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Dr Niall Madden, Lecturer in Mathematics

Biography

Lecturer in Mathematics at NUI Galway.

Biography:

  • BSc (Mathematics and Computing) University College Galway, 1994.
  • MSc (Mathematics) University College Cork, 1996
  • PhD (Mathematics) NUI Cork, 2000

 

Research Interests

  • The design, implementation and analysis of algorithms for solving differential equations, particularly ones whose solutions feature boundary and interior layers.
  • Finite difference and finite element methods for boundary values problems
  • Boundary and interior layer-resolving methods
  • Fast linear solvers for PDE discretisations
  • Applications of novel numerical schemes to problems in fluid dynamics

Selected Publications

2013

  • [DOI] C. Xenophontos, M. Melenk, N. Madden, L. Oberbroeckling, P. Panaseti, and A. Zouvani, “$hp$ finite element methods for fourth order singularly perturbed boundary value problems,” in Numerical analysis and its applications, Springer, Heidelberg, 2013, vol. 8236, pp. 532-539.
    [Bibtex]
    @incollection {MR3150028,
    AUTHOR = {Xenophontos, Christos and Melenk, Markus and Madden, Niall and
    Oberbroeckling, Lisa and Panaseti, Pandelitsa and Zouvani,
    Antri},
    TITLE = {{$hp$} finite element methods for fourth order singularly
    perturbed boundary value problems},
    BOOKTITLE = {Numerical analysis and its applications},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {8236},
    PAGES = {532--539},
    PUBLISHER = {Springer, Heidelberg},
    YEAR = {2013},
    MRCLASS = {65L11 (65L60)},
    MRNUMBER = {3150028},
    DOI = {10.1007/978-3-642-41515-9_61},
    URL = {http://dx.doi.org/10.1007/978-3-642-41515-9_61},
    }
  • [DOI] S. MacLachlan and N. Madden, “Robust solution of singularly perturbed problems using multigrid methods,” Siam j. sci. comput., vol. 35, iss. 5, p. A2225–A2254, 2013.
    [Bibtex]
    @article {MR3106486,
    AUTHOR = {MacLachlan, Scott and Madden, Niall},
    TITLE = {Robust solution of singularly perturbed problems using
    multigrid methods},
    JOURNAL = {SIAM J. Sci. Comput.},
    FJOURNAL = {SIAM Journal on Scientific Computing},
    VOLUME = {35},
    YEAR = {2013},
    NUMBER = {5},
    PAGES = {A2225--A2254},
    ISSN = {1064-8275},
    MRCLASS = {65L11 (65L12 65N06 65N55)},
    MRNUMBER = {3106486},
    MRREVIEWER = {Gabriela Schranz-Kirlinger},
    DOI = {10.1137/120889770},
    URL = {http://dx.doi.org/10.1137/120889770},
    }
  • [DOI] C. G. Enright, M. G. Madden, and N. Madden, “Bayesian networks for mathematical models: techniques for automatic construction and efficient inference,” Internat. j. approx. reason., vol. 54, iss. 2, pp. 323-342, 2013.
    [Bibtex]
    @article {MR3021575,
    AUTHOR = {Enright, Catherine G. and Madden, Michael G. and Madden,
    Niall},
    TITLE = {Bayesian networks for mathematical models: techniques for
    automatic construction and efficient inference},
    JOURNAL = {Internat. J. Approx. Reason.},
    FJOURNAL = {International Journal of Approximate Reasoning},
    VOLUME = {54},
    YEAR = {2013},
    NUMBER = {2},
    PAGES = {323--342},
    ISSN = {0888-613X},
    CODEN = {IJARE4},
    MRCLASS = {68T30 (62H99)},
    MRNUMBER = {3021575},
    DOI = {10.1016/j.ijar.2012.10.004},
    URL = {http://dx.doi.org/10.1016/j.ijar.2012.10.004},
    }

2012

  • N. Madden and M. Stynes, “A curious property of oscillatory FEM solutions of one-dimensional convection-diffusion problems,” in Applications of mathematics 2012, Acad. Sci. Czech Repub. Inst. Math., Prague, 2012, pp. 188-196.
    [Bibtex]
    @incollection {MR3204411,
    AUTHOR = {Madden, Niall and Stynes, Martin},
    TITLE = {A curious property of oscillatory {FEM} solutions of
    one-dimensional convection-diffusion problems},
    BOOKTITLE = {Applications of mathematics 2012},
    PAGES = {188--196},
    PUBLISHER = {Acad. Sci. Czech Repub. Inst. Math., Prague},
    YEAR = {2012},
    MRCLASS = {65L60},
    MRNUMBER = {3204411},
    MRREVIEWER = {Kailash C. Patidar},
    }
  • N. Madden, “John Todd and the development of modern numerical analysis,” Irish math. soc. bull., iss. 69, pp. 11-24, 2012.
    [Bibtex]
    @article {MR3026423,
    AUTHOR = {Madden, Niall},
    TITLE = {John {T}odd and the development of modern numerical analysis},
    JOURNAL = {Irish Math. Soc. Bull.},
    FJOURNAL = {Irish Mathematical Society Bulletin},
    NUMBER = {69},
    YEAR = {2012},
    PAGES = {11--24},
    ISSN = {0791-5578},
    MRCLASS = {01A60},
    MRNUMBER = {3026423},
    }

