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Volumn 6, Issue 6, 2013, Pages 2099-2119

Automating the solution of PDEs on the sphere and other manifolds in FEniCS 1.2

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EID: 84924417848     PISSN: 1991959X     EISSN: 19919603     Source Type: Journal    
DOI: 10.5194/gmd-6-2099-2013     Document Type: Article
Times cited : (49)

References (42)
  • 1
    • 85104396254 scopus 로고    scopus 로고
    • UFL: A finite element form language
    • of Lecture Notes in Computational Science and Engineering, edited by: Logg, A., Mardal, K.-A., and Wells, G. N., chap. 17, Springer
    • Alnæs, M. S.: UFL: a finite element form language, in: Automated Solution of Differential Equations by the Finite Element Method, Vol. 84 of Lecture Notes in Computational Science and Engineering, edited by: Logg, A., Mardal, K.-A., and Wells, G. N., chap. 17, Springer, 2012.
    • (2012) Automated Solution of Differential Equations by the Finite Element Method , vol.84
    • Alnæs, M.S.1
  • 3
    • 85104473935 scopus 로고    scopus 로고
    • UFC: A finite element code generation interface
    • of Lecture Notes in Computational Science and Engineering, edited by: Logg, A., Mardal, K.-A., and Wells, G. N., chap. 16, Springer
    • Alnæs, M. S., Logg, A., and Mardal, K.-A.: UFC: a finite element code generation interface, in: Automated Solution of Differential Equations by the Finite Element Method, Volume 84 of Lecture Notes in Computational Science and Engineering, edited by: Logg, A., Mardal, K.-A., and Wells, G. N., chap. 16, Springer, 2012.
    • (2012) Automated Solution of Differential Equations by the Finite Element Method , vol.84
    • Alnæs, M.S.1    Logg, A.2    Mardal, K.-A.3
  • 4
    • 84994547901 scopus 로고    scopus 로고
    • Unified form language: A domain-specific language for weak formulations of partial differential equations
    • (last access: 13 December 2013)
    • Alnæs, M. S., Logg, A., Ølgaard, K. B., Rognes, M. E., and Wells, G. N.: Unified Form Language: a domain-specific language for weak formulations of partial differential equations, ACM Trans. Mathe. Softw., available at: http://arxiv.org/abs/1211.4047 (last access: 13 December 2013), 2013.
    • (2013) ACM Trans. Mathe. Softw.
    • Alnæs, M.S.1    Logg, A.2    Ølgaard, K.B.3    Rognes, M.E.4    Wells, G.N.5
  • 5
    • 0025588929 scopus 로고
    • Energy conserving and potentialenstrophy dissipating schemes for the shallow water equations
    • Arakawa, A. and Hsu, Y.-J. G.: Energy conserving and potentialenstrophy dissipating schemes for the shallow water equations, Mon. Weather Rev., 118, 1960-1969, 1990.
    • (1990) Mon. Weather Rev. , vol.118 , pp. 1960-1969
    • Arakawa, A.1    Hsu, Y.-J.G.2
  • 6
    • 0000094119 scopus 로고
    • Computational design of the basic dynamical processes of the UCLA general circulation model
    • Arakawa, A. and Lamb, V.: Computational design of the basic dynamical processes of the UCLA general circulation model, Meth. Computat. Phys., 17, 174-267, 1977.
    • (1977) Meth. Computat. Phys. , vol.17 , pp. 174-267
    • Arakawa, A.1    Lamb, V.2
  • 11
    • 34250118577 scopus 로고
    • Two families of mixed finite elements for second order elliptic problems
    • Brezzi, F., Douglas, J., and Marini, L. D.: Two families of mixed finite elements for second order elliptic problems, Numer. Math., 47, 217-235, 1985.
    • (1985) Numer. Math. , vol.47 , pp. 217-235
    • Brezzi, F.1    Douglas, J.2    Marini, L.D.3
  • 12
    • 0000076512 scopus 로고    scopus 로고
    • Runge-kutta discontinuous galerkin methods for convection-dominated problems
    • Cockburn, B. and Shu, C.-W.: Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, J. Sci. Comput., 16, 173-261, 2001.
