UFC: A finite element code generation interface

Lecture Notes in Computational Science and Engineering

Volumn 84, Issue , 2012, Pages 283-302

  Alnæs, Martin Sandve ^a   Logg, Anders ^a   Mardal, Kent Andre ^a  

^a UNIVERSITY OF OSLO   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

C++ (PROGRAMMING LANGUAGE); CODES (SYMBOLS); DATA TRANSFER; DIFFERENTIAL EQUATIONS; GALERKIN METHODS; LIBRARIES;

ASSEMBLY CODE; CENTRAL COMPONENT; DISCONTINUOUS GALERKIN METHODS; FINITE ELEMENT CODES; FINITE ELEMENT PROBLEMS; FINITE ELEMENT PROGRAMS; MIXED FINITE ELEMENTS; UNIFIED FORM;

FINITE ELEMENT METHOD;

EID: 85104473935     PISSN: 14397358     EISSN: 21977100     Source Type: Book Series    
DOI: 10.1007/978-3-642-23099-8__16     Document Type: Chapter

References (464)

1. S. Adams and B. Cockburn. A mixed finite element method for elasticity in three dimensions. Journal of Scientific Computing, 25(3):515-521, 2005. URL http://dx.doi.org/10.1007/s10915-004-4807-3.
2. M. Ainsworth and J. Coyle. Hierarchic finite element bases on unstructured tetrahedral meshes. International Journal for Numerical Methods in Engineering, 58(14):2103-2130, 2003. URL http://dx.doi.org/10.1002/nme.847.
3. M. Ainsworth and J. T. Oden. A unified approach to a posteriori error estimation using element residual methods. Numerische Mathematik, 65(1):23-50, 1993. URL http://dx.doi.org/10.1007/BF01385738.
4. M. Ainsworth and J. T. Oden. A Posteriori Error Estimation in Finite Element Analysis. Wiley and Sons, New York, 2000.
5. J. Alastruey, K. H. Parker, J. Peiro, S. M. Byrd, and S. J. Sherwin. Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. Journal of Biomechanics, 40(8):1794-1805, 2007. URL http://dx.doi.org/10.1016/j.jbiomech.2006.07.008.
6. B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson. Molecular Biology of the Cell. Garland, 4th edition, 2002.
7. V. Alfred, R. Sethi, and D. U. Jeffrey. Compilers: Principles, Techniques and Tools. Addison-Wesley, Reading, Massachusetts, 1986.
8. M. S. Alnæs, A. Logg, K.-A. Mardal, O. Skavhaug, and H. P. Langtangen. UFC Specification and User Manual, 2007. URL http://fenicsproject.org.
9. M. S. Alnæs and A. Logg. UFL Specification and User Manual, 2009. URL http://fenicsproject.org.
10. M. S. Alnæs and K.-A. Mardal. SyFi, 2009. URL http://fenicsproject.org.
11. M. S. Alnæs and K.-A. Mardal. On the efficiency of symbolic computations combined with code generation for finite element methods. ACM Trans. Math. Softw., 37:6:1-6:26, 2010. URL http://dx.doi.org/10.1145/1644001.1644007.
12. M. S. Alnæs, A. Logg, K.-A. Mardal, O. Skavhaug, and H. P. Langtangen. Unified framework for finite element assembly. International Journal of Computational Science and Engineering, 4(4):231-244, 2009.
13. N. Alperin, M. Mazda, T. Lichtor, and S. H. Lee. From cerebrospinal fluid pulsation to noninvasive intracranial compliance and pressure measured by MRI flow studies. Current Medical Imaging Reviews, 2:117-129, 2006.
14. J. H. Argyris, I. Fried, and D. W. Scharpf. The TUBA family of plate elements for the matrix displacement method. The Aeronautical Journal of the Royal Aeronautical Society, 72:701-709, 1968.
15. D. N. Arnold. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal., 19(4), 1982. URL: Http://dx.doi.org/10.1137/0719052.
16. D. N. Arnold and R. S. Falk. A uniformly accurate finite element method for the Reissner-Mindlin plate. SIAM J. Num. Anal., 26:1276-1290, 1989. URL http://dx.doi.org/10.1137/0726074.
17. D. N. Arnold and M. E. Rognes. Stability of Lagrange elements for the mixed Laplacian. Calcolo, 46 (4):245-260, 2009. URL http://dx.doi.org/10.1007/s10092-009-0009-6.
18. D. N. Arnold and R. Winther. Mixed finite elements for elasticity. Numer. Math., 92(3):401-419, 2002. URL http://dx.doi.org/10.1007/s002110100348.
19. D. N. Arnold, F. Brezzi, and J. Douglas, Jr. PEERS: A new mixed finite element for plane elasticity. Japan J. Appl. Math., 1(2):347-367, 1984a. URL http://dx.doi.org/10.1007/BF03167064.
20. D. N. Arnold, F. Brezzi, and M. Fortin. A stable finite element for the Stokes equations. Calcolo, 21(4): 337-344, 1984b. URL http://dx.doi.org/10.1007/BF02576171.
21. D. N. Arnold, R. S. Falk, and R. Winther. Preconditioning in H(div) and applications. Mathematics of Computation, 66(219):957-984, 1997. URL http://dx.doi.org/10.1090/S0025-5718-97-00826-0.
22. D. N. Arnold, R. S. Falk, and R. Winther. Multigrid in H(div) and H(curl). Numerische Mathematik, 85(2):197-217, 2000. URL http://dx/doi.org/10.1007/PL00005386.
23. D. N. Arnold, R. S. Falk, and R. Winther. Finite element exterior calculus, homological techniques, and applications. Acta Numerica, 15:1-155, 2006a. URL http://dx.doi.org/10.1017/S0962492906210018.
24. D. N. Arnold, R. S. Falk, and R. Winther. Differential complexes and stability of finite element methods. II. The elasticity complex. In Compatible spatial discretizations, volume 142 of IMA Vol. Math. Appl., pages 47-67. Springer, New York, 2006b.
25. D. N. Arnold, R. S. Falk, and R. Winther. Mixed finite element methods for linear elasticity with weakly imposed symmetry. Mathematics of Computation, 76(260):1699-1723, 2007.
26. D. N. Arnold, G. Awanou, and R. Winther. Finite elements for symmetric tensors in three dimensions. Math. Comp., 77(263):1229-1251, 2008.
27. O. Axelsson. A general incomplete block-matrix factorization method. Linear Algebra and its Applications, 74:179-190, 1986. ISSN 0024-3795.
28. I. Babuška. The finite element method with Lagrangian multipliers. Numer. Math., 20:179-192, 1973. URL http://dx.doi.org/10.1007/BF01436561.
29. I. Babuška and W. C. Rheinboldt. A posteriori error estimates for the finite element method. Int. J. Numer. Meth. Engrg., pages 1597-1615, 1978.
30. I. Babuška, U. Banerjee, and J. E. Osborn. Survey of meshless and generalized finite element methods: A unified approach. Acta Numerica, 12:1-125, 2003.
31. B. Bagheri and L. R. Scott. About Analysa. Technical Report TR-2004-09, University of Chicago, Department of Computer Science, 2004. URL http://www.cs.uchicago.edu/research/publications/techreports/TR-2004-09.
32. S. Balay, K. Buschelman, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, B. F. Smith, and H. Zhang. PETSc web page, 2001. URL http://www.mcs.anl.gov/petsc.
33. S. Balay, K. Buschelman, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, B. F. Smith, and H. Zhang. PETSc users manual. Technical Report ANL-95/11-Revision 2.1.5, Argonne National Laboratory, 2004.
34. W. Bangerth, R. Hartmann, and G. Kanschat. deal.II-a general-purpose object-oriented finite element library. ACM Trans. Math. Softw., 33(4), 2007. URL http://dx.doi.org/10.1145/1268776.1268779.
35. R. E. Bank and A. Weiser. Some a posteriori error estimators for elliptic partial differential equations. Mathematics of Computation, pages 283-301, 1985.
36. G. K. Batchelor. An Introduction to Fluid Dynamics. Cambridge University Press, 1967.
37. C. Bauer, A. Frink, and R. Kreckel. Introduction to the GiNaC framework for symbolic computation within the C++ programming language. Journal of Symbolic Computation, 33(1):1-1, 2002. URL http://dx.doi.org/10.1006/jsco.2001.0494.
38. D. M. Beazley. SWIG: An easy to use tool for integrating scripting languages with C and C++. In Proceedings of the 4th conference on USENIX Tcl/Tk Workshop, volume 4, Berkeley, 1996. USENIX Association. URL http://portal.acm.org/citation.cfm?id=1267498.1267513.
39. E. B. Becker, G. F. Carey, and J. T. Oden. Finite Elements: An Introduction. Prentice-Hall, Englewood-Cliffs, 1981.
40. R. Becker and R. Rannacher. An optimal control approach to a posteriori error estimation in finite element methods. Acta Numerica, 10:1-102, 2001.
41. S. Beji and K. Nadaoka. A formal derivation and numerical modelling of the improved Boussinesq equations for varying depth. Ocean engineering, 23(8):691, 1996. ISSN 0029-8018.
42. W. N. Bell, L. N. Olson, and J. Schroder. PyAMG: Algebraic multigrid solvers in Python, 2011. URL http://www.pyamg.org.
43. T. Belytschko and T. Black. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45(5):601-620, 1999.
44. F. Bengzon and M. G. Larson. Adaptive finite element approximation of multiphysics problems: A fluid-structure interaction model problem. International Journal for Numerical Methods in Engineering, 2010.
45. M. Benzi, G. H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numerica, 14:1-137, 2005.
46. D. M. Bers. Excitation-Contraction Coupling and Cardiac Contractile Force. Kluwer Academic Publishers, Dordrecht, 2nd edition, 2001.
47. D. J. Beuckelmann and W. G. Wier. Mechanism of release of calcium from sarcoplasmic reticulum of guinea-pig cardiac cells. J. Physiol., 405:233-255, Nov 1988.
48. P. Bientinesi, J. A. Gunnels, M. E. Myers, E. S. Quintana-Ortí, and R. A. van de Geijn. The science of deriving dense linear algebra algorithms. ACM Transactions on Mathematical Software, 31(1):1-26, 2005. URL http://dx.doi.org/10.1145/1055531.1055532.
49. H. B. Bingham, P. A. Madsen, and D. R. Fuhrman. Velocity potential formulations of highly accurate Boussinesq-type models. Coastal Engineering, Article in Press, 2008.
