Published Journal Articles and Refereed Conference Proceedings
Scott P. MacLachlan, Niall Madden, Thái Anh Nhan.
A Boundary-Layer Preconditioner for Singularly Perturbed
Convection
Diffusion. arxiv.org/abs/2108.13468. SIAM
Journal on Matrix Analysis and Applications, Vol. 43,
Iss. 2 (2022) 10.1137/21M1443297.
Róisín Hill and Niall Madden.
Generating layer-adapted meshes using mesh partial differential
equations.
Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 559-588.
DOI: 10.4208/nmtma.OA-2020-0187. Preprint
and and FEniCS code available
from osf.io/dpexh/.
Nanda Poddar, Kajal Kumar Mondal and Niall Madden.
Layer-adapted meshes for solute dispersion in a steady flow
through an annulus with wall absorption: Application to a
catheterized artery.
Korea-Australia Rheology Journal 33, 11-24 (2021).
DOI:
10.1007/s13367-021-0002-4.
Thái Anh Nhan and
Niall Madden.
An analysis of diagonal and incomplete Cholesky
preconditioners for singularly perturbed problems
on layer-adapted meshes.
J. Appl. Math. Comput. 65, 245-272
(2021). DOI: 10.1007/s12190-020-01390-z
Russell, Stephen, and Niall Madden.
An introduction to the analysis and implementation of sparse
grid finite element methods. Computational Methods in Applied
Mathematics 17, no. 2 (2017):
299-322. DOI: doi.org/10.1515/cmam-2016-0042. Source code is available from
https://github.com/niallmadden/SparseGrids/
P. Panaseti, A. Zouvani, N. Madden and
C. Xenophontos,
A C^{1}-conforming hp Finite Element Method for fourth order singularly perturbed
boundary value problems, Applied Numerical Mathematics
Volume 104 (2016), Pages 81-97.
doi:10.1016/j.apnum.2016.02.002.
Stephen Russell and Niall Madden.
A multiscale sparse grid technique for a
two-dimensional convection-diffusion problem
with exponential layers.Proc. BAIL 2014,
Vol 108 Lect. Notes Comput. Sci. Eng. Springer (2016), 245-255.
Abstract
Christos Xenophontos, Markus Melenk, Niall Madden,
Lisa Oberbroeckling, Pandelitsa Panaseti, and Antri Zouvani.
hp Finite Element Methods for Fourth Order
Singularly Perturbed Boundary Value Problems.
Dimov, Faragó, Vulkov (Eds.): Proc. NAA
2012, Springer
Lecture Notes in Computer Science, Vol 8236, pp. 532-539, 2013
N. Madden
and M. Stynes. A
curious property of oscillatory FEM solutions of one-dimensional
convection-diffusion problems.
Applications
of Mathematics 2012, Proc. of Conference in Honour of 60th
birthday of Michal Křížek, 2--5 May 2012),
J. Brandts, J. Chleboun, S. Korotov, K. Segeth, J.
Šístek & T. Vejchodský (Eds.),
Czech Academy of Sciences, Prague, 2012, ISBN 978-80-85823-60-8, pp.188--196.
C.G. Enright, M.G. Madden, N. Madden and J.G. Laffey.
Clinical Time Series Data Analysis Using Mathematical Models and
DBNs, Artificial
Intelligence in Medicine, Lecture Notes in Computer Science,
2011, Volume 6747/2011,159-168.
Naresh M. Chadha and Niall Madden,
A two-weight scheme for a time-dependent
advection-diffusion problem.
In C. Carmelo, J. L. Gracia, and F. J. Lisbona, (eds), BAIL 2010 -
Boundary and Interior Layers, Computational and Asymptotic Methods,
Vol 81 of Lect. Notes Comput. Sci. Eng., 99--108. Springer, 2011.
Abstract.
[MR2849732]
[Full text at RIAN.ie]
Niall Madden and Kajal Kumar Mondal.
Improved mathematical and numerical modelling of dispersion of a solute from
a continuous source,
In C. Carmelo, J. L. Gracia, and F. J. Lisbona, (eds), BAIL 2010 -
Boundary and Interior Layers, Computational and Asymptotic Methods,
Vol 81
of Lect. Notes Comput. Sci. Eng., 177--185. Springer, 2011.
Abstract.
