Mathematical and Statistical Sciences

Dr Niall Madden

BSc, MSc, PhD

Contact Details

Senior Lecturer
Áras de Brún
E: Niall.Madden@UniversityOfGalway.ie

Biography

BSc (Mathematics and Computing) UCG, 1994
MSc (Mathematics) UCC, 1996
PhD (Mathematics) NUI Cork, 2000

Personal Webpage: https://www.niallmadden.ie

My research is mainly in the field of numerical analysis, particularly on algorithms for the approximate solution of differential equations. I have particular expertise in solving singularly perturbed differential equations, by finite element and finite difference methods, and in algorithms for solving resulting linear systems, and adaptive mesh generation. I am also active in the application of novel methods to problems in numerical modelling.

I joined University of Galway (then called NUI Galway) as a lecturer in Mathematics in 2000, shortly after completing a PhD in Mathematics at UCC. My doctoral research combined applied and theoretical numerical analysis of equations arising in this area of fluid dynamics.

From July 2018 to March 2020, I was the Vice dean for Equality, Diversity and Inclusion for the College of Science in NUI Galway. I am involved in NUI Galway's Athena SWAN activities - I was a member of our Institutional SAT from its foundation in 2015 to 2021, and am chair of the School of Maths SAT. I was a member of the NUI Galway Gender Equality Task Force chaired by Prof. Jane Grimson.

Research Interests

Numerical analysis of singularly perturbed differential equations. Finite element and finite difference methods. Layer resolving meshes. Numerical linear algebra. Sparse grids.

Research Projects

Project	Start Date	End Date
IRC POSTGRADUATE SCHOLARSHIP 2017 RÓISÍN HILL - BALANCED DISCONTINUOUS GALERKIN METHODS FOR FLUID FLOW PROBLEMS: DESIGN, IMPLEMENTATION AND APPLICATION	01-OCT-17	30-SEP-21
Stokes Modelling Workshop: Mathematics for Industry COST Action (MI-NET)	05-JUN-17	09-JUN-17
SIAM UK AND IRELAND NATIONAL STUDENT CONFERENCE 2017	27-MAR-17	26-MAY-17
IRCSET EMBARK POSTGRAD MULTIGRID METHODS FOR SINGULARLY PERTURBED PROBLEMS (ANH THAI NHAN) RS/2011/179 NIALL MADDEN	01-SEP-11	31-AUG-15
SFI RFP NUMERICAL MODELLING OF ADVECTION-DIFFUSION	01-SEP-08	01-NOV-12
IRCSET EMBARK 04 MEGHAN STEPHENS MADDEN	01-SEP-04	30-APR-09
MF2005 FAST PARALLEL SOLVERS N MADDEN	01-NOV-05	19-JUN-09
MF2003 MF 89 03 M NIALL MADDEN	01-JAN-04	28-FEB-07

Contract Researchers

	Researcher Name	Project	Role	Funding Body
	Naresh Mohan Chadha	RFP/CMS/1205	Postdoctoral researcher
	Kajal Kumar Mondol	Novel methods for modelling dispersion of polutants	Post-doctoral researcher

