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OXFORD UNIVERSITY  COMPUTING LABORATORY

Bibliography for Andy Wathen

    Book

    Elman, H.C., Silvester, D.J. and Wathen, A.J.,
    Finite Elements and Fast Iterative Solvers: with applications in incompressible fluid dynamics,
    Oxford University Press, Oxford, 2005.

    Invited papers

  1. Wathen, A.J., Fischer, B. and Silvester, D.J., 1997, `The convergence of iterative solution methods for symmetric and indefinite linear systems', in `Numerical Analysis 1997', Eds. D.F. Griffiths and G.A. Watson, Pitman Research Notes in Mathematics Series, Addison Wesley Longman, Harlow, England, pp. 230-243. (Also available as a report)
  2. Silvester, D.J. and Wathen, A.J., 1996, `Fast and robust solvers for time-discretised incompressible Navier-Stokes equations', in `Numerical Analysis 1995', Eds. D.F. Griffiths and G.A. Watson, Addison Wesley Longman, Harlow, England, pp. 154-168. (Also available as a report)
  3. Golub, G.H., Silvester, D.J. and Wathen, A.J., 1996, `Diagonal dominance and positive definiteness of upwind approximations for advection diffusion problems', in `Numerical Analysis: A.R. Mitchell 75th Birthday Volume', Eds. D.F. Griffiths and G.A. Watson, World Scientific, Singapore, pp. 125-131. (Also available as a report)
  4. Elman, H.E., Silvester, D.J. and Wathen, A.J., 1997, `Iterative methods for problems in Computational Fluid Dynamics', in `Iterative Methods in Scientific Computing', Eds. R.H. Chan, T.F. Chan and G.H. Golub, Springer-Verlag, Singapore, pp. 271-327. (Also available as a report)
  5. Wathen, A.J., 2000, `Preconditioned iterative methods for implicit equations', in `Developments in numerical methods for very high resolution global models', European Centre for Medium-Range Weather Forcasts, Reading, UK, pp. 167-176. (Also available as a report)
  6. Wathen, A.J., 2004, `Preconditioning and fast solvers for incompressible flow', procedings of ICFD conference on `Numerical methods for Fluid Dynamics', Eds. M.J.~Baines, M.J.P.~Cullen, C.~Farmer, M.B.~Giles and M.Rabbitt, ICFD, Oxford. (Available as a report)
  7. Dollar, H.S., Gould, N.I.M and and Wathen, A.J., 2004, `On implicit-factorization constraint preconditioners', `Large-Scale Nonlinear Optimization', Eds. G.~Di~Pillo, Gianni and M.~Roma, Springer Verlag, Heidelberg, Berlin, New York, pp. 61-82. (Available as a report)
  8. Benzi, M. and Wathen, A.J., 2007, `Some Preconditioning Techniques for Saddle Point Problems', To appear in Model Order Reduction: Theory, Research Aspects and Applications, W. Schilders and H. A. van der Vorst, eds., Springer-Verlag (Series: Mathematics in Industry).