2011

  • [DOI] N. Madden and K. K. Mondal, “Improved mathematical and numerical modelling of dispersion of a solute from a continuous source,” in BAIL 2010—boundary and interior layers, computational and asymptotic methods, Springer, Heidelberg, 2011, vol. 81, pp. 177-185.
    [Bibtex]
    @incollection {MR2849740,
    AUTHOR = {Madden, Niall and Mondal, Kajal Kumar},
    TITLE = {Improved mathematical and numerical modelling of dispersion of
    a solute from a continuous source},
    BOOKTITLE = {B{AIL} 2010---boundary and interior layers, computational and
    asymptotic methods},
    SERIES = {Lect. Notes Comput. Sci. Eng.},
    VOLUME = {81},
    PAGES = {177--185},
    PUBLISHER = {Springer, Heidelberg},
    YEAR = {2011},
    MRCLASS = {76R50 (76F99 76M25 86A05 86A10)},
    MRNUMBER = {2849740 (2012j:76090)},
    DOI = {10.1007/978-3-642-19665-2_19},
    URL = {http://dx.doi.org/10.1007/978-3-642-19665-2_19},
    }
  • [DOI] N. M. Chadha and N. Madden, “A two-weight scheme for a time-dependent advection-diffusion problem,” in BAIL 2010—boundary and interior layers, computational and asymptotic methods, Springer, Heidelberg, 2011, vol. 81, pp. 99-108.
    [Bibtex]
    @incollection {MR2849732,
    AUTHOR = {Chadha, Naresh M. and Madden, Niall},
    TITLE = {A two-weight scheme for a time-dependent advection-diffusion
    problem},
    BOOKTITLE = {B{AIL} 2010---boundary and interior layers, computational and
    asymptotic methods},
    SERIES = {Lect. Notes Comput. Sci. Eng.},
    VOLUME = {81},
    PAGES = {99--108},
    PUBLISHER = {Springer, Heidelberg},
    YEAR = {2011},
    MRCLASS = {65M06 (76M20 76R50)},
    MRNUMBER = {2849732 (2012j:65241)},
    DOI = {10.1007/978-3-642-19665-2_11},
    URL = {http://dx.doi.org/10.1007/978-3-642-19665-2_11},
    }

2010

  • T. Linss and N. Madden, “Analysis of an alternating direction method applied to singularly perturbed reaction-diffusion problems,” Int. j. numer. anal. model., vol. 7, iss. 3, pp. 507-519, 2010.
    [Bibtex]
    @article {MR2644287,
    AUTHOR = {Linss, Torsten and Madden, Niall},
    TITLE = {Analysis of an alternating direction method applied to
    singularly perturbed reaction-diffusion problems},
    JOURNAL = {Int. J. Numer. Anal. Model.},
    FJOURNAL = {International Journal of Numerical Analysis and Modeling},
    VOLUME = {7},
    YEAR = {2010},
    NUMBER = {3},
    PAGES = {507--519},
    ISSN = {1705-5105},
    MRCLASS = {65M06 (65M15)},
    MRNUMBER = {2644287 (2011d:65215)},
    MRREVIEWER = {Fausto Cavalli},
    }