    • (2001) J. Sci. Comput. , vol.16 , pp. 173-261
    • Cockburn, B.1    Shu, C.-W.2
  • 13
    • 0000397713 scopus 로고
    • A lagrange multiplier approach for the metric terms of semi-lagrangian models on the sphere
    • Côté, J.: A Lagrange multiplier approach for the metric terms of semi-Lagrangian models on the sphere, Q. J. Roy. Meteorol. Soc., 114, 1347-1352, 1988.
    • (1988) Q. J. Roy. Meteorol. Soc. , vol.114 , pp. 1347-1352
    • Côté, J.1
  • 14
    • 84865399743 scopus 로고    scopus 로고
    • Mixed finite elements for numerical weather prediction
    • Cotter, C. and Shipton, J.: Mixed finite elements for numerical weather prediction, J. Computat. Phys., 231, 7076-7091, doi:10.1016/j.jcp.2012.05.020, 2012.
    • (2012) J. Computat. Phys. , vol.231 , pp. 7076-7091
    • Cotter, C.1    Shipton, J.2
  • 15
    • 56949088800 scopus 로고    scopus 로고
    • A mixed discontinuous/continuous finite element pair for shallowwater ocean modelling
    • Cotter, C. J., and Ham., D. A., and Pain, C. C.: A mixed discontinuous/continuous finite element pair for shallowwater ocean modelling, Ocean Modell., 26, 86-90, doi:10.1016/j.ocemod.2008.09.002, 2009.
    • (2009) Ocean Modell. , vol.26 , pp. 86-90
    • Cotter, C.J.1    Ham, D.A.2    Pain, C.C.3
  • 16
    • 78650605818 scopus 로고    scopus 로고
    • A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the DUNE-FEM module
    • Dedner, A., Klöfkorn, R., Nolte, M., and Ohlberger, M.: A generic interface for parallel and adaptive discretization schemes: abstraction principles and the DUNE-FEM module, Computing, 90, 165-196, 2010.
    • (2010) Computing , vol.90 , pp. 165-196
    • Dedner, A.1    Klöfkorn, R.2    Nolte, M.3    Ohlberger, M.4
  • 17
    • 84994665397 scopus 로고    scopus 로고
    • Tools for the solution of PDEs defined on curved manifolds with deal.II
    • (last access: 13 December 2013)
    • DeSimone, A., Heltai, L., and Manigrasso, C.: Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II, International School for Advanced Studies (SISSA), available at: http://hdl.handle.net/1963/3700 (last access: 13 December 2013), 2009.
    • (2009) International School for Advanced Studies (SISSA)
    • DeSimone, A.1    Heltai, L.2    Manigrasso, C.3
  • 18
    • 33644960862 scopus 로고    scopus 로고
    • High-order triangle-based discontinuous galerkin methods for hyperbolic equations on a rotating sphere
    • Giraldo, F. X.: High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on a rotating sphere, J. Computat. Phys., 214, 447-465, 2006.
    • (2006) J. Computat. Phys. , vol.214 , pp. 447-465
    • Giraldo, F.X.1
  • 19
    • 84967566823 scopus 로고    scopus 로고
    • Geometric mechanics - Part I
    • Imperial College Press
    • Holm, D.: Geometric Mechanics - Part I: Dynamics and Symmetry, Imperial College Press, 2008.
    • (2008) Dynamics and Symmetry
    • Holm, D.1
  • 21
    • 12744252825 scopus 로고    scopus 로고
    • Algorithm 839: Fiat, a new paradigm for computing finite element basis functions
    • Kirby, R. C.: Algorithm 839: FIAT, a new paradigm for computing finite element basis functions, ACM T. Math. Software, 30, 502-516, doi:10.1145/1039813.1039820, 2004.
    • (2004) ACM T. Math. Software , vol.30 , pp. 502-516
    • Kirby, R.C.1
  • 22
    • 33749341848 scopus 로고    scopus 로고
    • A compiler for variational forms
    • Kirby, R. C. and Logg, A.: A compiler for variational forms, ACM T. Math. Software, 32, 417-444, doi:10.1145/1163641.1163644, 2006.
    • (2006) ACM T. Math. Software , vol.32 , pp. 417-444
    • Kirby, R.C.1    Logg, A.2
  • 23
    • 84994665341 scopus 로고    scopus 로고
    • Gram determinant
    • Springer (last access: 2 July 2013)
    • Kuptsov, L.: Gram Determinant, in: Encyclopedia of Mathematics, Springer, available at: http://www.encyclopediaofmath.org/index.php/Gram-determinant?%oldid=18442 (last access: 2 July 2013), 2011.