50. C. Bischof, A. Carle, G. Corliss, and A. Griewank. ADIFOR: Automatic differentiation in a source translator environment. In Papers from the international symposium on Symbolic and algebraic computation, pages 294-302, Berkeley, California, 1992. URL http://dx.doi.org/10.1145/143242.143335.
51. C. H. Bischof, P. D. Hovland, and B. Norris. Implementation of automatic differentiation tools. In Proceedings of the 2002 ACM SIGPLAN workshop on Partial evaluation and semantics-based program manipulation, pages 98-107, Portland, Oregon, 2002. URL http://dx.doi.org/10.1145/503032.503047.
52. H. Blackburn. Semtex, 2011. URL http://users.monash.edu.au/~bburn/semtex.html.
53. H. M. Blackburn and S. J. Sherwin. Formulation of a Galerkin spectral element-Fourier method for three-dimensional incompressible flows in cylindrical geometries. J. Comput. Phys., 197:759-778, 2004. URL http://dx.doi.org/10.1016/j.jcp.2004.02.013.
54. B. Blankenbach, F. Busse, U. Christensen, et al. A benchmark comparison for mantle convection codes. Geophys. J. Int., 98:23-28, 1989.
55. D. Boffi. Three-dimensional finite element methods for the Stokes problem. SIAM J. Numer. Anal., 34 (2):664-670, 1997. URL http://dx.doi.org/10.1137/S0036142994270193.
56. D. Boffi, F. Brezzi, and L. Gastaldi. On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form. Math. Comp., 69(229):121-140, 2000.
57. J. Bonet and R. D. Wood. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, 1997.
58. A. Bossavit. Computational Electromagnetics: Variational Formulations, Complementarity, Edge Elements. Academic Press, 1998.
59. L. Boussel, V. Rayz, C. McCulloch, A. Martin, G. Acevedo-Bolton, M. Lawton, R. Higashida, W. S. Smith, W. L. Young, and D. Saloner. Aneurysm growth occurs at region of low wall shear stress: Patient-specific correlation of hemodynamics and growth in a longitudinal study. Stroke, 39(11): 2997-3002, 2008. URL http://dx.doi.org/10.1161/STROKEAHA.108.521617.
60. D. Braess. Finite Elements. Cambridge University Press, third edition, 2007. ISBN 978-0-521-70518-9.
61. J. H. Bramble. Multigrid Methods, volume 294 of Pitman Research Notes in Mathematical Sciences. Longman Scientific & Technical, Essex, England, 1993.
62. J. H. Bramble and M. Zlámal. Triangular elements in the finite element method. Mathematics of Computation, pages 809-820, 1970.
63. A. Brandt. Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation, pages 333-390, 1977.
64. S. C. Brenner and L. R. Scott. The Mathematical Theory of Finite Element Methods, volume 15 of Texts in Applied Mathematics. Springer, New York, third edition, 2008. URL http://dx.doi.org/10.1007/978-0-387-75934-0.
65. F. Brezzi. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. RAIRO Anal. Numér., R-2:129-151, 1974.
66. F. Brezzi and R. S. Falk. Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal., 28(3): 581-590, 1991.
67. F. Brezzi and M. Fortin. Mixed and Hybrid Finite Element Methods, volume 15 of Springer Series in Computational Mathematics. Springer-Verlag, New York, 1991.
68. F. Brezzi, J. Douglas, Jr., and L. D. Marini. Two families of mixed finite elements for second order elliptic problems. Numer. Math., 47(2):217-235, 1985a.
69. F. Brezzi, J. Douglas Jr., and L D. Marini. Variable degree mixed methods for second order elliptic problems. Mat. Apl. Comput., 4(1):19-34, 1985b.
70. F. Brezzi, J. Douglas, R. Duran, and M. Fortin. Mixed finite elements for second order elliptic problems in three variables. Numerische Matematik, 51:237-250, 1987a.
71. F. Brezzi, J. Douglas, Jr., M. Fortin, and L. D. Marini. Efficient rectangular mixed finite elements in two and three space variables. RAIRO Modél. Math. Anal. Numér., 21(4):581-604, 1987b.
72. A. N. Brooks and T. J. R. Hughes. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 32(1-3):199-259, Sept. 1982. URL http://dx.doi.org/10.1016/0045-7825(82)90071-8.
73. A. Buffa, P. Houston, and I. Perugia. Discontinuous Galerkin computation of theMaxwell eigenvalues on simplicial meshes. Journal of Computational and Applied Mathematics, 204(2):317-333, 2007. URL http://dx.doi.org/DOI:10.1016/j.cam.2006.01.042.
74. K. Burke, B. Steinberger, T. H. Torsvik, and M. A. Smethurst. Plume generation zones at the margins of large low shear velocity provinces on the core-mantle boundary. Earth and Planetary Science Letters, 265:49-60, 2008.
75. J. Cahouet and J.-P. Chabard. Some fast 3D finite element solvers for the generalized Stokes problem. International Journal for Numerical Methods in Fluids, 8(8):869-895, 1988.
76. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang. Spectral Methods. Springer-Verlag, 2007. URL http://dx.doi.org/10.1007/978-3-540-30728-0.
77. C. A. P. Castigliano. Théorie de l’équilibre des systèmes élastiques et ses applications. A.F. Negro ed., Torino, 1879.
78. J. R. Cebral, M. A. Castro, J. E. Burgess, R. S. Pergolizzi, M. J. Sheridan, and C. M. Putman. Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models. American Journal of Neuroradiology, 26(10):2550-2559, 2005. URL http://www.ajnr.org/cgi/content/abstract/26/10/2550.
79. O. Certík, F. Seoane, P. Peterson, et al. sympy: Python library for symbolic mathematics, 2009. URL http://sympy.org.
80. CGAL. Software package. URL http://www.cgal.org.
81. D. Chapelle and K.-J. Bathe. The inf-sup test. Comput. & Structures, 47(4-5):537-545, 1993.
82. G. Chavent and P. Lemmonier. Identification de la non-linearite’ d’une equation parabolique quasi-lineare. Applied Math. and Opt., 26:121-162, 1974.
83. Y. Chen and P. L.-F. Liu. Modified Boussinesq equations and associated parabolic models for water wave propagation. J. Fluid Mech., 288:351-381, 1994.
84. J. Chessa, P. Smolinski, and T. Belytschko. The extended finite element method (XFEM) for solidification problems. International Journal for Numerical Methods in Engineering, 53(8):1959-1977, 2002.
85. A. J. Chorin. Numerical solution of the Navier-Stokes equations. Math. Comp., 22:745-762, 1968.
86. I. Christie, D. Griffiths, A. R. Mitchell, and O. C. Zienkiewicz. Finite element methods for second order differential equations with significant first derivatives. International Journal for Numerical Methods in Engineering, 10(6):1389-1396, 1976.
87. V. V. Chudanov, A. G. Popkov, A. G. Churbanov, P. N. Vabishchevich, and M. M. Makarov. Operatorsplitting schemes for the streamfunction-vorticity formulation. Comput. Fluids, v24(7):771-786, 2007.
88. P. G. Ciarlet. Lectures on the finite element method. Lectures on Mathematics and Physics, Tata Institute of Fundamental Research, Bombay, 49, 1975.
89. P. G. Ciarlet. Numerical Analysis of the Finite Element Method. Les Presses de l’Universite de Montreal, 1976.
90. P. G. Ciarlet. The Finite Element Method for Elliptic Problems, volume 40 of Classics in AppliedMathematics. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2002.
91. P. G. Ciarlet and P.-A. Raviart. General Lagrange and Hermite interpolation in Rn with applications to finite element methods. Arch. Rational Mech. Anal., 46:177-199, 1972.
92. R. Cimrman et al. SfePy: Simple Finite Elements in Python, 2008. URL http://sfepy.org.
93. G. Compère, J.-F. Remacle, J. Jansson, and J. Hoffman. Transient mesh adaptivity applied to large domain deformations. To appear in Int. J. Numer. Meth. Eng., 2009.
94. COMSOL. Comsol multiphysics, 2009. URL http://www.comsol.com.
95. M. Costabel and M. Dauge. Weighted Regularization of Maxwell Equations in Polyhedral Domains. Numerische Mathematik, 93(2):239-277, 2002. ISSN 0029-599X.
96. R. Courant. Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc., pages 1-23, 1943.
97. M. Crouzeix and R. S. Falk. Nonconforming finite elements for the Stokes problem. Mathematics of Computation, 52:437-456, 1989. URL http://dx.doi.org/10.2307/2008475.
98. M. Crouzeix and P. A. Raviart. Conforming and non-conforming finite element methods for solving the stationary Stokes equations. RAIRO Anal. Numer., 7:33-76, 1973.
99. Cython. Software package. URL http://cython.org.
100. D. B. Davidson. Computational Electromagnetics for RF and Microwave Engineers. Cambridge University Press, Cambridge, second edition, 2011. ISBN 9780521518918.
101. P. F. Davies, A. Remuzzi, E. J. Gordon, C. F. Dewey, and M. Gimbrone. Turbulent fluid shear stress induces vascular endothelial cell turnover in vitro. Proc. Natl. Acad. Sci. USA, 83:2114-2117, 1986.
102. T. A. Davis. Algorithm 832: Umfpack v4.3-an unsymmetric-pattern multifrontal method. ACM Transactions on Mathematical Software, 30(2):196-199, 2004. URL http://dx.doi.org/10.1145/992200.992206.
103. DDD. Software package. URL http://www.gnu.org/software/ddd.
104. R. V. de Abreu, N. Jansson, and J. Hoffman. Adaptive computation of aeroacoustic sources for a 4-wheel rudimentary landing gear benchmark problem. In Proc. Workshop on Benchmark Problems Airframe Noise Computation (BANC-I), 2010.
105. D. A. di Pietro, S. L. Forte, and N. Parolini. Mass preserving finite element implementations of the level set method. Applied Numerical Mathematics, 56:1179-1195, 2006.
106. B. M. Dillon and J. P. Webb. A comparison of formulations for the vector finite element analysis of waveguides. IEEE Trans. Microwave Theory Tech., 42(2):308-316, February 1994.
107. Building and installing Python modules. URL http://docs.python.org/library/distutils.html.
108. V. Domínguez and F.-J. Sayas. Algorithm 884: A simple Matlab implementation of the Argyris element. ACM Transactions on Mathematical Software, 35(2):16:1-16:11, July 2008. URL http://dx.doi.org/10.1145/1377612.1377620.