2009

  • [DOI] M. Stephens and N. Madden, “A Schwarz technique for a system of reaction diffusion equations with differing parameters,” in BAIL 2008—boundary and interior layers, Springer, Berlin, 2009, vol. 69, pp. 247-255.
    [Bibtex]
    @incollection {MR2581492,
    AUTHOR = {Stephens, Meghan and Madden, Niall},
    TITLE = {A {S}chwarz technique for a system of reaction diffusion
    equations with differing parameters},
    BOOKTITLE = {B{AIL} 2008---boundary and interior layers},
    SERIES = {Lect. Notes Comput. Sci. Eng.},
    VOLUME = {69},
    PAGES = {247--255},
    PUBLISHER = {Springer, Berlin},
    YEAR = {2009},
    MRCLASS = {76R50 (65L11 76V05)},
    MRNUMBER = {2581492 (2010m:76135)},
    DOI = {10.1007/978-3-642-00605-0_20},
    URL = {http://dx.doi.org/10.1007/978-3-642-00605-0_20},
    }
  • [DOI] F. Liu, N. Madden, M. Stynes, and A. Zhou, “A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions,” Ima j. numer. anal., vol. 29, iss. 4, pp. 986-1007, 2009.
    [Bibtex]
    @article {MR2557053,
    AUTHOR = {Liu, Fang and Madden, Niall and Stynes, Martin and Zhou,
    Aihui},
    TITLE = {A two-scale sparse grid method for a singularly perturbed
    reaction-diffusion problem in two dimensions},
    JOURNAL = {IMA J. Numer. Anal.},
    FJOURNAL = {IMA Journal of Numerical Analysis},
    VOLUME = {29},
    YEAR = {2009},
    NUMBER = {4},
    PAGES = {986--1007},
    ISSN = {0272-4979},
    CODEN = {IJNADN},
    MRCLASS = {65N30 (65N15 65N50)},
    MRNUMBER = {2557053 (2010m:65282)},
    MRREVIEWER = {V{\'{\i}}t Dolej{\v{s}}{\'{\i}}},
    DOI = {10.1093/imanum/drn048},
    URL = {http://dx.doi.org/10.1093/imanum/drn048},
    }
  • [DOI] M. Stephens and N. Madden, “A parameter-uniform Schwarz method for a coupled system of reaction-diffusion equations,” J. comput. appl. math., vol. 230, iss. 2, pp. 360-370, 2009.
    [Bibtex]
    @article {MR2532330,
    AUTHOR = {Stephens, Meghan and Madden, Niall},
    TITLE = {A parameter-uniform {S}chwarz method for a coupled system of
    reaction-diffusion equations},
    JOURNAL = {J. Comput. Appl. Math.},
    FJOURNAL = {Journal of Computational and Applied Mathematics},
    VOLUME = {230},
    YEAR = {2009},
    NUMBER = {2},
    PAGES = {360--370},
    ISSN = {0377-0427},
    CODEN = {JCAMDI},
    MRCLASS = {65L10 (65L11 65L12 65L50)},
    MRNUMBER = {2532330 (2010d:65167)},
    MRREVIEWER = {Natalia Kopteva},
    DOI = {10.1016/j.cam.2008.12.009},
    URL = {http://dx.doi.org/10.1016/j.cam.2008.12.009},
    }
  • [DOI] T. Linß and N. Madden, “Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems,” Ima j. numer. anal., vol. 29, iss. 1, pp. 109-125, 2009.
    [Bibtex]
    @article {MR2470942,
    AUTHOR = {Lin{\ss}, Torsten and Madden, Niall},
    TITLE = {Layer-adapted meshes for a linear system of coupled singularly
    perturbed reaction-diffusion problems},
    JOURNAL = {IMA J. Numer. Anal.},
    FJOURNAL = {IMA Journal of Numerical Analysis},
    VOLUME = {29},
    YEAR = {2009},
    NUMBER = {1},
    PAGES = {109--125},
    ISSN = {0272-4979},
    CODEN = {IJNADN},
    MRCLASS = {65L50 (65L10 65L12)},
    MRNUMBER = {2470942 (2009m:65121)},
    MRREVIEWER = {Ian Gladwell},
    DOI = {10.1093/imanum/drm053},
    URL = {http://dx.doi.org/10.1093/imanum/drm053},
    }

2008

  • [DOI] R. B. Kellogg, N. Madden, and M. Stynes, “A parameter-robust numerical method for a system of reaction-diffusion equations in two dimensions,” Numer. methods partial differential equations, vol. 24, iss. 1, pp. 312-334, 2008.
    [Bibtex]
    @article {MR2371362,
    AUTHOR = {Kellogg, R. B. and Madden, Niall and Stynes, Martin},
    TITLE = {A parameter-robust numerical method for a system of
    reaction-diffusion equations in two dimensions},
    JOURNAL = {Numer. Methods Partial Differential Equations},
    FJOURNAL = {Numerical Methods for Partial Differential Equations. An
    International Journal},
    VOLUME = {24},
    YEAR = {2008},
    NUMBER = {1},
    PAGES = {312--334},
    ISSN = {0749-159X},
    MRCLASS = {65N06 (35B25 35J25 65N12 65N15)},
    MRNUMBER = {2371362 (2008k:65224)},
    MRREVIEWER = {Cl{\'e}ment Mouhot},
    DOI = {10.1002/num.20265},
    URL = {http://dx.doi.org/10.1002/num.20265},
    }

