메뉴 건너뛰기




Volumn 10, Issue 9, 2009, Pages

Scalable robust solvers for unstructured FE geodynamic modeling applications: Solving the Stokes equation for models with large localized viscosity contrasts

Author keywords

Algebraic multigrid; Incompressible stokes; Parallel solvers; Preconditioners; Unstructured grid; Viscosity contrast

Indexed keywords


EID: 72049125620     PISSN: 15252027     EISSN: 15252027     Source Type: Journal    
DOI: 10.1029/2009GC002526     Document Type: Article
Times cited : (29)

References (40)
  • 1
    • 0000014842 scopus 로고
    • The multigrid method for the diffusion equation with strongly discontinuous coefficients
    • Alcouffe, R., A. Brandt, J. E. Dendy, and J. Painter (1981), The multigrid method for the diffusion equation with strongly discontinuous coefficients, SIAM J. Sci. Stat. Comput., 2, 430-454.
    • (1981) SIAM J. Sci. Stat. Comput. , vol.2 , pp. 430-454
    • Alcouffe, R.1    Brandt, A.2    Dendy, J.E.3    Painter, J.4
  • 2
    • 0033884893 scopus 로고    scopus 로고
    • Multifrontal parallel distributed symmetric and unsymmetric solvers
    • Amestoy, P., I. Duff, and J. L'Excellent (2000), Multifrontal parallel distributed symmetric and unsymmetric solvers, Comput. Meth. Appl. Mech. Eng., 184, 501-520.
    • (2000) Comput. Meth. Appl. Mech. Eng. , vol.184 , pp. 501-520
    • Amestoy, P.1    Duff, I.2    L'Excellent, J.3
  • 4
    • 0001124450 scopus 로고
    • Three-dimensional treatment of convective flow in the Earth's mantle
    • Baumgardner, J. (1985), Three-dimensional treatment of convective flow in the Earth's mantle, J. Stat. Phys., 39, 501-511.
    • (1985) J. Stat. Phys. , vol.39 , pp. 501-511
    • Baumgardner, J.1
  • 5
    • 20044390432 scopus 로고    scopus 로고
    • Numerical solution of saddle point problems
    • Benzi, M., G. Golubt, and J. Liesen (2005), Numerical solution of saddle point problems, Acta Numerica, 14, 1-137.
    • (2005) Acta Numerica , vol.14 , pp. 1-137
    • Benzi, M.1    Golubt, G.2    Liesen, J.3
  • 6
    • 84966214346 scopus 로고
    • A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems
    • Bramble, J. H., and J. E. Pasciak (1988), A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems, Math. Comput., 50(181), 1-17.
    • (1988) Math. Comput. , vol.50 , Issue.181 , pp. 1-17
    • Bramble, J.H.1    Pasciak, J.E.2
  • 7
    • 55649087107 scopus 로고    scopus 로고
    • DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems
    • doi:10.1016/j.pepi.2008.05.003
    • Braun, J., C. Thieulot, P. Fullsack, M. DeKool, C. Beaumont, and R. Huismans (2008), DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems, Phys. Earth Planet. Inter., 171(1-4), 76-91, doi:10.1016/j.pepi.2008.05.003.
    • (2008) Phys. Earth Planet. Inter. , vol.171 , Issue.1-4 , pp. 76-91
    • Braun, J.1    Thieulot, C.2    Fullsack, P.3    DeKool, M.4    Beaumont, C.5    Huismans, R.6
  • 9
    • 63249129443 scopus 로고    scopus 로고
    • Parallel scalable adjoint-based adaptive solution for variable-viscosity Stokes flows
    • Burstedde, C., O. Ghattas, G. Stadler, T. Tu, and L. Wilcox (2009), Parallel scalable adjoint-based adaptive solution for variable-viscosity Stokes flows, Comput. Meth. Appl. Mech. Eng., 198, 1691-1700.
    • (2009) Comput. Meth. Appl. Mech. Eng. , vol.198 , pp. 1691-1700
    • Burstedde, C.1    Ghattas, O.2    Stadler, G.3    Tu, T.4    Wilcox, L.5
  • 10
    • 34447262603 scopus 로고    scopus 로고
    • Dipus: A new tool to study the dynamics of planetary interiors
    • Choblet, G., O. Čadek, F. Couturier, and C. Dumoulin (2007), dipus: A new tool to study the dynamics of planetary interiors, Geophys. J. Int., 170(1), 9-30.
    • (2007) Geophys. J. Int. , vol.170 , Issue.1 , pp. 9-30
    • Choblet, G.1    Čadek, O.2    Couturier, F.3    Dumoulin, C.4
  • 12
    • 0026918640 scopus 로고
    • An ILU preconditioner with coupled node fill-in for iterative solution of the mixed finite element formulation of the 2D and 3D Navier-Stokes equations, Int. J
    • doi:10.1002/fld.1650150503