109. J. Donea and A. Huerta. Finite Element Methods for Flow Problems. Wiley, 2003.
110. J. Donea, S. Giuliani, and J. Halleux. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Computer Methods in Applied Mechanics and Engineering, 33(1-3):689-723, 1982.
111. J. Donea, A. Huerta, J. P. Ponthot, and A. Rodrıguez-Ferran. Arbitrary Lagrangian-Eulerian methods. Encyclopedia of Computational Mechanics, 1:1-25, 2004.
112. W. Dörfler. A convergent adaptive algorithm for Poisson’s equation. SIAM Journal on Numerical Analysis, 33(3):1106-1124, 1996.
113. M. Dubiner. Spectral methods on triangles and other domains. Journal of Scientific Computing, 6(4): 345-390, 1991.
114. P. Dular and C. Geuzaine. GetDP Reference Manual, 2005.
115. D. A. Dunavant. High degree efficient symmetrical Gaussian quadrature rules for the triangle. International Journal for Numerical Methods in Engineering, 21(6):1129-1148, 1985
116. T. Dunne. An Eulerian approach to fluid-structure interaction and goal-oriented mesh adaptation. International Journal for Numerical Methods in Fluids, 51(9-10):1017-1039, 2006.
117. T. Dunne. Adaptive Finite Element Approximation of Fluid-Structure Interaction Based on Eulerian and Arbitrary Lagrangian-Eulerian Variational Formulations. PhD thesis, Ruprecht-Karls-UniversitÃd’t, Heidelberg, 2007.
118. T. Dunne and R. Rannacher. Adaptive finite element approximation of fluid-structure interaction based on an Eulerian variational formulation. Lecture Notes In Computational Science And Engineering, 53:110, 2006.
119. D. Dutykh and F. Dias. Dissipative Boussinesq equations. Comptes Rendus Mecanique, 335:559, 2007. URL doi:10.1016/j.crme.2007.08.003.
120. S. V. Eden, W. J. Meurer, B. N. Sanchez, L. D. Lisabeth, M. A. Smith, D. L. Brown, and L. B. Morgenstern. Gender and ethnic differences in subarachnoid hemorrhage. Neurology, 71:731-735, 2008.
121. H. C. Elman, D. J. Silvester, and A. J. Wathen. Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford, 2005.
122. M. S. Engelman, R. L. Sani, P.M. Gresho, and M. Bercovier. Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements. International Journal for Numerical Methods in Fluids, 2(1):25-42, 1982. ISSN 1097-0363. doi: 10.1002/fld.1650020103. URL http://dx.doi.org/10.1002/fld.1650020103.
123. K. Eriksson and C. Johnson. Adaptive finite element methods for parabolic problems III: Time steps variable in space. in preparation.
124. K. Eriksson and C. Johnson. Adaptive finite element methods for parabolic problems I: A linear model problem. SIAM J. Numer. Anal., 28, No. 1:43-77, 1991.
125. K. Eriksson and C. Johnson. Adaptive finite element methods for parabolic problems II: Optimal error estimates in l∞l2 and l∞l∞. SIAM Journal on Numerical Analysis, 32:706, 1995a.
126. K. Eriksson and C. Johnson. Adaptive finite element methods for parabolic problems IV: Nonlinear problems. SIAM Journal on Numerical Analysis, pages 1729-1749, 1995b.
127. K. Eriksson and C. Johnson. Adaptive finite element methods for parabolic problems V: Long-time integration. SIAM J. Numer. Anal., 32:1750-1763, 1995c.
128. K. Eriksson, D. Estep, P. Hansbo, and C. Johnson. Introduction to adaptive methods for differential equations. Acta Numerica, 4:105-158, 1995.
129. K. Eriksson, D. Estep, P. Hansbo, and C. Johnson. Computational Differential Equations. Cambridge University Press, 1996.
130. K. Eriksson, C. Johnson, and S. Larsson. Adaptive finite element methods for parabolic problems VI: Analytic semigroups. SIAM J. Numer. Anal., 35:1315-1325, 1998.
131. A. Ern and J.-L. Guermond. Theory and Practice of Finite Elements, volume 159 of Applied Mathematical Sciences. Springer-Verlag, 2004.
132. C. R. Ethier and D. A. Steinmann. Exact fully 3D Navier-Stokes solution for benchmarking. Internat. J. Numer. Methods Fluids, 19:369-375, 1994.
133. A. J. Evans, F. Iwai, T. A. Grist, H. D. Sostman, L.W. Hedlund, C. E. Spritzer, R. Negro-Vilar, C. A. Beam, and N. J. Pelc. Magnetic resonance imaging of blood flow with a phase subtraction technique. in vitro and in vivo validation. Investigative Radiology, 28(2), 1993.
134. F2PY. Software package. URL http://cens.ioc.ee/projects/f2py2e.
135. R. D. Falgout and U. M. Yang. Hypre: A library of high performance preconditioners. In Proceedings of the International Conference on Computational Science-Part III, pages 632-641. Springer-Verlag, 2002.
136. M. Farhloul and M. Fortin. Dual hybrid methods for the elasticity and the Stokes problems: A unified approach. Numer. Math., 76(4):419-440, 1997.
137. V. Feigin. Stroke epidemiology in the developing world. The Lancet, 365(9478):2160-2161, 2005. URL http://dx.doi.org/10.1016/S0140-6736(05)66755-4.
138. P. Fernandes and M. Raffetto. Characterization of spurious-free finite element methods in electromagnetics. COMPEL-The International Journal for Computation andMathematics in Electrical and Electronic Engineering, 21:147-164, 2002. URL http://dx.doi.org/10.1108/03321640210410814.
139. M. D. Ford, N. Alperin, S. H. Lee, D. W. Holdsworth, and D. A. Steinman. Characterization of volumetric flow rate waveforms in the normal internal cartoid and vertebral arteries. Physiological Measurement, 26:477-488, 2005.
140. L. Formaggia and F. Nobile. A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements. East-West Journal of Numerical Mathematics, 7:105-132, 1999.
141. S. A. Forth, M. Tadjouddine, J. D. Pryce, and J. K. Reid. Jacobian code generated by source transformation and vertex elimination can be as efficient as hand-coding. ACM Trans. Math. Softw., 30(3): 266-299, 2004. URL http://dx.doi.org/10.1145/1024074.1024076.
142. C. Franzini-Armstrong, F. Protasi, and V. Ramesh. Shape, size, and distribution of Ca2+ release units and couplons in skeletal and cardiac muscles. Biophys. J., 77(3):1528-1539, Sep 1999. URL http://www.biophysj.org/cgi/content/full/77/3/1528.
143. Y. C. Fung. Biodynamics: Circulation. Springer-Verlag, 1984.
144. Y. C. Fung. Biomechanics: Mechanical Properties of Living Tissues. Springer-Verlag, 1993.
145. B. G. Galerkin. Series solution of some problems in elastic equilibrium of rods and plates. Vestnik inzhenerov i tekhnikov, 19:897-908, 1915.
146. E. Gamma, R. Helm, R. Johnson, and J. Vlissides. Design Patterns: Elements of Reusable Object-Oriented Software. Addison Wesley, 1995.
147. GDB. Software package. URL http://www.gnu.org/software/gdb.
148. M. W. Gee, C. M. Siefert, J. J. Hu, R. S. Tuminaro, and M. G. Sala. ML 5.0 smoothed aggregation user’s guide. Technical Report SAND2006-2649, Sandia National Laboratories, 2006.
149. W. J. German and S. P. W. Black. Cervical ligation for internal carotid aneurysms. Journal of Neurosurgery, 23(6):572-577, 1965. URL http://dx.doi.org/10.3171/jns.1965.23.6.0572.
150. C. Geuzaine and J.-F. Remacle. Gmsh-a 3d mesh generator.
151. R. Giering and T. Kaminski. Recipes for adjoint code construction. ACM Trans. Math. Softw., 24(4): 437-474, 1998. URL http://dx.doi.org/10.1145/293686.293695.
152. M. Giles and E. Süli. Adjoint methods for PDEs: A posteriori error analysis and postprocessing by duality. Acta Numer., 11:145-236, 2002.
153. D. T. Gillespie. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem., 81(25): 2340-2361, 1977. URL http://dx.doi.org/10.1021/j100540a008.
154. V. Girault and P.-A. Raviart. Finite element methods for Navier-Stokes equations, volume 5 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 1986.
155. M. S. Gockenbach. Understanding and Implementing the Finite Element Method. Society for Industrial and Applied Mathematics, 2006.
156. K. Goda. A multistep technique with implicit difference schemes for calculating two-or threedimensional cavity flows. Journal of Computational Physics, 30(1):76-95, 1979. URL http://dx.doi.org/10.1016/0021-9991(79)90088-3.
157. G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, third edition, 1996.
158. D. C. Grahame. The electrical double layer and the theory of electrocapillarity. Chem Rev, 41(3): 441-501, Dec 1947.
159. T. Grätsch and K. Bathe. Goal-oriented error estimation in the analysis of fluid flows with structural interactions. Computer Methods in Applied Mechanics and Engineering, 195(41-43):5673-5684, 2006.
160. H. Gray. Anatomy, Descriptive and Surgical. Lea Brothers, 1897.
161. J. L. Greenstein and R. L. Winslow. An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release. Biophys. J., 83(6):2918-2945, Dec 2002. URL http://dx.doi.org/10.1016/S0006-3495(02)75301-0.
162. A. Griewank. On automatic differentiation. In M. Iri and K. Tanabe, editors, Mathematical Programming: Recent Developments and Applications, pages 83-108. Kluwer Academic Publishers, 1989.
163. F. F. Grinstein, L. G. Margolin, and W. J. Rider. Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics. Cambridge University Press, New York, 2007.
164. J. L. Guermond and J. Shen. A new class of truly consistent splitting schemes for incompressible flows. J. Comput. Phys., 192(1):262-276, 2003. URL http://dx.doi.org/10.1016/j.jcp.2003.07.009.
165. J. L. Guermond, P. Minev, and J. Shen. An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Engrg, 41:112-134, 2006.
166. A. Guia, M. D. Stern, E. G. Lakatta, and I. R. Josephson. Ion concentration-dependence of rat cardiac unitary l-type calcium channel conductance. Biophys J, 80(6):2742-2750, 2001. URL http://dx.doi.org/10.1016/S0006-3495(01)76242-X.
167. S. Gupta, M. Soellinger, P. Boesiger, D. Pulikako, and V. Kurtcuoglu. Three-dimensional computational modeling of subject-specific cerebrospinal fluid flow in the subarachnoid space. J. Biomech. Eng., 131, 2009.