2007

  • [DOI] T. Linß and N. Madden, “Parameter uniform approximations for time-dependent reaction-diffusion problems,” Numer. methods partial differential equations, vol. 23, iss. 6, pp. 1290-1300, 2007.
    [Bibtex]
    @article {MR2355160,
    AUTHOR = {Lin{\ss}, Torsten and Madden, Niall},
    TITLE = {Parameter uniform approximations for time-dependent
    reaction-diffusion problems},
    JOURNAL = {Numer. Methods Partial Differential Equations},
    FJOURNAL = {Numerical Methods for Partial Differential Equations. An
    International Journal},
    VOLUME = {23},
    YEAR = {2007},
    NUMBER = {6},
    PAGES = {1290--1300},
    ISSN = {0749-159X},
    MRCLASS = {65L50},
    MRNUMBER = {2355160 (2008i:65154)},
    MRREVIEWER = {Othmar Koch},
    DOI = {10.1002/num.20220},
    URL = {http://dx.doi.org/10.1002/num.20220},
    }

2005

  • [DOI] N. Kopteva, N. Madden, and M. Stynes, “Grid equidistribution for reaction-diffusion problems in one dimension,” Numer. algorithms, vol. 40, iss. 3, pp. 305-322, 2005.
    [Bibtex]
    @article {MR2189409,
    AUTHOR = {Kopteva, Natalia and Madden, Niall and Stynes, Martin},
    TITLE = {Grid equidistribution for reaction-diffusion problems in one
    dimension},
    JOURNAL = {Numer. Algorithms},
    FJOURNAL = {Numerical Algorithms},
    VOLUME = {40},
    YEAR = {2005},
    NUMBER = {3},
    PAGES = {305--322},
    ISSN = {1017-1398},
    MRCLASS = {65L50 (65L10 65L12)},
    MRNUMBER = {2189409 (2006h:65099)},
    MRREVIEWER = {Othmar Koch},
    DOI = {10.1007/s11075-005-7079-6},
    URL = {http://dx.doi.org/10.1007/s11075-005-7079-6},
    }

2004

  • [DOI] T. Linß and N. Madden, “A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations,” Appl. math. comput., vol. 148, iss. 3, pp. 869-880, 2004.
    [Bibtex]
    @article {MR2024550,
    AUTHOR = {Lin{\ss}, Torsten and Madden, Niall},
    TITLE = {A finite element analysis of a coupled system of singularly
    perturbed reaction-diffusion equations},
    JOURNAL = {Appl. Math. Comput.},
    FJOURNAL = {Applied Mathematics and Computation},
    VOLUME = {148},
    YEAR = {2004},
    NUMBER = {3},
    PAGES = {869--880},
    ISSN = {0096-3003},
    CODEN = {AMHCBQ},
    MRCLASS = {65L60 (34E15 35B25)},
    MRNUMBER = {2024550 (2004j:65104)},
    DOI = {10.1016/S0096-3003(02)00955-4},
    URL = {http://dx.doi.org/10.1016/S0096-3003(02)00955-4},
    }

2003

  • [DOI] T. Linss and N. Madden, “An improved error estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations,” Comput. methods appl. math., vol. 3, iss. 3, p. 417–423 (electronic), 2003.
    [Bibtex]
    @article {MR2058038,
    AUTHOR = {Linss, Torsten and Madden, Niall},
    TITLE = {An improved error estimate for a numerical method for a system
    of coupled singularly perturbed reaction-diffusion equations},
    NOTE = {Dedicated to John J. H. Miller on the occasion of his 65th
    birthday},
    JOURNAL = {Comput. Methods Appl. Math.},
    FJOURNAL = {Computational Methods in Applied Mathematics},
    VOLUME = {3},
    YEAR = {2003},
    NUMBER = {3},
    PAGES = {417--423 (electronic)},
    ISSN = {1609-4840},
    MRCLASS = {65L12 (65L10 65L50)},
    MRNUMBER = {2058038 (2005e:65105)},
    MRREVIEWER = {Ian Gladwell},
    DOI = {10.2478/cmam-2003-0027},
    URL = {http://dx.doi.org/10.2478/cmam-2003-0027},
    }
  • [DOI] N. Madden and M. Stynes, “A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems,” Ima j. numer. anal., vol. 23, iss. 4, pp. 627-644, 2003.
    [Bibtex]
    @article {MR2011343,
    AUTHOR = {Madden, Niall and Stynes, Martin},
    TITLE = {A uniformly convergent numerical method for a coupled system
    of two singularly perturbed linear reaction-diffusion
    problems},
    JOURNAL = {IMA J. Numer. Anal.},
    FJOURNAL = {IMA Journal of Numerical Analysis},
    VOLUME = {23},
    YEAR = {2003},
    NUMBER = {4},
    PAGES = {627--644},
    ISSN = {0272-4979},
    CODEN = {IJNADN},
    MRCLASS = {65L10 (34E15 65L12 65L70)},
    MRNUMBER = {2011343 (2004j:65095)},
    MRREVIEWER = {Bernhard A. Schmitt},
    DOI = {10.1093/imanum/23.4.627},
    URL = {http://dx.doi.org/10.1093/imanum/23.4.627},
    }

Professional Activites

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