    Refereed journal papers

  9. Golub, G.H., Stoll, M. and Wathen, A.J., `Approximation of the scattering amplitude and linear systems', to appear in Elect. Trans. Numer. Anal., 2008.
  10. Stoll, M. and Wathen, A.J., 2008, `Combination preconditioning and the Bramble-Pasciak$^{+}$ preconditioner', SIAM J Matrix Anal. Appl. {\bf 30}(2), pp. 582-608.
  11. Navarro, M.C., Herrero, H., Mancho, A.M. and Wathen, A.J., 2008, `Efficient solution of a generalized eigenvalue problem arising in a thermoconvective instability', Communications in Computational Physics {\bf 3}(2), pp. 308-329.
  12. Ferris, M.C., Wathen, A.J. and Armand, P., 2007, `Limited memory solution of bound constrained convex quadratic problems arising in video games' RAIRO-Operations Research {\bf 41}(1), pp. 19-34.
  13. Wathen, A.J., 2007, `Preconditioning and convergence in the right norm', Int. J. Comput. Math. {\bf 84}(8), pp. 1199-1209.
  14. Dollar, H.S., Gould, N.I.M., Schilders,W.H.A. and Wathen, A.J., `Using constraint preconditioners with regularized saddle-point problems', Comput. Optim. Appl. {\bf 36}(2-3), pp. 249-270.
  15. Dollar, H.S., Gould, N.I.M., Schilders,W.H.A. and Wathen, A.J., 2006, `Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems', SIAM J. Matrix Anal. Appl. {\bf 28}(1), pp. 170-189.
  16. Dollar, H.S. and Wathen, A.J., `Approximate factorization constraint preconditioners for saddle-point matrices', accepted for publication in SIAM J. Sci. Comput., 2004. (Unrevised manuscript available as a report)
  17. Griffiths, M., Shafi, M., Popper, S., Hemmingway, C., Kortok, M., Wathen, A., Rockett, K., Mott, R., Levin, M., Newton, C., Marsh, K., Relman, D. and Kwiatkowski, D., 2005, ` Genonwide analysis of the host response to maleria in Kenyan children', J. Infectious Diseases 191, pp. 1599-1611.
  18. Papadopoulos, A., Duff, I.S. and Wathen, A.J., 2005, ` A class of incomplete orthogonal factorization methods II: implementation and results', BIT 45, pp. 159-179.
  19. Arioli, M., Loghin, D. and Wathen, A.J., 2005, ` Stopping criteria for iterations in finite element methods', Numer. Math. 99, pp. 381-410.
  20. Madzvamuse, A., Maini, P.K. and Wathen, A.J., 2005, ` A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains', J. Sci. Comput. 24, pp. 247-262.
  21. Holland, R.M., Wathen, A.J. and Shaw, G.J., 2005, ` Sparse approximate inverses and target matrices', SIAM J. Sci. Comput. 26, pp. 1000 - 1011.
  22. Loghin, D. and Wathen, A.J., 2004, ` Analysis of preconditioners for saddle-point problems', SIAM J. Sci. Comput. 25, pp. 2029 - 2049.
  23. Nijhout, F.H., Maini, P.K., Madzvamuse, A., Wathen, A.J., and Sekimura, T., 2003, `Pigmentation pattern formation in Butterflies: -- Experiments and Models', Comptes Rendus Biologies 328(8) pp. 717-727.
  24. Madzvamuse, A., Maini, P.K. and Wathen, A.J., 2003, `A moving grid finite element method applied to a model biological pattern generator', J. Comp. Phys. 190, pp. 478-500.
  25. Loghin, D., Elman, H.C. and Wathen, A.J., 2003, ` Preconditioning techniques for Newton's method for the incompressible Navier-Stokes equations', BIT 43, pp. 961-974.
  26. Elman, H.C., Silvester, D.J. and Wathen, A.J., 2002, ` Block preconditioners for the discrete incompressible Navier-Stokes equations', Int. J. Numer. Meths. Fluids 40, pp. 333-344.
  27. Loghin, D. and Wathen, A.J., 2003, ` Schur complement preconditioning for elliptic systems of partial differential equations', Numer. Linear Algebra Appl. 10, pp. 423-443.
  28. Madzvamuse, A., Maini, P.K, Wathen, A.J. and Sekimura, T., 2002, ` A predictive model for colour pattern formation in the butterfly wing of Papilio Dardanus', Hiroshima Math. J. 32, pp. 325-336.
  29. Kay, D., Loghin, D. and Wathen, A.J., 2002, ` A preconditioner for the steady-state Navier-Stokes equations', SIAM J. Sci. Comput. 24, pp. 237-256.
  30. Madzvamuse, A., Thomas, R.D.K., Maini, P.K. and Wathen, A.J., 2002, `A numerical approach to the study of spatial pattern formation in the ligaments of arcoid bivalves', Bull. Math. Biol. 64, pp. 501-530. (Available as a report)
  31. Loghin, D. and Wathen, A.J., 2002, ` Schur complement preconditioners for the Navier-Stokes equations', Int. J. Numer. Meths. Fluids. 40, pp. 403-412.
  32. Hemmingsson, L. and Wathen, A.J., 2001, ` A nearly optimal preconditioner for the Oseen equations', Numer. Linear Algebra Appl. 8(4), pp. 229-243.
  33. Elman, H.E., Silvester, D.J. \& Wathen, A.J., 2002, ` Performance and analysis of saddle point preconditioners for the discrete Steady-state Navier-Stokes equations', Numer. Math. 90(4), pp. 665-688.
  34. Bai, Z-z., Duff, I.S. and Wathen, A.J., 2001, ` A class of incomplete orthogonal factorization methods . I:Methods and theories', BIT 41(1), pp. 53-70.
