**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

**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

- 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

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

- 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}, }`

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- Professor Michel Destrade
- Prof. Michael Tuite