Peer Reviewed Journals

	Year	Publication
	(2024)	'Layer-adapted meshes for singularly perturbed problems via mesh partial differential equations and a posteriori information' Róisín Hill and Niall Madden (2024) 'Layer-adapted meshes for singularly perturbed problems via mesh partial differential equations and a posteriori information'. Computers And Mathematics With Applications, 168 :1-9 [DOI] [Details]
	(2023)	'The Gender Pay Gap and Irish Higher Education: University of Galway, a Case Study' Laura Loftus, Niall Madden, P. Anne Scott, Aoife Cooke, and Nichola McNicholas (2023) 'The Gender Pay Gap and Irish Higher Education: University of Galway, a Case Study'. Administrative Sciences, 13 (11):1-16 [Details]
	(2022)	'Boundary-Layer Preconditioner for Singularly Perturbed Convection Diffusion' Scott P. MacLachlan, Niall Madden, Thái Anh Nhan (2022) 'Boundary-Layer Preconditioner for Singularly Perturbed Convection Diffusion'. SIAM Journal on Matrix Analysis and Applications, 43 (2):561-583 [DOI] [Details]
	(2021)	'A weighted and balanced FEM for singularly perturbed reaction-diffusion problem' Niall Madden, Martin Stynes (2021) 'A weighted and balanced FEM for singularly perturbed reaction-diffusion problem'. Calcolo, 58 :27-28 [DOI] [Details]
	(2021)	'Generating Layer-Adapted Meshes Using Mesh Partial Differential Equations' Róisín Hill and Niall Madden (2021) 'Generating Layer-Adapted Meshes Using Mesh Partial Differential Equations'. Numerical Mathematics-Theory Methods And Applications, 14 :559-588 [DOI] [Details]
	(2020)	'An analysis of diagonal and incomplete Cholesky preconditioners for singularly perturbed problems on layer-adapted meshes' Nhan, TA,Madden, N (2020) 'An analysis of diagonal and incomplete Cholesky preconditioners for singularly perturbed problems on layer-adapted meshes'. Journal Of Applied Mathematics And Computing, [DOI] [Details]
	(2020)	'ANALYSIS OF A GALERKIN FINITE ELEMENT METHOD APPLIED TO A SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEM IN THREE DIMENSIONS' Russell, S,Madden, N (2020) 'ANALYSIS OF A GALERKIN FINITE ELEMENT METHOD APPLIED TO A SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEM IN THREE DIMENSIONS'. International Journal Of Numerical Analysis And Modeling, 17 :297-315 [Details]
	(2020)	'Finite element modelling of geophysical electromagnetic data with goal-oriented hr-adaptivity' Jahandari, H,MacLachlan, S,Haynes, RD,Madden, N (2020) 'Finite element modelling of geophysical electromagnetic data with goal-oriented hr-adaptivity'. Computational Geosciences, [DOI] [Details]
	(2018)	'Boundary layer preconditioners for finite-element discretizations of singularly perturbed reaction-diffusion problems' Nhan, TA,MacLachlan, S,Madden, N (2018) 'Boundary layer preconditioners for finite-element discretizations of singularly perturbed reaction-diffusion problems'. Numerical Algorithms, 79 :281-310 [DOI] [Details]
	(2017)	'An Introduction to the Analysis and Implementation of Sparse Grid Finite Element Methods' Russell, S., Madden, N. (2017) 'An Introduction to the Analysis and Implementation of Sparse Grid Finite Element Methods'. Computational Methods In Applied Mathematics, 17 :299-322 [DOI] [Details]
	(2016)	'A first-order system Petrov-Galerkin discretization for a reaction-diffusion problem on a fitted mesh' Adler, J.; MacLachlan, S.; Madden, N. (2016) 'A first-order system Petrov-Galerkin discretization for a reaction-diffusion problem on a fitted mesh'. Ima Journal Of Numerical Analysis, 36 :1281-1309 [DOI] [Details]
	(2016)	'A C-1-conforming hp finite element method for fourth order singularly perturbed boundary value problems' Panaseti, P,Zouvani, A,Madden, N,Xenophontos, C (2016) 'A C-1-conforming hp finite element method for fourth order singularly perturbed boundary value problems'. Applied Numerical Mathematics, 104 :81-97 [DOI] [Details]
	(2016)	'An optimal time-stepping algorithm for unsteady advection-diffusion problems' Chadha, NM,Madden, N (2016) 'An optimal time-stepping algorithm for unsteady advection-diffusion problems'. Journal Of Computational And Applied Mathematics, 294 :57-77 [DOI] [Details]
	(2015)	'A multiscale sparse grid finite element method for a two-dimensional singularly perturbed reaction-diffusion problem' Madden, N,Russell, S (2015) 'A multiscale sparse grid finite element method for a two-dimensional singularly perturbed reaction-diffusion problem'. Advances In Computational Mathematics, 41 :987-1014 [DOI] [Details]
	(2013)	'Robust solution of singularly perturbed problems using multigrid methods' MacLachlan, Scott and Madden, Niall (2013) 'Robust solution of singularly perturbed problems using multigrid methods'. SIAM J. Sci. Comput, 35 (5):2225-2254 [DOI] [Details]