    • Dahl, O., and S. Ø. Wille (1992), An ILU preconditioner with coupled node fill-in for iterative solution of the mixed finite element formulation of the 2D and 3D Navier-Stokes equations, Int. J, Numer. Meth. Fluids, 15(5), 525 - 544, doi:10.1002/fld.1650150503.
    • (1992) Numer. Meth. Fluids , vol.15 , Issue.5 , pp. 525-544
    • Dahl, O.1    Wille S., Ø.2
  • 13
    • 0002160502 scopus 로고    scopus 로고
    • Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations
    • doi:10.1.1.25.265
    • Elman, H., and D. Silvester (1996), Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations, SIAM J. Sci. Comput., 17, 33-46, doi:10.1.1.25.265.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 33-46
    • Elman, H.1    Silvester, D.2
  • 14
    • 33750818187 scopus 로고    scopus 로고
    • An introduction to algebraic multigrid computing
    • Falgout, R. (2006), An introduction to algebraic multigrid computing, Comput. Sci. Eng., 8(6), 24-33.
    • (2006) Comput. Sci. Eng. , vol.8 , Issue.6 , pp. 24-33
    • Falgout, R.1
  • 17
    • 72049122314 scopus 로고    scopus 로고
    • Large scale, high resolution, mantle dynamics modeling
    • Fall Meet. Abstract T51B-0546
    • Geenen, T., A. P. Van Den Berg, and W. Spakman (2007), Large scale, high resolution, mantle dynamics modeling, Eos Trans. AGU, 88(52), Fall Meet. Suppl., Abstract T51B-0546.
    • (2007) Eos Trans. AGU , vol.88 , Issue.52 SUPPL.
    • Geenen, T.1    Van Den Berg, A.P.2    Spakman, W.3
  • 18
    • 72049090030 scopus 로고    scopus 로고
    • Scalable robust solvers for 3D unstructured modeling applications, solving the Stokes equation with large, localized, viscosity contrasts, abstract EGU2008-A-09460
    • presented at
    • Geenen, T., A. P. Van Den Berg, and W. Spakman (2008), Scalable robust solvers for 3D unstructured modeling applications, solving the Stokes equation with large, localized, viscosity contrasts, abstract EGU2008-A-09460 presented at European Geosciences Union General Assembly 2008, Vienna.
    • (2008) European Geosciences Union General Assembly 2008, Vienna
    • Geenen, T.1    Van Den Berg, A.P.2    Spakman, W.3
  • 19
    • 42449112999 scopus 로고    scopus 로고
    • Smoothed aggregation multigrid for a Stokes problem
    • Janka, A. (2008), Smoothed aggregation multigrid for a Stokes problem, Comput. Visual. Sci., 11(3), 169-180.
    • (2008) Comput. Visual. Sci. , vol.11 , Issue.3 , pp. 169-180
    • Janka, A.1
  • 20
    • 55649094185 scopus 로고    scopus 로고
    • Multigridbased simulation code for mantle convection in spherical shell using Yin-Yang grid
    • Kameyama, M., A. Kageyama, and T. Sato (2008), Multigridbased simulation code for mantle convection in spherical shell using Yin-Yang grid, Phys. Earth Planet. Inter., 171(1-4), 19-32.
    • (2008) Phys. Earth Planet. Inter. , vol.171 , Issue.1-4 , pp. 19-32
    • Kameyama, M.1    Kageyama, A.2    Sato, T.3
  • 22
    • 53549099921 scopus 로고    scopus 로고
    • Fast and robust solvers for pressure correction in bubbly flow problems
    • MacLachlan, S., J. Tang, and C. Vuik (2008), Fast and robust solvers for pressure correction in bubbly flow problems, J. Comput. Phys., 227, 9742-9761.
    • (2008) J. Comput. Phys. , vol.227 , pp. 9742-9761
    • MacLachlan, S.1    Tang, J.2    Vuik, C.3
  • 23
    • 55649096865 scopus 로고    scopus 로고
    • Preconditioned iterative methods for Stokes flow problems arising in computational geodynamics
    • May, D., and L. Moresi (2008), Preconditioned iterative methods for Stokes flow problems arising in computational geodynamics, Phys. Earth Planet. Inter., 171(1-4), 33-47.
    • (2008) Phys. Earth Planet. Inter. , vol.171 , Issue.1-4 , pp. 33-47
    • May, D.1    Moresi, L.2
  • 24
    • 0030432216 scopus 로고    scopus 로고
    • The accuracy of finite element solutions of Stokes' flow with strongly varying viscosity
    • Moresi, L., S. Zhong, and M. Gurnis (1996), The accuracy of finite element solutions of Stokes' flow with strongly varying viscosity, Phys. Earth Planet. Inter., 97, 83-94.
    • (1996) Phys. Earth Planet. Inter. , vol.97 , pp. 83-94
    • Moresi, L.1    Zhong, S.2    Gurnis, M.3
  • 25
    • 0001927801 scopus 로고    scopus 로고
    • An evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed problems
