10.1111/j.1365-246X.1992.tb00844.x, Internat. J.  Geophys. 108 (1992), 136–142. (1992) DOI10.1111/j.1365-246X.1992.tb00844.x
  23. 10.1111/j.1365-246X.2004.02338.x, Internat. J.  Geophys. 158 (2004), 401–408. (2004) DOI10.1111/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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