  35. Shen, J., Strang, G. and Wathen, A.J., 2001, ` The Potential Theory of several intervals and its applications', Appl. Math. Optim. 44, pp. 67-85.
  36. Silvester, D.J, Elman, H.E., Kay, D and Wathen, A.J., 2001, `Efficient preconditioning of the linearized Navier-Stokes equations', J. Comput. Appl. Math., 128, pp. 261-279. (Available as a report)
  37. Sekimura, T., Madzvamuse, A., Wathen, A.J. and Maini, P.K., 2000, ` A model for colour pattern formation in the butterfly wing of Papilio dardanus', Proc. Roy. Soc. series B. 267, No 1446, pp. 851-860.
  38. Keller, C., Gould, N.I.M. and Wathen, A.J., 2000, ` Constraint preconditioning for indefinite linear systems', SIAM J. Matrix Anal. Appl. 21(4), pp. 1300-1317.
  39. Murphy, M.F., Golub, G.H. and Wathen, A.J., 2000, ` A note on preconditioning for indefinite linear systems', SIAM J. Sci. Comput. 21(6), pp. 1969-1972.
  40. Blank, H., Rudgyard, M.A. and Wathen, A.J., 1999, ` Stabilised finite element methods for steady incompressible flow', Comput. Meths. Appl. Mech. Engrg. 174, pp. 91-105.
  41. Fischer, B., Ramage, A., Silvester, D.J. and Wathen, A.J., 1999, ` On parameter choice and iterative convergence of stabilised discretisations of advection-diffusion problems', Comput. Meths. Appl. Mech. Engrg. 179, pp. 185-202.
  42. Huang, Y., Wathen, A.J. and Li, L., 1998, `An iterative method for skew-symmetric systems', accepted for publication in Journal of Information.
  43. Fischer, B., Ramage, A., Silvester, D.J. and Wathen, A.J., 1998, ` Minimum residual methods for Augmented Systems', BIT 38(3), pp. 527-543.
  44. Budd, C.J., Humphries, A.R. and Wathen, A.J., 1997, ` The finite element approximation of semi-linear elliptic PDE's with critical exponents in the cube' SIAM J. Sci. Comput. 20(5), pp. 1875-1904.
  45. Golub, G.H. and Wathen, A.J., 1998, ` An iteration for indefinite systems and its application to the Navier-Stokes equations', SIAM J. Sci. Comput. 19(2), pp. 530-539.
  46. Selwood, P.M. and Wathen, A.J., 1996, ` Convergence rates and classification for one dimensional finite element meshes', IMA J. Numer. Anal. 16, pp. 65-74.
  47. Wathen, A.J., Fischer, B. and Silvester, D.J., 1995, `The convergence rate of the minimum residual method for the Stokes problem', Numer. Math. 71, pp. 121-134.
  48. Ramage, A. and Wathen, A.J., 1994, `Iterative solution techniques for the Stokes and Navier-Stokes equations', Int. J. Numer. Meths. Fluids 19(1), pp. 67-83.
  49. Silvester, D.J. and Wathen, A.J., 1994, `Fast iterative solution of stabilised Stokes systems Part II: Using general block preconditioners', SIAM J. Numer Anal. 31(5), pp. 1352-1367.
  50. Ramage, A. and Wathen, A.J., 1994, `On preconditioning for Finite Element equations on irregular grids', SIAM J. Matrix Anal. Appl. 15(3), pp. 909-921.
  51. Wathen, A.J. and Silvester, D.J., 1993, `Fast iterative solution of stabilised Stokes systems Part I: Using simple diagonal preconditioners', SIAM J. Numer. Anal. 30(3), pp. 630-649.
  52. Robinson, P.D. \& Wathen, A.J., 1992, `Variational bounds on the entries of the inverse of a matrix', IMA J. Numer. Anal. 12, pp. 463-486.
  53. Wathen, A.J., 1992, `Optimal moving grids for time-dependent partial differential equations', J. Comput. Phys. 101, pp. 51-54.
  54. Wathen, A.J., 1991, `On relaxation of Jacobi iteration for consistent and generalised Mass Matrices', Comm. Appl. Numer. Meths. 7, pp. 93-102.
  55. Lee, H-C. and Wathen, A.J., 1991, `On Element-by-Element preconditioning for general elliptic problems', Comput. Meths. Appl. Mech. Engrg. 92, pp. 215-229.
  56. Jimack, P.K. and Wathen, A.J., 1991, `Temporal derivatives in the Finite Element method on continuously deforming grids', SIAM J. Numer. Anal. 28, 990-1003.
  57. Loach, P.D. and Wathen, A.J., 1991, `On best least squares approximation of continuous functions using linear splines with free knots', IMA J. Numer. Anal. 11, pp. 393-409.
  58. Wathen, A.J., 1989, `An analysis of some Element-by-Element techniques', Comput. Meths. Appl. Mech. Engrg. 74, pp. 271-287.
  59. Johnson, I.W., Wathen, A.J. \and Baines, M.J., 1988, `Moving Finite Element methods for evolutionary problems II: Applications', J. Comput. Phys. 79, pp. 270-297.
  60. Baines, M.J. and Wathen, A.J., 1988, `Moving Finite Element methods for evolutionary problems I: Theory', J. Comput. Phys. 79, pp. 245-269.
  61. Wathen, A.J., 1987, `Realistic eigenvalue bounds for the Galerkin Mass Matrix', IMA J. Numer. Anal. 7, pp. 449-457.
  62. Baines, M.J. and Wathen, A.J., 1986, `Moving Finite Element modelling of compressible flow', Appl. Numer. Math. 2, pp. 495-503.
  63. Wathen, A.J., 1986, `Mesh-independent spectra in the Moving Finite Element equations', SIAM J. Numer. Anal. 23, pp. 797-814.
  64. Wathen, A.J. and Baines, M.J., 1985, `On the structure of the Moving Finite Element equations', IMA J. Numer. Anal. 5, pp. 161-182.

