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Three-field block preconditioners for models of coupled magma/mantle dynamics. (English) Zbl 1327.65055


MSC:

65F08 Preconditioners for iterative methods
76M10 Finite element methods applied to problems in fluid mechanics
86A17 Global dynamics, earthquake problems (MSC2010)
86-08 Computational methods for problems pertaining to geophysics

Software:

FEniCS; BoomerAMG; DOLFIN; ML
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Full Text: DOI arXiv

References:

[1] J. Brown, M. G. Knepley, D. A. May, L. C. McInnes, and B. Smith, Composable linear solvers for multiphysics, in Proceedings of the 11th International Symposium on Parallel and Distributed Computing (ISPDC), 2012, pp. 55–62.
[2] H. C. Elman, D. J. Silvester, and A. J. Wathen, Finite Elements and Fast Iterative Solvers, Numer. Math. Sci. Comput., Oxford University Press, Oxford, UK, 2005. · Zbl 1083.76001
[3] M. W. Gee, C. M. Siefert, J. J. Hu, R. S. Tuminaro, and M. G. Sala, ML 5.0 Smoothed Aggregation Users Guide, Tech. report SAND2006-2649, Sandia National Laboratories, 2006.
[4] P. P. Grinevich and M. A. Olshanskii, An iterative method for the Stokes-type problem with variable viscosity, SIAM J. Sci. Comput., 31 (2009), pp. 3939–3978. · Zbl 1410.76290
[5] V. E. Henson and U. M. Yang, BoomerAMG: A parallel algebraic multigrid solver and preconditioner, Appl. Numer. Math., 41 (2002), pp. 155–177. · Zbl 0995.65128
[6] R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed., Cambridge University Press, Cambridge, UK, 2013. · Zbl 1267.15001
[7] R. F. Katz, M. G. Knepley, B. Smith, M. Spiegelman, and E. T. Coon, Numerical simulation of geodynamic processes with the portable extensible toolkit for scientific computation, Phys. Earth Planet. In., 163 (2007), pp. 52–68.
[8] T. Keller, D. A. May, and B. J. P. Kaus, Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust, Geophys. J. Int., 195 (2013), pp. 1406–1442.
[9] A. Klawonn, Block-triangular preconditioners for saddle point problems with a penalty term, SIAM J. Sci. Comput., 19 (1998), pp. 172–184. · Zbl 0917.73069
[10] A. Logg, K.-A. Mardal, and G. N. Wells, eds., Automated Solution of Differential Equations by the Finite Element Method, Lect. Notes Comput. Sci. Eng. 84, Springer, New York, 2012. · Zbl 1247.65105
[11] A. Logg and G. N. Wells, DOLFIN: Automated finite element computing, ACM Trans. Math. Software, 37 (2010), pp. 20:1–20:28. · Zbl 1364.65254
[12] D. McKenzie, The generation and compaction of partially molten rock, J. Petrol., 25 (1984), pp. 713–765.
[13] S. Rhebergen and G. N. Wells, Supporting computer code, http://www.repository.cam.ac.uk/handle/1810/248270, (2015).
[14] S. Rhebergen, G. N. Wells, R. F. Katz, and A. J. Wathen, Analysis of block-preconditioners for models of coupled magma/mantle dynamics, SIAM J. Sci. Comput., 36 (2014), pp. A1960–A1977. · Zbl 1299.86001
[15] Y. Takei and R. F. Katz, Consequences of viscous anisotropy in a deforming, two-phase aggregate: Part 1. Governing equations and linearised analysis, J. Fluid Mech., 734 (2013), pp. 424–455. · Zbl 1294.76243
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