    • (2011) Encyclopedia of Mathematics
    • Kuptsov, L.1
  • 25
    • 14744282253 scopus 로고    scopus 로고
    • On some spurious mode issues in shallow-water models using a linear algebra approach
    • Le Roux, D., Sène, A., Rostand, V., and Hanert, E.: On some spurious mode issues in shallow-water models using a linear algebra approach, Ocean Modell., 10, 83-94, 2005.
    • (2005) Ocean Modell. , vol.10 , pp. 83-94
    • Le Roux, D.1    Sène, A.2    Rostand, V.3    Hanert, E.4
  • 26
    • 76249096812 scopus 로고    scopus 로고
    • DOLFIN: Automated finite element computing
    • 28
    • Logg, A. and Wells, G. N.: DOLFIN: automated finite element computing, ACM T. Math. Software, 37, 20: 1-20:28, doi:10.1145/1731022.1731030, 2010.
    • (2010) ACM T. Math. Software , vol.37 , Issue.20 , pp. 1-20
    • Logg, A.1    Wells, G.N.2
  • 32
    • 84994601519 scopus 로고    scopus 로고
    • Energy- and enstrophy-conserving schemes for the shallow-water equations, based on mimetic finite elements
    • (last access: 13 December 2013)
    • McRae, A. T. T and Cotter, C. J.: Energy- and enstrophy-conserving schemes for the shallow-water equations, based on mimetic finite elements, Q. J. R. Meteorol. Soc., http://arxiv.org/abs/1305.4477 (last access: 13 December 2013), 2013.
    • (2013) Q. J. R. Meteorol. Soc.
    • McRae, A.T.T.1    Cotter, C.J.2
  • 35
    • 84947145047 scopus 로고
    • A generalized inverse for matrices
    • Penrose, R.: A generalized inverse for matrices, Proc. Cambridge Philos. Soc, 51, 406-413, 1955.
    • (1955) Proc. Cambridge Philos. Soc , vol.51 , pp. 406-413
    • Penrose, R.1
  • 37
    • 84994552322 scopus 로고    scopus 로고
    • Expressive and scalable finite element simulation beyond 1000 cores
    • project report last access: 23 September 2013
    • Richardson, C. N., and Wells, G. N.: Expressive and scalable finite element simulation beyond 1000 cores, HECToR university distributed CSE project report, available at: http://www.hector.ac.uk/cse/distributedcse/reports/UniDOLFIN/, last access: 23 September 2013.
    • HECToR University Distributed CSE
    • Richardson, C.N.1    Wells, G.N.2
  • 38
    • 73249133532 scopus 로고    scopus 로고
    • Efficient assembly of H(div) and H(curl) conforming finite elements
    • Rognes, M. E., and Kirby., R. C., and Logg, A.: Efficient assembly of H(div) and H(curl) conforming finite elements, SIAM J. Sci. Comput., 31, 4130-4151, 2009.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 4130-4151
    • Rognes, M.E.1    Kirby, R.C.2    Logg, A.3
  • 39
    • 31644445169 scopus 로고    scopus 로고
    • Design of adaptive finite element software: The finite element toolbox
    • Springer
    • Schmidt, A., and Barth., T. J., and Siebert, K. G.: Design of adaptive finite element software: the finite element toolbox ALBERTA, Vol. 42, Springer, 2005.
    • (2005) Alberta , vol.42
    • Schmidt, A.1    Barth, T.J.2    Siebert, K.G.3
  • 40
    • 84994570387 scopus 로고    scopus 로고
    • last access: 2 July 2013
    • Sherwin, S., and Kirby., R. M., and the Nektar++ team, available at: http://www.nektar.info, last access: 2 July 2013.
    • Sherwin, S.1    Kirby, R.M.2
  • 41
    • 0001440358 scopus 로고
    • A standard test set for numerical approximations to the shallow water equations in spherical geometry
    • Williamson, D. L., and Drake., J. B., Hack, J. J., Jakob, R., and Swarztrauber, P. N.: A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Computat. Phys., 102, 211-224, 1992.
    • (1992) J. Computat. Phys. , vol.102 , pp. 211-224
    • Williamson, D.L.1    Drake, J.B.2    Hack, J.J.3    Jakob, R.4    Swarztrauber, P.N.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.