    • Oosterlee, C., and T. Washio (1998), An evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed problems, SIAM J. Sci. Comput., 19(1), 87-110.
    • (1998) SIAM J. Sci. Comput. , vol.19 , Issue.1 , pp. 87-110
    • Oosterlee, C.1    Washio, T.2
  • 27
    • 55649117735 scopus 로고    scopus 로고
    • Evolution of large amplitude 3D fold patterns: A FEM study
    • doi:10.1016/ j.pepi.2008.08.007
    • Schmid, D., M. Dabrowski, and M. Krotkiewski (2008), Evolution of large amplitude 3D fold patterns: A FEM study, Phys. Earth Planet. Inter., 171(1-4), 400-408, doi:10.1016/ j.pepi.2008.08.007.
    • (2008) Phys. Earth Planet. Inter. , vol.171 , Issue.1-4 , pp. 400-408
    • Schmid, D.1    Dabrowski, M.2    Krotkiewski, M.3
  • 29
    • 0027868620 scopus 로고
    • Effects of strongly temperature-dependent viscosity on time-dependent, three-dimensional models of mantle convection
    • Tackley, P. (1993), Effects of strongly temperature-dependent viscosity on time-dependent, three-dimensional models of mantle convection, Geophys. Res. Lett., 20(20), 2187-2190.
    • (1993) Geophys. Res. Lett. , vol.20 , Issue.20 , pp. 2187-2190
    • Tackley, P.1
  • 30
    • 55749083087 scopus 로고    scopus 로고
    • Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid
    • Tackley, P. (2008), Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid, Phys. Earth Planet. Inter., 171(1-4), 7-18.
    • (2008) Phys. Earth Planet. Inter. , vol.171 , Issue.1-4 , pp. 7-18
    • Tackley, P.1
  • 31
    • 49549125385 scopus 로고    scopus 로고
    • A comparison of preconditioners for incompressible Navier-Stokes solvers
    • Ur Rehman, M., C. Vuik, and G. Segal (2008), A comparison of preconditioners for incompressible Navier-Stokes solvers, Int. J. Numer. Meth. Fluids, 57(12), 1731-1751.
    • (2008) Int. J. Numer. Meth. Fluids , vol.57 , Issue.12 , pp. 1731-1751
    • Ur Rehman, M.1    Vuik, C.2    Segal, G.3
  • 33
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
    • doi:10.1007/ BF02238511
    • Vaněk, P., J. Mandel, and M. Brezina (1996), Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems, Computing, 56(3), 179-196, doi:10.1007/ BF02238511.
    • (1996) Computing , vol.56 , Issue.3 , pp. 179-196
    • Vaněk, P.1    Mandel, J.2    Brezina, M.3
  • 34
    • 0021211404 scopus 로고
    • A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problems
    • Verfurth, R. (1984), A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problems, IMA J. Numer. Anal., 4(4), 441-455.
    • (1984) IMA J. Numer. Anal. , vol.4 , Issue.4 , pp. 441-455
    • Verfurth, R.1
  • 35
    • 0029425967 scopus 로고
    • New insights in GMRES-like methods with variable preconditioners
    • Vuik, C. (1995), New insights in GMRES-like methods with variable preconditioners, J. Comput. Appl. Math., 61, 189-204.
    • (1995) J. Comput. Appl. Math. , vol.61 , pp. 189-204
    • Vuik, C.1
  • 36
    • 0034255121 scopus 로고    scopus 로고
    • The Krylov accelerated SIMPLE(R) method for flow problems in industrial furnaces
    • Vuik, C., A. Saghir, and G. Boerstoel (2000), The Krylov accelerated SIMPLE(R) method for flow problems in industrial furnaces, Int. J. Numer. Meth. Fluids, 33, 1027-1040.
    • (2000) Int. J. Numer. Meth. Fluids , vol.33 , pp. 1027-1040
    • Vuik, C.1    Saghir, A.2    Boerstoel, G.3
  • 37
    • 33846434817 scopus 로고    scopus 로고
    • Algebraic multigrid and incompressible fluid flow
    • Webster, R. (2007), Algebraic multigrid and incompressible fluid flow, Int. J. Numer. Meth. Fluids, 53(4), 669-690.
    • (2007) Int. J. Numer. Meth. Fluids , vol.53 , Issue.4 , pp. 669-690
    • Webster, R.1
  • 39
    • 0034351205 scopus 로고    scopus 로고
    • A matrix-dependent transfer multigrid method for strongly variable viscosity infinite Prandtl number thermal convection
    • Yang, W., and J. Baumgardner (2000), A matrix-dependent transfer multigrid method for strongly variable viscosity infinite Prandtl number thermal convection, Geophys. Astrophys. Fluid Dyn., 92(3-4), 151-195.
    • (2000) Geophys. Astrophys. Fluid Dyn. , vol.92 , Issue.3-4 , pp. 151-195
    • Yang, W.1    Baumgardner, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.