168. M. E. Gurtin. An Introduction to Continuum Mechanics. Academic Press, 1981.
169. W. Hackbusch. Iterative Solution of Large Sparse Systems of Equations. Springer-Verlag, 1994.
170. E. Hairer and G. Wanner. Solving Ordinary Differential Equations I — Nonstiff Problems. Springer Series in Computational Mathematics, vol. 8, 1991a.
171. E. Hairer and G. Wanner. Solving Ordinary Differential Equations. II, volume 14 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 1991b.
172. P. Hansbo. A Crank-Nicolson type space-time finite element method for computing on moving meshes. Journal of Computational Physics, 159:274-289, 2000.
173. P. Hansbo and M. G. Larson. Discontinuous Galerkin and the Crouzeix-Raviart element: Application to elasticity. Math. Model. Numer. Anal., 37:63-72, 2003. URL http://dx.doi.org/10.1051/m2an:2003020.
174. T. Hansen and G. Wollman. US secure hash algorithm 1 (SHA1). URL http://www.apps.ietf.org/rfc/rfc3174.html.
175. U. Hansen and A. Ebel. Time-dependent thermal convection-a possible explanation for a multiscale flow in the earth’s mantle. Geophysical Journal, 94:181-191, 1988.
176. U. Hansen and D. A. Yuen. Numerical simulation of thermal-chemical instabilities at the core-mantle boundary. Nature, 334:237-240, 1988.
177. V. Haughton, F. R. Korosec, J. E. Medow, M. T. Dolar, and B. J. Iskandar. Peak systolic and diastolic CSF velocity in the foramen magnum in adult patients with Chiari I malformations and in normal control participants. Am. J. Neuroradiol., 24:169-176, 2003.
178. J. D. Heiss, N. Patronas, H. L. DeVroom, T. Shawker, R. Ennis, W. Kammerer, A. Eidsath, T. Talbot, J. Morris, E. Eskioglu, and E. H. Oldfield. Elucidating the pathophysiology of syringomyelia. J. Neurosurg., 91:532-562, 1999.
179. S. Hentschel, K.-A. Mardal, A. E. Løvgren, S. Linge, and V. Haughton. Characterization of cyclical CSF flow in the foramen magnum and upper cervical spinal canal with MR flow imaging and computational fluid dynamics. American Journal of Neuroradiology, 31(6):997-1002, 2010.
180. J. Hermansson and P. Hansbo. A variable diffusion method for mesh smoothing. Communications in Numerical Methods in Engineering, 19(11):897-908, 2003.
181. V. Hernandez, J. E. Roman, and V. Vidal. SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Transactions on Mathematical Software, 31(3):351-362, Sept. 2005.
182. V. Hernandez, J. E. Roman, E. Romero, A. Tomas, and V. Vidal. SLEPc users manual. Technical Report DSIC-II/24/02-Revision 3.0.0, D. Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, 2009.
183. M. A. Heroux, R. A. Bartlett, V. E. Howle, R. J. Hoekstra, J. J. Hu, T. G. Kolda, R. B. Lehoucq, K. R. Long, R. P. Pawlowski, E. T. Phipps, A. G. Salinger, H. K. Thornquist, R. S. Tuminaro, J. M. Willenbring, A. Williams, and K. S. Stanley. An overview of the Trilinos project. ACM Trans. Math. Softw., 31(3):397-423, 2005. URL http://dx.doi.org/10.1145/1089014.1089021.
184. M. R. Hestenes and E. Stiefel. Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Stand, 49(6):409-436, 1952.
185. M. L. Hetland. Practical Python. APress, 2002.
186. H. M. Hilber, T. J. R. Hughes, and R. L. Taylor. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering and Structural Dynamics, 5(3):283-292, 1977.
187. B. Hille. Ion Channels of Excitable Membranes. Sinauer, Sunderland, MA, 2001.
188. R. Hiptmair. Multigrid method for H(div) in three dimensions. Electronic Transactions on Numerical Analysis, 6:133-152, 1997.
189. R. Hiptmair. Multigrid method for Maxwell’s equations. SIAM Journal on Numerical Analysis, 36(1): 204-225, 1999.
190. R. Hiptmair. Operator preconditioning. Computers & Mathematics with Applications, 52(5):699-706, 2006.
191. J. Hoffman. Computation of mean drag for bluff body problems using adaptive DNS/LES. SIAM J. Sci. Comput., 27(1):184-207, 2005.
192. J. Hoffman. Adaptive simulation of the turbulent flow past a sphere. J. Fluid Mech., 568:77-88, 2006.
193. J. Hoffman. Efficient computation of mean drag for the subcritical flow past a circular cylinder using general Galerkin G2. Int. J. Numer. Meth. Fluids, 2009.
194. J. Hoffman and N. Jansson. A computational study of turbulent flow separation for a circular cylinder using skin friction boundary conditions. In Proceedings of Workshop for Quality and Reliability of Large-Eddy Simulations II, 2009.
195. J. Hoffman and C. Johnson. A new approach to computational turbulence modeling. Comput.Methods Appl. Mech. Engrg., 195:2865-2880, 2006.
196. J. Hoffman and C. Johnson. Computational Turbulent Incompressible Flow. Springer, 2007. URL http://dx.doi.org/10.1007/978-3-540-46533-1.
197. J. Hoffman and C. Johnson. Resolution of d’Alembert’s paradox. J. Math. Fluid Mech., Online First December 2008, 2008.
198. J. Hoffman, J. Jansson, and M. Stöckli. Unified continuum modeling of fluid-structure interaction. Mathematical Models and Methods in Applied Sciences, 2011.
199. J. Hoffman, J. Jansson, and R. V. de Abreu. Adaptive modeling of turbulent flow with residual based turbulent kinetic energy dissipation. Comput. Meth. Appl. Mech. Eng., 200(37-40):2758-2767, 2011a
200. E. Hofmann, M. Warmuth-Metz, M. Bendszus, and L. Solymosi. Phase-contrast MR imaging of the cervical CSF and spinal cord: Volumetric motion analysis in patients with Chiari i malformation. AJNR Am J Neuroradiol, 21:151-158, 2000.
201. G. A. Holzapfel. Nonlinear Solid Mechanics: A Continuum Approach for Engineering. John Wiley & Sons, 2000.
202. th).
203. J. Hu, R. Tuminaro, P. Bochev, C. Garasi, and A. Robinson. Toward an h-independent algebraic multigrid method for Maxwell’s equations. SIAM Journal on Scientific Computing, 27(5):1669-1688, 2006.
204. J. Huang, L. Guo, and Z. Shi. Vibration analysis of Kirchhoff plates by the Morley element method. Journal of Computational and Applied Mathematics, 213(1):14-34, 2008.
205. W. X. Huang and T. Itoh. Complex modes in lossless shielded microstrip lines. IEEE Transactions on Microwave Theory and Techniques, 36(1):163-165, 1988.
206. T. J. R. Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, 1987.
207. T. J. R. Hughes, L. P. Franca, and M. Balestra. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering, 59:85-99, 1986.
208. T. J. R. Hughes, J. A. Cottrell, and Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194 (39-41):4135-4195, 2005.
209. J. D. Humphrey. Cardiovascular Solid Mechanics. Springer, 2001. Hypre. Software package. URL http://www.llnl.gov/CASC/hypre/.
210. M. G. Imhof and A. K. Sharma. Seismostratigraphic inversion: Appraisal, ambiguity, and uncertainty. Geophysics, 72(4):R51-R65, 2007.
211. T. Ingebrigtsen, M. K. Morgan, K. Faulder, L. Ingebrigtsen, T. Sparr, and H. Schirmer. Bifurcation geometry and the presence of cerebral artery aneurysms. J Neurosurg., 101:108-113, 2004. URL http://dx.doi.org/10.3171/jns.2004.101.1.0108.
212. A. Ismail-Zadeh and P. Tackley. Computational Methods for Geodynamics. Cambridge University Press, 2010.
213. T. Itoh, P. Silvester, and G. Pelosi. Finite Element Software for Microwave Engineering. John Wiley & Sons, Inc. New York, NY, USA, 1996.
214. M. S. Jafri, J. J. Rice, and R. L. Winslow. Cardiac Ca2+ dynamics: The roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys. J., 74(3):1149-68, Mar 1998. URL http://www.biophysj.org/cgi/content/full/74/3/1149.
215. P. Jäger, P. Steinmann, and E. Kuhl. Modeling three-dimensional crack propagation-a comparison of crack path tracking strategies. International Journal for Numerical Methods in Engineering, 76(9): 1328-1352, 2008.
216. J. Jansson. Performance optimization of unicorn. Technical report, 2009.
217. N. Jansson. High performance adaptive finite element methods for turbulent fluid flow. Licentiate thesis, Royal Institute of Technology, School of Computer Science and Engineering, 2011. TRITA-CSC-A 2011:02.
218. N. Jansson, J. Hoffman, and J. Jansson. Performance of Dolfin and Unicorn on modern highperformance distributed memory architectures. Technical Report KTH-CTL-4012, Computational Technology Laboratory, 2010. http://www.publ.kth.se/trita/ctl-4/012/.
219. G. T. Jarvis and J. P. Lowman. Survival times of subducted slab remnants in numerical models of mantle flow. Earth and Planetary Science Letters, 260(1-2):23-36, 2007. URL http://dx.doi.org/10.1016/j.epsl.2007.05.009.
220. J. Jiang, K. Johnson, K. Valen-Sendstad, K.-A. Mardal, O. Wieben, and C. Strother. Flow characteristics in a canine aneurysm model: A comparison of 4-D accelerated phase-contrast MR measurements and computational fluid dynamics simulations. 2011. Accepted in Medical Physics. J. Jin. The Finite Element Method in Electromagnetics. John Wiley & Sons, Inc., New York, 2nd edition, 2002. ISBN 0471438189.
221. V. John and P. Knobloch. On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations: Part I-A review. Computer Methods in Applied Mechanics and Engineering, 196(17-20):2197-2215, 2007. URL http://dx.doi.org/10.1016/j.cma.2006.11.013.
222. R. S. Johnson. A Modern Introduction to the Mathematical Theory of Water Waves. Cambridge Texts in Applied Mathematics. Cabridge University Press, Cambridge, 1997.
223. E. Jones, T. Oliphant, P. Peterson, et al. SciPy: Open source scientific tools for Python, 2009. URL http://scipy.org.
