Publications

Published Journal Articles and Refereed Conference Proceedings

  1. Róisín Hill and Niall Madden. Layer-adapted meshes for singularly perturbed problems via mesh partial differential equations and a posteriori information. Computers & Mathematics with Applications, Volume 168, 2024, Pages 1-9. doi.org/10.1016/j.camwa.2024.05.019 (Open Access).
  2. Ram Shiromani, Niall Madden,and V. Shanthi. A finite difference scheme for two-dimensional singularly perturbed convection-diffusion problem with discontinuous source term . Jan 2024. arXiv:2401.02331
  3. Laura Loftus, Niall Madden, P. Anne Scott, Aoife Cooke, and Nichola McNicholas. The Gender Pay Gap and Irish Higher Education: University of Galway, a Case Study. Adm. Sci. 2023, 13(11), 239. https://doi.org/10.3390/admsci13110239
  4. 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.
  5. Niall Madden and Martin Stynes. A weighted and balanced FEM for singularly perturbed reaction-diffusion problems. Calcolo 58, 28 (2021). DOI: 10.1007/s10092-021-00421-w. Preprint at ResearchGate.
  6. 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/.
  7. 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.
  8. 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
  9. H. Jahandari, S. MacLachlan, R. Haynes, and N. Madden. Finite element modelling of geophysical electromagnetic data with goal-oriented hr-adaptivity. Computational Geosciences volume 24, p 1257-1283 (March 2020)
  10. J. H. Adler, S. MacLachlan, and N. Madden. First-order system least squares finite-elements for singularly perturbed reaction-diffusion equations. In Ivan Lirkov and Svetozar Margenov, editors, Large-Scale Scientific Computing, Vol 11958 of Lecture Notes in Computer Science, pages 3-14. Springer, Cham, 2020.
  11. Stephen Russell and Niall Madden. Analysis of a Galerkin finite element method applied to a singularly perturbed reaction-diffusion problem in three dimensions. Int. J. Numer. Anal. Mod., 17 (2020), pp. 297-315. Abstract.
  12. Thái Anh Nhan, Scott MacLachlan and Niall Madden Boundary layer preconditioners for finite-element discretizations of singularly perturbed reaction-diffusion problems Numerical Algorithms (2018) 79: 281. https://doi.org/10.1007/s11075-017-0437-3 Abstract.
  13. José Luis Gracia, Niall Madden and Thái Anh Nhan. Applying a patched mesh method to efficiently solve a singularly perturbed reaction-diffusion problem . In: Bock H., Phu H., Rannacher R., Schlöder J. (eds) Modeling, Simulation and Optimization of Complex Processes HPSC 2015. Springer (2017). Abstract
  14. 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/
  15. P. Panaseti, A. Zouvani, N. Madden and C. Xenophontos, A C1-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.
  16. James Adler, Scott MacLachlan, and Niall Madden. A first-order system Petrov-Galerkin discretization for a reaction-diffusion problem on a fitted mesh . IMA J. Numer. Anal. (2016) 36 (3): 1281-1309. doi: 10.1093/imanum/drv045. Abstract
  17. Naresh M. Chadha and Niall Madden, An optimal time-stepping algorithm for unsteady advection-diffusion problems , Journal of Computational and Applied Mathematics, 294 (2016), 57-77. doi:10.1016/j.cam.2015.07.029
  18. 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
  19. Thái Anh Nhan and Niall Madden. Cholesky factorisation of linear systems coming from finite difference approximations of singularly perturbed problems. Proc. BAIL 2014, Vol 108 Lect. Notes Comput. Sci. Eng. Springer (2016), 209-220. Abstract
  20. S. Russell and N. Madden. A multiscale sparse grid finite element method for a two-dimensional singularly perturbed reaction-diffusion problem. Advances in Computational Mathematics Volume 41, Issue 6, pp 987-1014. 2015. DOI: 10.1007/s10444-014-9395-7.
  21. Scott MacLachlan and Niall Madden, Robust solution of singularly perturbed problems using multigrid methods. SIAM J. Sci. Comput. 35-5 (2013), pp. A2225-A2254. http://dx.doi.org/10.1137/120889770. Abstract
  22. 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
  23. Catherine G. Enright, Michael G. Madden, and Niall Madden. Bayesian Networks for Mathematical Models: Techniques for Automatic Construction and Efficient Inference. International Journal of Approximate Reasoning, Vol. 54 (2), 2013, pp 323-342. DOI 10.1016/j.ijar.2012.10.004 [Zbl 06175673]. [MR3021575]
  24. Niall Madden, John Todd and the development of modern numerical analysis. Irish Math. Soc. Bulletin, Number 69, Summer 2012, 11-23. Abstract [MR3026423].
  25. 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.
  26. 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.
  27. 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]
  28. 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]
  29. T. Linß and N. Madden, Analysis of an alternating direction method applied to singularly perturbed reaction-diffusion problems, International Journal of Numerical Analysis and Modelling, Volume 7, Number 3, p507-519 (2010). [MR2644287] [Zbl 1195.65119]
  30. 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.
  31. 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).
  32. M. Stephens and N. Madden A Schwarz technique for a system of reaction diffusion equations with differing parameters. Proc. BAIL 2008 - Boundary and Interior Layers , Lecture Notes in Computational Science and Engineering, Vol. 69 Hegarty, A.F.; Kopteva, N.; O' Riordan, E.; Stynes, M. (Eds.). p247-255 (2009) [Zbl 1181.65107] [MR2581492]
  33. 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]
  34. 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]
  35. 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
  36. 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.
  37. J. Newell, D. Higgins, N. Madden, J. Cruickshank, J. Einbeck, K. McMillan, K., R. McDonald, Software for Calculating Blood Lactate Endurance Markers, Journal of Sports Sciences, Vol 25, Issue 12, 1403--1409, 2007.
  38. 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.
  39. N. Kopteva, N. Madden, and M. Stynes, Grid equidistribution for reaction-diffusion problems in one dimension, Numerical Algorithms, Volume 40, No. 3, 305--322, 2005. [Abstract],
  40. T. Linß and N. Madden, A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations. Applied Mathematics and Computation, Vol 148 (2004), Issue 3 pp 869-880 Abstract. PS file, "Prescreen" PDF. [Zbl 1042.65065] [MR2024550]
  41. 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
  42. T. Linß and N. Madden, An improved estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations, Computational Methods in Applied Mathematics (CMAM), Vol. 3 (2003), No.3, 417-423. [Zbl 1040.65066] [MR2058038]
  43. N. Madden and M. Stynes, A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems. IMA Journal of Numerical Analysis, Vol. 23 (2003), No. 4, pp627-644. Abstract. [Zbl 1048.65076] [MR2011343]
  44. N. Madden M. Stynes and G.P. Thomas, On the development of complete flow models for wave-current interactions, in "Coastal Dynamics 97" (Conference Proceedings of the Third Coastal Dynamics Conference held in Plymouth, UK, June 1997), by Edward B. Thornton, ed. Reston, VA: ASCE, 0-7844-0321-X, 1998. Abstract.
  45. 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
  46. N. Madden and M. Stynes, Linear enhancements of the streamline diffusion method for convection-diffusion problems, Computers Math. Applic. 32 (1996), 29-42. Abstract. doi:10.1016/S0898-1221(96)00184-8. [Zbl 0870.65100] [MR1426204]