    Conference papers

  65. Thomas, R.D.K., Madzvamuse, A., Maini, P.K. \& Wathen, A.J., 2000, `Growth patterns of noetiid ligaments: implications of developmental models for the origin of an evolutionary novelty among arcoid bivalves', To appear in: `The Evolutionary Biology of the Bivalvia', Harper, E.M., Taylor, J.D. and Crame, J.A., eds. Geological Society Special Publication No. 177, pp. 279-290.
  66. Ramage, A., Fischer, B., Silvester, D.J. and Wathen, A.J., 1995, ` Minimum residual methods for the Navier-Stokes equations: Indefiniteness vs Asymmetry', In `Numerical Methods for Fluid Dynamics V', Eds. K.W. Morton and M.J. Baines, OUP, Oxford, pp. 541-547.
  67. Humphries, A.R., Budd, C.J. and Wathen, A.J., 1995, `Finite element method solutions for semi-linear elliptic partial differential equations with critical Sobolev exponents on non-spherical domains', in procedings of International Conference on Differential Equations - Equadif 95, Lisbon, Eds. L.T. Magalhaes, C. Rocha and L. Sanchez, World Scientific.
  68. Ramage, A. and Wathen, A.J., 1993, `Iterative solution techniques for the Navier-Stokes equations', in `Finite Elements in Fluids: New Trends and Applications Part I', Eds. K. Morgan, E. Onate, J. Periaux, J. Peraire \& O.C. Zienkiewicz, CIMNE/Pineridge Press, Swansea, pp. 278-286.
  69. Wathen, A.J., 1992, `Singular element preconditioning for the Finite Element method', in `Iterative Methods in Linear Algebra', Eds. R. Beauwens and P. de Groen, North Holland, Amsterdam, pp. 531-540.
  70. Wathen, A.J. and Silvester, D.J., 1992, `The convergence of Krylov-space methods for the Stokes problem in Computational Fluid Dynamics', in Proc. of Copper Mountain conference on Iterative Methods, Eds. T. Manteuffel and S. McCormick, Computational Math Group, University of Colorado at Denver.
  71. Ramage, A. and Wathen, A.J., 1992. `Iterative techniques for Finite Element discretisations of fluid flow problems', in Proc. of Copper Mountain conference on Iterative Methods, Eds. T. Manteuffel and S. McCormick, Computational Math Group, University of Colorado at Denver.
  72. Ramage, A. and Wathen, A.J., 1992, `Iterative solution techniques for the Lagrange-Galerkin method', In `Numerical Methods for Fluid Dynamics IV' (1994), Eds. K.W. Morton and M.J. Baines, OUP, Oxford.
  73. Wathen, A.J., 1991, `Fast iteration for Taylor Galerkin and other time-dependent Finite Element equations', In Proc. of MAFELAP (1990), Ed. J.R. Whiteman, Academic Press, London, pp. 163-171.
  74. Wathen, A.J., 1988, `Spectral bounds and preconditioning methods using Element-by-Element analysis for Galerkin Finite Element equations', In Proc. of MAFELAP (1987), Ed. J.R. Whiteman, Academic Press, London, pp. 157-168.
  75. Wathen, A.J., Baines, M.J. and Morton, K.W., 1985, `Moving Finite Element methods for the solution of evolutionary equations in one- and two-dimensions'. In Proc. of MAFELAP (1984), ed. J.R. Whiteman, Academic Press, London, pp. 421-430.

    Technical Reports

    can be found in the Numerical Analysis Technical Report list

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