224. J. Karczmarczuk. Functional differentiation of computer programs. Higher-Order and Symbolic Computation, 14(1):35-57, 2001. URL http://dx.doi.org/10.1023/A:1011501232197.
225. G. E. Karniadakis and S. J. Sherwin. Spectral/hp Element Methods for Computational Fluid Dynamics. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford, second edition, 2005.
226. M. Keegan, D. Ridzal, and P. Bochev. Sparse-grid integration in finite element spaces. CSRI Summer Proceedings, page 32, 2008.
227. B. L. N. Kennett and H.-P. Bunge. Geophysical Continua. Cambridge University Press, 2008. J. T. Kirby. Funwave homepage, 1998. URL http://chinacat.coastal.udel.edu/programs/funwave/funwave.html.
228. R. C. Kirby. Algorithm 839: FIAT, a new paradigm for computing finite element basis functions. ACM Trans. Math. Softw., 30:502-516, 2004. URL http://dx.doi.org/10.1145/1039813.1039820.
229. R. C. Kirby. FIAT, 2006a. URL http://fenicsproject.org.
230. R. C. Kirby. Optimizing FIAT with level 3 BLAS. ACM Trans. Math. Softw., 32:223-235, 2006b. URL http://dx.doi.org/10.1145/1141885.1141889.
231. R. C. Kirby. Singularity-free evaluation of collapsed-coordinate orthogonal polynomials. ACM Trans. Math. Softw., 37:5:1-5:16, 2010a. URL http://dx.doi.org/10.1145/1644001.1644006.
232. R. C. Kirby. From functional analysis to iterative methods. SIAM Review, 52:269-293, 2010b. URL http://dx.doi.org/10.1137/070706914.
233. R. C. Kirby. Fast simplicial finite element algorithms using Bernstein polynomials. Numerische Mathematik, 117(4):631-652, 2011.
234. R. C. Kirby and A. Logg. A compiler for variational forms. ACM Trans. Math. Softw., 32:417-444, 2006. URL http://dx.doi.org/10.1145/1163641.1163644.
235. R. C. Kirby and A. Logg. Efficient compilation of a class of variational forms. ACM Transactions on Mathematical Software, 33(3), 2007.
236. R. C. Kirby and A. Logg. Benchmarking domain-specific compiler optimizations for variational forms. ACM Transactions on Mathematical Software, 35(2):1-18, 2008. URL http://dx.doi.org/10.1145/1377612.1377614.
237. R. C. Kirby and L. R. Scott. Geometric optimization of the evaluation of finite element matrices. SIAM J. Sci. Comput., 29:827-841, 2007. URL http://dx.doi.org/10.1137/060660722.
238. R. C. Kirby, M. G. Knepley, A. Logg, and L. R. Scott. Optimizing the evaluation of finite element matrices. SIAM J. Sci. Comput., 27(6):741-758, 2005.
239. R. C. Kirby, A. Logg, L. R. Scott, and A. R. Terrel. Topological optimization of the evaluation of finite element matrices. SIAM Journal on Scientific Computing, 28(1):224-240, 2006. URL http://dx.doi.org/10.1137/050635547.
240. J. Kiusalaas. Numerical Methods in Engineering with Python. Cambridge University Press, second edition, 2009.
241. M. G. Knepley and D. A. Karpeev. Mesh algorithms for PDE with Sieve I: Mesh distribution. Scientific Programming, 17(3):215-230, 2009.
242. X. Koh, B. Srinivasan, H. S. Ching, and A. Levchenko. A 3D Monte Carlo analysis of the role of dyadic space geometry in spark generation. Biophys. J., 90(6):1999-2014, 2006. URL http://dx.doi.org/10.1529/biophysj.105.065466.
243. G. L. Kongable, G. Lanzino, T. P. Germanson, L. L. Truskowski, W. M. Alves, J. C. Torner, and N. F. Kassell. Gender-related differences in aneurysmal subarachnoid hemorrhage. Journal of Neurosurgery, 84:43-48, 1996.
244. J. Korelc. Automatic generation of finite-element code by simultaneous optimization of expressions. Theoretical Computer Science, 187(1-2):231-248, 1997. URL http://dx.doi.org/10.1016/S0304-3975(97)00067-4.
245. J. Korelc. Multi-language and multi-environment generation of nonlinear finite element codes. Engineering with Computers, 18(4):312-327, 2002. URL http://dx.doi.org/10.1007/s003660200028.
246. J. Krejza, P. Szydlik, D. S. Liebeskind, J. Kochanowicz, O. Bronov, Z. Mariak, and E. R. Melhem. Age and sex variability and normal reference values for the vMCA/vICA index. American Journal of Neuroradiology, 26(4):730-735, 2005. URL http://www.ajnr.org/cgi/content/abstract/26/4/730.
247. A. Kuchling. Python’s dictionary implementation: Being all things to all people. In A. Oram and G. Wilson, editors, Beautiful Code, chapter 18, pages 293-302. O’Reilly, 2007. URL http://portal.acm.org/citation.cfm?id=1407867.
248. J. D. Lambert. Numerical Methods for Ordinary Differential Systems. John Wiley & Sons Ltd., Chichester, 1991.
249. L. Landweber. An iteration formula for Fredholm integral equations of the first kind. Amer. J. Math., 73:615-624, 1951.
250. G. A. Langer and A. Peskoff. Calcium concentration and movement in the diadic cleft space of the cardiac ventricular cell. Biophys. J., 70(3):1169-1182, 1996. URL http://dx.doi.org/10.1016/S0006-3495(96)79677-7.
251. M. Langner, D. Cafiso, S. Marcelja, and S. McLaughlin. Electrostatics of phosphoinositide bilayer membranes. Theoretical and experimental results. Biophys. J., 57(2):335-349, 1990. URL http://dx.doi.org/10.1016/S0006-3495(90)82535-2.
252. H. P. Langtangen. Python Scripting for Computational Science, volume 3 of Texts in Computational Science and Engineering. Springer, third edition, 2008. URL http://dx.doi.org/10.1007/978-3-540-73916-6.
253. H. P. Langtangen. A Primer on Scientific Programming with Python, volume 6 of Texts in Computational Science and Engineering. Springer, second edition, 2011. URL http://dx.doi.org/10.1007/978-3-642-18366-9.
254. H. P. Langtangen and K.-A. Mardal. Using Diffpack from Python scripts. In H. P. Langtangen and A. Tveito, editors, Advanced Topics in Computational Partial Differential Equations-Numerical Methods and Diffpack Programming, Lecture Notes in Computational Science and Engineering, pages 321-360. Springer-Verlag, 2003.
255. H. P. Langtangen and G. Pedersen. Computational models for weakly dispersive nonlinear water waves. Computer Methods in Applied Mechanics and Engineering, 160(3-4):337-358, 1998. URL http://dx.doi.org/10.1016/S0045-7825(98)00293-X.
256. P. Lascaux and P. Lesaint. Some nonconforming finite elements for the plate bending problem. Rev. Française Automat. Informat. Recherche Operationnelle RAIRO Analyse Numérique, 9(R-1):9-53, 1975.
257. P. D. Lax and A. N. Milgram. Parabolic equations. Annals of Mathematics Studies, 33:167-190, 1954.
258. J.-F. Lee. Finite element analysis of lossy dielectric waveguides. IEEE Transactions onMicrowave Theory Techniques, 42(5):1025-1031, June 1994.
259. J.-F. Lee, D.-K. Sun, and Z. J. Cendes. Full-wave analysis of dielectric waveguides using tangential vector finite elements. IEEE Trans. Microwave Theory Tech., 39(8):1262-1271, August 1991.
260. A. Lenardic and W. M. Kaula. A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces. J. Geophys. Res., 98(B5):8243-8260, 1993.
261. X. Li. An overview of SuperLU: Algorithms, implementation, and user interface. ACM Transactions on Mathematical Software, 31(3):302-325, 2005.
262. B. Q. Lin. Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer. Computational Fluid and Solid Mechanics. Springer-Verlag, 2006. URL http://dx.doi.org/10.1007/1-84628-205-5.
263. H. Lindekleiv, K. Valen-Sendstad, M. F. Morgan, K.-A. Mardal, K. Faulder, J. Magnus, K. Waterloo, B. Romner, and T. Ingebrigtsen. Sex differences in intracranial arterial bifurcations. Gender Medicine, 7(2):149-155, 2010. URL http://dx.doi.org/10.1016/j.genm.2010.03.003.
264. S. Linge, V. Haughton, A. E. Løvgren, K.-A. Mardal, and H. P. Langtangen. CSF flow dynamics at the craniovertebral junction studied with an idealized model of the subarachnoid space and computational flow analysis. American Journal of Neuroradiology, 31(1):185-192, 2010. URL http://dx.doi.org/10.3174/ajnr.A1766.
265. S. Linge, V. Haughton, A. E. Løvgren, K.-A.Mardal, A. Helgeland, and H. P. Langtangen. Effect of tonsilar herniation on cyclic CSF flow studied with computational flow analysis. American Journal of Neuroradiology, 32(8):1474-1481, 2011. URL http://dx.doi.org/10.3174/ajnr.A2496.
266. A. Logg. Multi-adaptive time-integration. Applied Numerical Mathematics, 48(3-4):339-354, 2004. URL http://dx.doi.org/10.1016/j.apnum.2003.11.004.
267. A. Logg. Automating the Finite Element Method. Arch. Comput. Methods Eng., 2(14):93-138, 2007.
268. A. Logg. Efficient representation of computational meshes. International Journal of Computational Science and Engineering, 4(4):283-295, 2009.
269. A. Logg and K.-A. Mardal. Exterior, 2009. URL http://fenicsproject.org.
270. A. Logg and G. N. Wells. DOLFIN: Automated finite element computing. ACM Transactions on Mathematical Software, 32(2):1-28, 2010. URL http://dx.doi.org/10.1145/1731022.1731030.
271. K. Long. Sundance, a rapid prototyping tool for parallel PDE-constrained optimization. In Large-Scale PDE-Constrained Optimization, Lecture Notes in Computational Science and Engineering. Springer-Verlag, 2003.
272. K. Long. Sundance 2.0 tutorial. Technical Report TR-2004-09, Sandia National Laboratories, 2004a.
273. K. Long. Efficient discretization and differentiation of partial differential equations through automatic functional differentiation, 2004b. http://www.autodiff.org/ad04/abstracts/Long.pdf.
274. W. T. Longstreth, L. M. Nelson, and G. T. D. Koepsell andvan Belle. Subarachnoid hemorrhage and hormonal factors in women: A population-based case-control study. Ann Intern Med, 121(3): 168-173, 1994.