[MR2849740]
[Full text at RIAN.ie]
C.G. Enright,
M.G. Madden, S. Russell,
N. Aleks, G.T. Manley, J. Laffey, B. Harte, A. Mulvey, N. Madden.
Modelling
glycaemia in ICU patients: A dynamic Bayesian network
approach BIOSIGNALS 2010 - Proceedings of the 3rd
International Conference on Bio-inpsired Systems and Signal
Processing, Proceedings 2010, Pages 452-459.
T. Linß
and N. Madden, Layer-adapted
meshes for a system of coupled singularly perturbed
reaction-diffusion
problems. IMA
J Numer Anal 29 (1): 86-108; doi:10.1093/imanum/drm049 (2009).
Fang Liu, Niall Madden, Martin Stynes, and Aihui Zhou, A two-scale
sparse grid method for a singularly perturbed
reaction-diffusion problem in two
dimensions, IMA
J Numer Anal 29 (4): 986-1007,
doi:10.1093/imanum/drn048 (2009)
[MR2557053]
M. Stephens and N. Madden, A Parameter-Uniform Schwarz Method for a Coupled
System of Reaction Diffusion Equations, Journal
of Computational and Applied Mathematics, Volume 230, Issue 2, Pages
360-370 (15 August 2009).
[MR2532330]
R. Bruce Kellogg, Niall Madden and
Martin Stynes, A parameter-robust
numerical method for a system of
reaction-diffusion equations in two
dimensions, Numerical Methods for
Partial Differential Equations, Volume
24 (1), pp312--334, 2008.
Abstract. DOI: 10.1002/num.20265
T. Linß
and N. Madden, Parameter uniform approximations for time-dependent
reaction-diffusion problems,
Numerical Methods for Partial Differential Equations, Volume 23, Issue 6, 1290--1300, 2007. Abstract.
J. Newell,
J. Einbeck, N. Madden, K. McMillan, K.,
Model free endurance markers based on the
second derivative of blood lactate curves, in
Statistical Solutions to Modern Problems, (A.R. Francis,
K.M. Matawie, A. Oshlack, and G.K. Smyth,
eds.),
Proceedings of the 20th International Workshop on Statistical
Modelling, Sydney, Australia, 2005,
p357--364.
T. Linß
and N. Madden,
Accurate solution of a system of coupled singularly perturbed
reaction-diffusion equations,
Computing Vol 73 (2004), No 2, 121-133.
Abstract. DOI: 10.1007/s00607-004-0065-3
N. Madden and M. Stynes,
Efficient generation of oriented meshes for solving
convection-diffusion
problems, Int. J. Numer. Methods Engrg. 40 (1997), 565-576. Gzipped postscript
file
R. Bruce Kellogg, N. Madden, and Martin Stynes, On the numerical
solution of a system of M
reaction-diffusion equations two
dimensions, In: I. Farago,
P. Vabishchevich, L. Vulkov (eds.), Finite Difference Methods: Theory and Applications. Pro. IVth Int. Conf. FDM: T&A (Lozenetz, Bulgaria, 26-29 August 2006), Rousse 2007, 252-257.
N. Kopteva, N. Madden
and
M. Stynes,
On equidistribution for reaction-diffusion problems, in Numerical
Methods for Problems with Layer Phenomena (A. R. Ansari, A. F. Hegarty
& G. I. Shishkin, eds.), Proceedings of the 3rd Annual Workshop,
Department of Mathematics & Statistics, University of Limerick,
Ireland, February 2004, 46-51.
Numerical Methods for the Accurate Solution of Singularly
Perturbed Convection-Diffusion Problems, M.Sc., Dept of
Mathematics, University College Cork, Ireland. 1996. Supervisor: Prof. Martin Stynes.
Numerical Methods for Wave-Current interactions, Ph.D., Dept of
Mathematics, NUI Cork, Ireland, 2000. Supervisor:
Prof.
Martin Stynes.
ENTCS Volume
74. The Second Irish Conference on the Mathematical
Foundations of Computer Science and Information Technology (MFCSIT
2002) Galway, Ireland, 18th and 19th of July 2002. Online
Publication Date: October 2003 Guest Editors: Sharon Flynn, Ted
Hurley, Micheal Mac an Airchinnigh, Niall Madden, Michael McGettrick,
Michel Schellekens and Anthony Seda.