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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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