275. N. Lopes. Relatório do Curso de Formação avançada: Alguns Modelos de Propagação de Ondas Marítimas.
276. PhD report, Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, 2007.
277. N. D. Lopes, P. J. S. Pereira, and L. Trabucho. A numerical analysis of a class of generalized Boussinesq-type equations using continuous/discontinuous FEM. International Journal for Numerical Methods in Fluids, 2011 URL http://dx.doi.org/10.1002/fld.2631.
278. E. J. López, N. M. Nigro, and M. A. Storti. Simultaneous untangling and smoothing of moving grids. International Journal for Numerical Methods in Engineering, 76(7):994-1019, 2008.
279. F. Loth, M. A. Yardimci, and N. Alperin. Hydrodynamic modeling of cerebrospinal fluid motion within the spinal cavity. J. Biomech. Eng., 123:71-79, 2001.
280. J. Lotz, C. Meier, A. Leppert, and M. Galanski. Cardiovascular flow measurement with phase-contrast MR imaging: Basic facts and implementation. Radiographics, 22(3):651-671, 2002.
281. F. Løvholt and G. Pedersen. Instabilities of Boussinesq models in non-uniform depth. International Journal for Numerical Methods in Fluids, 61(6):606-637, 2009. ISSN 0271-2091.
282. J. Lubliner. Plasticity Theory. Dover Publications, 2008.
283. M. Lutz. Programming Python. O’Reilly, third edition, 2006.
284. M. Lutz. Learning Python. O’Reilly, third edition, 2007.
285. P. J. Lynett and P. L.-F. Liu. Coulwave model page, 2004. URL https://ceprofs.civil.tamu.edu/plynett/COULWAVE/default.htm.
286. Y. Maday, A. Patera, and E. Rønquist. The PN × PN−2 method for the approximation of the Stokes problem. Technical report, Department of Mechanical Engineering, Massachusetts Institute of Technology, 1992.
287. P. A. Madsen and Y. Agnon. Accuracy and convergence of velocity formulations for water waves in the framework of Boussinesq theory. J. Fluid Mech., 477:285-319, 2003.
288. P. A. Madsen, R. Murray, and O. R. Sørensen. A new form of the Boussinesq equations with improved linear dispersion characteristics. Coastal Engineering, 15(4):371-388, 1991. URL http://dx.doi.org/10.1016/0378-3839(91)90017-B.
289. P. A. Madsen, H. B. Bingham, and H. A. Schäffer. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 459(2033):1075-1104, 2003. URL http://dx.doi.org/10.1098/rspa.2002.1067.
290. M. R. Malik, T. R. Zang, and M. Y. Hussaini. A spectral collocation method for the Navier-Stokes equations. Technical Report 172365, ICASE report no. 84-19., NASA, 1984.
291. D. S. Malkus. Eigenproblems associated with the discrete LBB condition for incompressible finite elements. Internat. J. Engrg. Sci., 19(10):1299-1310, 1981.
292. D. S. Malkus. The Finite Element Method, chapter 4.II, pages 276-303. Dover, 2000.
293. T. A. Manteuffel. An incomplete factorization technique for positive definite linear systems. Mathematics of Computation, 34(150):473-497, 1980.
294. G. Marckmann and E. Verron. Comparison of hyperelastic models for rubber-like materials. Rubber chemistry and technology, 79(5):835-858, 2006.
295. K.-A. Mardal and R. Winther. Uniform preconditioners for the time dependent Stokes problem. Numerische Mathematik, 98(2):305-327, 2004. ISSN 0029-599X.
296. K.-A. Mardal and R. Winther. Preconditioning discretizations of systems of partial differential equations. Numerical Linear Algebra with Applications, 18(1):1-40, 2011. URL http://dx.doi.org/10.1002/nla.716.
297. K. A. Mardal, X.-C. Tai, and R. Winther. A robust finite element method for Darcy-Stokes flow. SIAM J. Numer. Anal., 40(5):1605-1631, 2002.
298. A. Martelli. Python in a Nutshell. O’Reilly, second edition, 2006.
299. A. Martelli and D. Ascher. Python Cookbook. O’Reilly, second edition, 2005.
300. MayaVi2. Software package. URL http://code.enthought.com/projects/mayavi/.
301. B. W. McCormick. Aerodynamics, Aeronautics and Flight Mechanics. John Wiley and Sons, second edition, 1995.
302. S. G. McLaughlin, G. Szabo, and G. Eisenman. Divalent ions and the surface potential of charged phospholipid membranes. J. Gen. Physiol., 58(6):667-687, Dec 1971. URL http://www.jgp.org/cgi/reprint/58/6/667.
303. A. K. McNamara and S. Zhong. Thermochemical structures beneath Africa and the Pacific Ocean. Nature, 437:1136-1139, 2005.
304. A. K. McNamara, E. J. Garnero, and S. Rost. Tracking deep mantle reservoirs with ultra-low velocity zones. Earth and Planetry Science Letters, 299:1-9, 2010.
305. M. K. McNutt. Superswells. Rev. Geophys., 36:211-244, 1998.
306. MeshBuilder. Software package. URL http://launchpad.net/meshbuilder.
307. C. N. Mhurchu, C. Anderson, K. Jamrozik, G. Hankey, and D. Dunbabin. Hormonal factors and risk of aneurysmal subarachnoid hemorrhage: An international population-based, case-control study. Stroke, 32:606-612, 2001.
308. T. Milhorat and P. A. Bolognese. Tailored operative technique for chiari type i malformations using intraoperative color doppler ultrasonography. Neurosurgery, 53(4):899-906, 2003.
309. W. Ming and J. Xu. The Morley element for fourth order elliptic equations in any dimensions. Numerische Mathematik, 103(1):155-169, 2006.
310. N. Moës, J. Dolbow, and T. Belytschko. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46(1):231-150, 1999.
311. P. Monk. Finite Element Methods for Maxwell’s Equations. Oxford University Press, Oxford, 2003.
312. N. L. Montague, H. L. Kellogg, and M. Manga. High Rayleigh number thermo-chemical models of a dense boundary layer in D”. Geophys. Res. Lett., 25(13):2345-2348, 1998.
313. L. S. D. Morley. The triangular equilibrium element in the solution of plate bending problems. Aero. Quart., 19:149-169, 1968.
314. L. S. D. Morley. The constant-moment plate-bending element. The Journal of Strain Analysis for Engineering Design, 6(1):20-24, 1971.
315. M. Mortensen, H. P. Langtangen, and J. Myre. CBC.RANS-a new flexible, programmable software framework for computational fluid dynamics. In H. I. Andersson and B. Skallerud, editors, Sixth National Conference on Computational Mechanics (MekIT’11). Tapir, 2011.
316. M. Mortensen, H. P. Langtangen, and G. N. Wells. A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations. Advances in Water Resources, 34(9):1082-1101, 2011. URL http://dx.doi.org/10.1016/j.advwatres.2011.02.013.
317. MTL4. Software package. URL http://www.mtl4.org.
318. C. J. L. Murray and A. D. Lopez. Alternative projections of mortality and disability by cause 1990-2020: Global burden of disease study. The Lancet, 349(9064):1498-1504, 1997. URL http://dx.doi.org/10.1016/S0140-6736(96)07492-2.
319. J. C. Nagtegaal, D. M. Parks, and J. R. Rice. On numerically accurate finite element solutions in the fully plastic range. Computer Methods in Applied Mechanics and Engineering, 4(2):153-177, 1974. URL http://dx.doi.org/10.1016/0045-7825(74)90032-2.
320. M. Nazarov. An adaptive finite element method for the compressible Euler equations. Licentiate thesis, 2009.
321. M. Nazarov. Adaptive Algorithms and High Order Stabilization for Finite Element Computation of Turbulent Compressible Flow. PhD thesis, KTH, Numerical Analysis, NA, 2011. QC 20110627.
322. J.-C. Nédélec. Mixed finite elements in R3. Numer. Math., 35(3):315-341, 1980. URL http://dx.doi.org/10.1007/BF01396415.
323. J.-C. Nédélec. A new family of mixed finite elements in R3. Numer. Math., 50(1):57-81, 1986.
324. M. Nikbakht and G. N. Wells. Automated modelling of evolving discontinuities. Algorithms, 2(3): 1008-1030, 2009. URL http://dx.doi.org/10.3390/a2031008.
325. O. Nwogu. Alternative form of Boussinesq equations for nearshore wave propagation. Journal of Waterway, Port, Coastal, and Ocean Engineering, 119(6):618-638, 1993.
326. J. T. Oden and L. Demkowicz. Applied Functional Analysis. CRC press, 1996.
327. R. W. Ogden. Nonlinear Elastic Deformations. Dover Publications, 1997.
328. E. H. Oldfield, K. Muraszko, T. H. Shawker, and N. J. Patronas. Pathophyiology of syringomyelia associated with chiari i malformation of the cerebellar tonsils. Neurosurg., 80:3-15, 1994.
329. K. B. Ølgaard and G. N. Wells. Optimisations for quadrature representations of finite element tensors through automated code generation. ACM Transactions on Mathematical Software, 37(1):8:1-8:23, 2010. URL http://dx.doi.org/10.1145/1644001.1644009.
330. K. B. Ølgaard, A. Logg, and G. N. Wells. Automated code generation for discontinuous Galerkin methods. SIAM J. Sci. Comput., 31(2):849-864, 2008. URL http://dx.doi.org//10.1137/070710032.
331. S. A. Orzag. Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech., 50:689-703, 1971. URL http://dx.doi.org/10.1017/S0022112071002842.
332. S. K. Pandit, J. C. Kalita, and D. C. Dalal. A transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular. Journal of Computational Physics, 225(1):1100-1124, 2007.
333. R. L. Panton. Incompressible Flow. John Wiley & Sons Inc, 1984.
334. ParaView. Software package. URL http://www.paraview.org.
335. ParMETIS. Software package. URL http://glaros.dtc.umn.edu/gkhome/metis/parmetis/overview.
336. PaStiX. Software package. URL http://pastix.gforge.inria.fr/.
337. B. A. Pearlmutter and J. M. Siskind. Lazy multivariate higher-order forward-mode AD. In Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pages 155-160, Nice, France, 2007. URL http://dx.doi.org/10.1145/1190216.1190242.
338. G. Pedersen and F. Løvholt. Documentation of a global Boussinesq solver. Technical report, 2008. URL http://www.math.uio.no/eprint/appl_math/2008/01-08.html.