Unrefereed technical reports and conference proceedings

  1. Scott MacLachlan and Niall Madden, Robust solution of singularly perturbed problems using multigrid methods: analysis and results in one and two dimensions. . Aug 2012.
  2. 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.
  3. 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.
  4. N. Madden, M. Stynes, and G.P. Thomas, On the application of robust numerical methods to a complete-flow wave-current model, Boundary and Interior Layers (BAIL), Toulouse, July 2004. Abstract. Also available from here, here, and from RIAN.ie.
  5. T. Linß and N. Madden, Uniform convergence of a finite difference scheme for a system of coupled reaction-diffusion equations. Proceedings in Applied Mathematics and Mechanics 3 (2003) 1, 567-568.

Theses (supervised by me)

  • Faiza Alssaedi. Algorithms for the accurate and efficient solution of fourth order boundary-layer problems Ph.D. thesis, NUI Galway 2021.
  • Stephen Russell. Sparse grid methods for singularly perturbed problems Ph.D. thesis, NUI Galway 2016.
  • Nhan Anh Thai. Preconditioning techniques for singularly perturbed differential equations. Ph.D. thesis, NUI Galway 2015.
  • Stephen Russell. Sparse grid methods for the two-dimensional Poisson problem. M.Sc. thesis, NUI Galway 2012.
  • Nhan Anh Thai. Numerical Solutions of Models for Glucose and Insulin Levels in Critically Ill Patients. M.Sc. thesis, NUI Galway 2011.
  • Meghan Stephens. Numerical Methods for Singularly Perturbed Differential Equations. Ph.D. thesis, NUI Galway 2009.

Theses (written by me)

  • 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.

Other

  • 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.