339. F. Pellegrini. Scotch. URL http://www.labri.fr/perso/pelegrin/scotch.
340. G. Pelosi, R. Coccioli, and S. Selleri. Quick Finite Elements for Electromagnetic Waves. ArtechHouse, Norwood, 1998.
341. D. H. Peregrine. Long waves on a beach. Journal of Fluid Mechanics Digital Archive, (27):815-827, 1967. URL http://dx.doi.org/10.1017/S0022112067002605.
342. A. Peskoff, J. A. Post, and G. A. Langer. Sarcolemmal calcium binding sites in heart: II. Mathematical model for diffusion of calcium released from the sarcoplasmic reticulum into the diadic region. J. Membr. Biol., 129(1):59-69, Jul 1992. URL http://dx.doi.org/10.1007/BF00232055.
343. PETSc. Software package. URL http://www.anl.gov/petsc.
344. G. Pinna, F. Alessandrini, A. Alfieri, M. Rossi, and A. Bricolo. Cerebrospinal fluid flow dynamics study in Chiari I malformation: Implications for syrinx formation. Neurosurg Focus 8, 3(3), 2000.
345. U. Piomelli and E. Balaras. Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech., 34: 349-374, 2002.
346. A. C. Polycarpou, M. Lyons, and C. A. Balanis. Finite element analysis ofMMIC waveguide structures with anisotropic substrates. IEEE Trans. Microwave Theory Tech., 44(10):1650-1663, October 1996.
347. D. M. Pozar. Microwave Engineering. John Wiley & Sons, Inc., third edition, 2005.
348. R. C. Prim. Shortest connection networks and some generalizations. Bell System Technical Journal, 36 (6):1389-1401, 1957. URL http://bstj.bell-labs.com/BSTJ/images/Vol36/bstj36-6-1389.pdf.
349. C. Prud’homme. Life: Overview of a unified c++ implementation of the finite and spectral element methods in 1d, 2d and 3d. In Workshop On State-Of-The-Art In Scientific And Parallel Computing, Lecture Notes in Computer Science, page 10. Springer-Verlag, dec 2006a.
350. C. Prud’homme. A domain specific embedded language in C++ for automatic differentiation, projection, integration and variational formulations. Sci. Program., 14(2):81-110, 2006b. URL http://portal.acm.org/citation.cfm?id=1376891.1376895.
351. Pyrex. Software package. URL http://www.cosc.canterbury.ac.nz/greg.ewing/python/Pyrex/.
352. Python C-API. Python C API Reference Manual. URL http://docs.python.org/c-api.
353. J. Qin. On the Convergence of Some Simple Finite Elements for Incompressible Flows. PhD thesis, Penn State, 1994.
354. A. Quarteroni and A. Valli. Numerical Approximation of Partial Differential Equations, volume 23 of Springer Series in Computational Mathematics. Springer Verlag, 2008. URL http://dx.doi.org/10.1007/978-3-540-85268-1.
355. M. F. Quigley, B. J. Iskandar, M. A. Quigley, M. N. Nicosia, and V. Haughton. Cerebrospinal fluid flow in foramen magnum: Temporal and spatial patterns at MR imaging in volunteers and in patients with Chiari I malformation. Radiology, 232:229-236, 2004.
356. S. Ramo, J. R. Whinnery, and T. Van Duzer. Fields and Waves in Communication Electronics. John Wiley & Sons, New York, third edition, 1994.
357. R. Rannacher and S. Turek. A simple nonconforming quadrilateral Stokes element. Numer. Meth. Parth. Diff. Equ., 8:97-111, 1992.
358. P.-A. Raviart and J. M. Thomas. A mixed finite element method for 2nd order elliptic problems. In Mathematical aspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome, 1975), pages 292-315. Lecture Notes in Math., Vol. 606. Springer, Berlin, 1977.
359. Rayleigh. On the theory of resonance. Trans. Roy. Soc., A161:77-118, 1870.
360. Y. Ricard. Physics of mantle convection, volume 7 of Treatise on geophysics, pages 1-30. 2009.
361. W. Ritz. Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. J. reine angew. Math., 135:1-61, 1908.
362. M.-C. Rivara. Mesh refinement processes based on the generalized bisection of simplices. SIAM Journal on Numerical Analysis, 21(3):604-613, 1984. URL http://dx.doi.org/10.1137/0721042.
363. M.-C. Rivara. Local modification of meshes for adaptive and/or multigrid finite-element methods. Journal of Computational and Applied Mathematics, 36(1):78-89, 1992.
364. J. C. Rivenæs. Application of a dual-lithology, depth-dependent diffusion equation in stratigraphic simulation. Basin Research, 4:133-146, 1992.
365. J. C. Rivenæs. A Computer Simulation Model for Siliciclastic Basin Stratigraphy. PhD thesis, NTH-Trondheim, 1993.
366. M. E. Rognes. Automated stability condition tester (ASCoT). 2009. URL https://launchpad.net/ascot.
367. M. E. Rognes, R. C. Kirby, and A. Logg. Efficient assembly of H(div) and H(curl) conforming finite elements. SIAM Journal on Scientific Computing, 31(6):4130-4151, 2009.
368. M. E. Rognes and A. Logg. Automated Goal-Oriented Error Control I: Stationary Variational Problems 2011. Submitted.
369. A. Roldan, V. Wieben, O. Haughton, T. Osswald, and N. Chesler, N. Characterization of complex CSF hydrodynamics at the cranio-vertebral junction with computational flow analysis: Healthy and Chiari I malformation. American Journal of Neuroradiology, 30(5):941-946, 2009.
370. S. Rüdiger, J. W. Shuai, W. Huisinga, C. Nagaiah, G. Warnecke, I. Parker, and M. Falcke. Hybrid stochastic and deterministic simulations of calcium blips. Biophys. J., 93(6):1847-1857, Sep 2007. URL http://dx.doi.org/10.1529/biophysj.106.099879.
371. T. Rusten and R. Winther. A preconditioned iterative method for saddlepoint problems. SIAM Journal on Matrix Analysis and Applications, 13(3):887-904, 1992.
372. Y. Saad. ILUT: A dual threshold incomplete LU factorization. Numerical Linear Algebra with Applications, 1(4):387-402, 1994.
373. Y. Saad. Iterative Methods for Sparse Linear Systems. SIAM, second edition, 2003.
374. Y. Saad and M. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7(3):856-869, 1986.
375. P. Sagaut. Large-Eddy Simulation for Incompressible Flows — An Introduction. Springer-Verlag, 2005.
376. P. Sagaut, S. Deck, and M. Terracol. Multiscale and Multiresolution Approaches in Turbulence. Imperial College Press, 2006.
377. M. Sala, W. F. Spotz, and M. A. Heroux. PyTrilinos: High-performance distributed-memory solvers for python. ACM Trans. Math. Softw., 34(2):1-33, 2008. ISSN 0098-3500. URL http://doi.acm.org/10.1145/1326548.1326549.
378. H. J. Schroll. Dual Problems in Depositional Modeling. Research Report, Simula Research Laboratory, 2008.
379. U. Schumann. Subgrid-sclae model for finite difference simulation of turbulent flows in plane channels and annuli. J. Comput. Phys., 18:376-404, 1975.
380. C. Schwab. p-and hp-Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics. Oxford University Press, 1998.
381. L. R. Scott and M. Vogelius. Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. RAIRO Modél. Math. Anal. Numér., 19(1):111-143, 1985
382. K. Selim, A. Logg, H. Narayanan, and M. G. Larson. An adaptive finite element method for fluid-structure interaction. Submitted.
383. H. Si. TetGen. a quality tetrahedral mesh generator and three-dimensional delaunay triangulator., 2007. URL http://tetgen.berlios.de.
384. SILOON. Software package. URL http://acts.nersc.gov/siloon/index.html.
385. D. Silvester and A. Wathen. Fast iterative solution of stabilised Stokes systems. Part I: Using simple diagonal preconditioners. SIAM Journal on Numerical Analysis, 30(3):630-649, 1993.
386. D. Silvester and A. Wathen. Fast iterative solution of stabilized Stokes systems. Part II: Using block diagonal preconditioners. SIAM Journal on Numerical Analysis, 31(5):1352-1367, 1994.
387. P. P. Silvester. Finite-element solution of homogeneous waveguide problems. Alta Frequenza, 38: 313-317, 1969.
388. J. C. Simo and F. Armero. Unconditional stability and long-term behavior of transient algorithms for the incompressible Navier-Stokes and Euler equations. Computer Methods in Applied Mechanics and Engineering, 111:111-154, 1994.
389. J. C. Simo and T. J. R. Hughes. Computational Inelasticity. Springer Verlag, 1998.
390. J. C. Simo and R. L. Taylor. Consistent tangent operators for rate-independent elastoplasticity. Computer Methods in Applied Mechanics and Engineering, 48(1):101-118, 1985. URL http://dx.doi.org/10.1016/0045-7825(85)90070-2.
391. SIP. Software package. URL http://www.riverbankcomputing.com/software/sip/intro.
392. J. M. Siskind and B. A. Pearlmutter. Nesting forward-mode AD in a functional framework. Higher Order Symbol. Comput., 21(4):361-376, 2008. URL http://dx.doi.org/10.1007/s10990-008-9037-1.
393. O. Skavhaug and O. Certík. Swiginac Python interface to GiNaC, 2009. URL http://swiginac.berlios.de/.
394. B. W. Smith, J. G. Chase, G. M. Shaw, and R. I. Nokes. Simulating transient ventricular interaction using a minimal cardiovascular system model. Physiological Measurement, pages 165-179, 2006.
395. G. S. Smith. An Introduction to Classical Electromagnetic Radiation. Cambridge University Press, 1997.
396. C. Soeller and M. B. Cannell. Numerical simulation of local calcium movements during l-type calcium channel gating in the cardiac diad. Biophys. J., 73(1):97-111, Jul 1997. URL http://www.pubmedcentral.gov/articlerender.fcgi?tool=pubmed&pubmedid=9199775.
397. C. Soeller and M. B. Cannell. Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques. Circ. Res., 84(3):266-75, 1999. URL http://circres.ahajournals.org/cgi/content/full/84/3/266.
398. P. Šolín, K. Segeth, and I. Doležel. Higher-order Finite Element Methods. Studies in Advanced Mathematics. Chapman & Hall/CRC, 2004.
399. P. R. Spalart and K. M. Mejia. Analysis of experimental and numerical studies of the rudimentary landing gear. In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, number AIAA-2011-355, 2011.
400. W. E. Stehbens. Ultrastructure of aneurysms. Arch Neurol, 32(12):798-807, 1975. URL http://dx.doi.org/10.1001/archneur.1975.00490540042005.
401. R. Stenberg. Analysis of mixed finite elements methods for the Stokes problem: A unified approach. Mathematics of Computation, 42(165):9-23, 1984.
402. M. D. Stern, L. S. Song, H. Cheng, J. S. Sham, H. T. Yang, K. R. Boheler, and E. Ríos. Local control models of cardiac excitation-contraction coupling. a possible role for allosteric interactions between ryanodine receptors. J. Gen. Physiol., 113(3):469-489, 1999.
403. G. Strang and G. J. Fix. An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs, 1973.
404. B. Stroustrup. The C++ Programming Language. Addison-Wesley, July 1997. SWIG. Software package. URL http://www.swig.org.
405. B. Szabó, B. Szabó, and I. Babuška. Finite Element Analysis. Wiley-Interscience, 1991.
406. E. M. Tadjouddine. Vertex-ordering algorithms for automatic differentiation of computer codes. The Computer Journal, 51(6):688-699, Nov. 2008. URL http://dx.doi.org/10.1093/comjnl/bxm115.
407. X.-C. Tai and R. Winther. A discrete de Rham complex with enhanced smoothness. Calcolo, 43: 287-306, 2006.
408. E. Tan and M. Gurnis. Metastable superplumes and mantle compressibility. Geophys. Res. Lett., 32: 1-4, 2005.
409. A. J. Tanskanen, J. L. Greenstein, A. Chen, S. X. Sun, and R. L. Winslow. Protein geometry and placement in the cardiac dyad influence macroscopic properties of calcium-induced calcium release. Biophys. J., 92(10):3379-3396, May 2007. URL http://dx.doi.org/10.1529/biophysj.106.089425.
410. C. Taylor and P. Hood. A numerical solution of the Navier-Stokes equations using the finite element technique. Internat. J. Comput. & Fluids, 1(1):73-100, 1973. URL http://dx.doi.org/10.1016/0045-7930(73)90027-3.
411. R. Temam. Sur l’approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. Arc. Ration. Mech. Anal., 32:377-385, 1969.
412. A. R. Terrel, L. R. Scott, M. G. Knepley, and R. C. Kirby. Automated FEM discretizations for the Stokes equation. BIT Numerical Mathematics, 48(2):389-404, 2008. URL http://dx.doi.org/10.1007/s10543-008-0178-8.
413. T. E. Tezduyar and Y. J. Park. Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comp. Methods Appl. Mech. Eng., 59(3):307-325, 1986.
414. The Python Tutorial. The python tutorial. http://docs.python.org/tutorial/.
415. L. N. Trefethen. Spectral Methods in Matlab. Springer-Verlag, New York, 2006. Trilinos. Software package. URL http://trilinos.sandia.gov/.
416. U. Trottenberg, C. Oosterlee, and A. Schuller. Multigrid. Academic Press, 2001.
417. C. A. Truesdell and W. Noll. The Non-linear Field Theories (Handbuch der Physik, band III). Springer, Berlin, 1965.
418. C. A. Truesdell and R. A. Toupin. The Classical Field Theories (Handbuch der Physik, band III/1). Springer-Verlag, Berlin, 1960.
419. S. Turek. Recent benchmark computations of laminar flow around a cylinder. In 3rd World Conference in Applied Computational Fluid Mechanics, Freiburg, 1996.
420. S. Turek. Efficient Solvers for Incompressible Flow Problems. Springer, 1999.
421. uBLAS. Software package. URL http://www.boost.org/libs/numeric/ublas/doc/.
422. Valgrind. Software package. URL http://valgrind.org.
423. A. P. van den Berg, P. E. van Keken, and D. A. Yuen. The effects of a composite non-Newtonian and Newtonian rheology on mantle convection. Geophys. J. Int., 115:62-78, 1993.
424. D. G. van derMeer, W. Spakman, D. J. J. van Hinsbergen, M. L. Amaru, and T. H. Torsvik. Towards absolute plate motions constrained by lower-mantle slab remnants. Nature Geoscience, 3:36-40, 2010.
425. H. A. van der Vorst. Bi-CGSTAB: A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 13(2):631-644, 1992. URL http://dx.doi.org/10.1137/0913035.
426. K. G. van der Zee. Goal-Adaptive Discretization of Fluid-Structure Interaction. PhD thesis, Delft University of Technology, 2009.
427. K. G. van der Zee, E. H. van Brummelen, and R. de Borst. Goal-oriented error estimation for Stokes flow interacting with a flexible channel. International Journal for Numerical Methods in Fluids, 56(8): 1551-1557, 2008.
428. P. E. van Keken, S. D. King, H. Schmeling, et al. A comparison of methods for the modeling of thermochemical convection. J. Geophys. Res., 102(B10):22477-22495, 1997.
429. G. van Rossum et al. Python. URL http://www.python.org/.
430. L. Vardapetyan and L. Demkowicz. hp-vector finite elements method for the full-wave analysis of waveguides with no spurious modes. Electromagnetics, 22(5):419-428, 2002.
431. Vascular Modeling Toolkit. Software package. URL http://vmtk.org/.
432. O. Certík et al. SymPy, 2009. URL http://docs.sympy.org.
433. R. Verfürth. A posteriori error estimation and adaptive mesh-refinement techniques. In Proceedings of the Fifth International Conference on Computational and Applied Mathematics, pages 67-83. Amsterdam, Elsevier Science Publishers, 1994.
434. R. Verfürth. A review of a posteriori error estimation techniques for elasticity problems. Computer Methods in Applied Mechanics and Engineering, 176(1-4):419-440, 1999.
435. I. E. Vignon-Clementel, C. A. Figueroa, K. E. Jansen, and C. A. Taylor. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Computer Methods in Applied Mechanics and Engineering, 195(29-32):3776-3796, 2006. URL http://dx.doi.org/10.1016/j.cma.2005.04.014.
436. Viper. Software package. URL https://launchpad.net/fenics-viper.
437. VMTK. Software package. URL http://www.vmtk.org.
438. VTK. Software package. URL http://www.kitware.com.
439. M. Walkley. A Numerical Method for Extended Boussinesq Shallow-Water Wave Equations. PhD thesis, The University of Leeds, School of Computer Studies, 1999.
440. M. Walkley and M. Berzins. A finite element method for the two-dimensional extended Boussinesq equations. Internat. J. Numer. Methods Fluids, 39(10):865-885, 2002.
441. T. Warburton. An explicit construction for interpolation nodes on the simplex. Journal of Engineering Mathematics, 2005. Weave. Software package. URL http://scipy.org/Weave.
442. J. P. Webb. Edge elements and what they can do for you. IEEE Trans. Magn., 29(2):1460-1465, March 1993.
443. G. Wei and J. T. Kirby. Time-dependent numerical code for extended Boussinesq equations. Journal of Waterway, Port, Coastal, and Ocean Engineering, 121(5):251-261, 1995. URL http://dx.doi.org/10.1061/(ASCE)0733-950X(1995)121:5(251).
444. G. Wei, J. T. Kirby, and A. Sinha. Generation of waves in Boussinesq models using a source function method. Coastal Engineering, 36:271-279, 1999.
445. B. Weir. Unruptured intracranial aneurysms: A review. Journal of Neurosurgery, 96(1):3-42, 2002. URL http://dx.doi.org/10.3171/jns.2002.96.1.0003.
446. G. N. Wells and L. J. Sluys. A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering, 50(12):2667-2682, 2001. URL http://dx.doi.org/10.1002/nme.143.
447. J. R. Welty, C. E. Wicks, and R. E. Wilson. Fundamentals of Momentum, Heat, and Mass Transfer. John Wiley & Sons Inc, 2001.
448. P. Wesseling. An Introduction to Multigrid Methods. Wiley & Sons, 1992.
449. R. C. Whaley, A. Petitet, and J. J. Dongarra. Automated empirical optimization of software and the ATLAS project. Parallel Computing, 27(1-2):3-35, 2001. URL http://dx.doi.org/10.1016/S0167-8191(00)00087-9.
450. F. M. White. Viscous Fluid Flow. McGraw-Hill, 1991.
451. F. M. White. Fluid Mechanics. McGraw-Hill, fourth edition, 1999.
452. G. B. Whitham. Linear and Nonlinear Waves. John Wiley & Sons, New York, 1974.
453. I. M. Wilbers, H. P. Langtangen, and A. Ødegård. Using Cython to speed up numerical Python programs. In B. Skallerud and H. I. Andersson, editors, Proceedings of MekIT’09, pages 495-512.
454. Norwegian University of Science and Technology, Tapir Academic Press, 2009. ISBN 978-82-519-2421-4.
455. M. M. Wolf and M. T. Heath. Combinatorial optimization of matrix-vector multiplicaion in finite element assembly. SIAM J. Sci. Comput., 31:2960, 2009.
456. S.-B. Woo and P.-F. Liu. Finite element model for modified Boussinesq equations i: Model development. Journal of Waterway, Port, Coastal and Ocean Engineering, 130(1):1-16, 2004a.
457. S.-B. Woo and P.-F. Liu. Finite element model for modified Boussinesq equations II: Applications to nonlinear harbor oscillations. Journal of Waterway, Port, Coastal and Ocean Engineering, 130(1):17-28, 2004b.
458. T. Y. Wu. Long waves in ocean and coastal waters. Journal of the Engineering Mechanics, 107(3):501-522, 1981.
459. M. M. Zdravkovich. Flow Around Circular Cylinders. Oxford University Press, 2003.
460. M. Zhao, B. Teng, and L. Cheng. A new form of generalized Boussinesq equations for varying water depth. Ocean Engineering, 31:2047-2072, 11 2004. URL http://dx.doi.org/10.1016/j.oceaneng.2004.03.010.
461. Y. Zhu and A. C. Cangellaris. Multigrid Finite Element Methods for Electromagnetic Field Modelling. IEEE Press, New York, 2006.
462. O. C. Zienkiewicz and R. L. Taylor. The Finite Element Method: Fluid dynamics, volume 3. Butterworth-Heinemann, 5 edition, 2000.
463. O. C. Zienkiewicz and J. Z. Zhu. A simple error estimator and adaptive procedure for practical engineerng analysis. International Journal for Numerical Methods in Engineering, 24(2), 1987.
464. O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu. The Finite Element Method — Its Basis and Fundamentals. Elsevier, 6th edition, 2005.