	(2013)	'Bayesian networks for mathematical models: Techniques for automatic construction and efficient inference' Enright, CG,Madden, MG,Madden, N (2013) 'Bayesian networks for mathematical models: Techniques for automatic construction and efficient inference'. International Journal Of Approximate Reasoning, 54 :323-342 [DOI] [Details]
	(2012)	'John Todd and the development of modern numerical analysis' Niall Madden (2012) 'John Todd and the development of modern numerical analysis'. Bulletin Of The Irish Mathematical Society, 69 (Summer):11-23 [ARAN Link] [Details]
	(2010)	'ANALYSIS OF AN ALTERNATING DIRECTION METHOD APPLIED TO SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS' Linss, T;Madden, N (2010) 'ANALYSIS OF AN ALTERNATING DIRECTION METHOD APPLIED TO SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS'. International Journal Of Numerical Analysis And Modeling, 7 :507-519 [Details]
	(2010)	'ANALYSIS OF AN ALTERNATING DIRECTION METHOD APPLIED TO SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS' Linss, T,Madden, N (2010) 'ANALYSIS OF AN ALTERNATING DIRECTION METHOD APPLIED TO SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS'. International Journal Of Numerical Analysis And Modeling, 7 :507-519 [Details]
	(2009)	'A Parameter-Uniform Schwarz Method for a Coupled System of Reaction Diffusion Equations' Stephens, M., Madden, N. (2009) 'A Parameter-Uniform Schwarz Method for a Coupled System of Reaction Diffusion Equations'. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 230 (2):360-370 [DOI] [Details]
	(2009)	'A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions' Liu, F,Madden, N,Stynes, M,Zhou, AH (2009) 'A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions'. Ima Journal Of Numerical Analysis, 29 :986-1007 [DOI] [Details]
	(2009)	'Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems' Linss, T,Madden, N (2009) 'Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems'. Ima Journal Of Numerical Analysis, 29 :109-125 [DOI] [Details]
	(2008)	'A parameter-robust numerical method for a system of reaction-diffusion equations in two dimensions' Kellogg, RB,Madden, N,Stynes, M (2008) 'A parameter-robust numerical method for a system of reaction-diffusion equations in two dimensions'. Numerical Methods For Partial Differential Equations, 24 :312-334 [DOI] [Details]
	(2007)	'Software for calculating blood lactate endurance markers' Newell, J;Higgins, D;Madden, N;Cruickshank, J;Einbeck, J;McMillan, K;McDonald, R (2007) 'Software for calculating blood lactate endurance markers'. Journal Of Sports Sciences, 25 :1403-1409 [DOI] [Details]
	(2007)	'Parameter uniform approximations for time-dependent reaction-diffusion problems' Linss, T,Madden, N (2007) 'Parameter uniform approximations for time-dependent reaction-diffusion problems'. Numerical Methods For Partial Differential Equations, 23 :1290-1300 [DOI] [Details]
	(2007)	'Software for calculating blood lactate endurance markers' Newell, J ; Higgins, D; Madden, N; Cruickshank, J; Einbeck, J; McMillan, K; McDonald, R (2007) 'Software for calculating blood lactate endurance markers'. Journal Of Sports Sciences, [Details]
	(2005)	'Grid equidistribution for reaction-diffusion problems in one dimension' Kopteva, N,Madden, N,Stynes, M (2005) 'Grid equidistribution for reaction-diffusion problems in one dimension'. Numerical Algorithms, 40 :305-322 [DOI] [Details]
	(2004)	'Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations' Linss, T;Madden, N (2004) 'Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations'. Computing, 73 :121-133 [DOI] [Details]
	(2003)	'A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems' Madden, N;Stynes, M (2003) 'A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems'. Ima Journal Of Numerical Analysis, 23 :627-644 [Details]
	(2004)	'Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations' Linss, T,Madden, N (2004) 'Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations'. Computing, 73 :121-133 [DOI] [Details]
	(2004)	'A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations' Linss, T,Madden, N (2004) 'A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations'. Applied Mathematics And Computation, 148 :869-880 [DOI] [Details]
	(2003)	'An improved error estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations' Linss, Torsten and Madden, Niall (2003) 'An improved error estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations'. Comput. Methods Appl. Math, 3 (3):417-423 [DOI] [Details]
	(2003)	'An improved estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations' Linss, T., Madden, N. (2003) 'An improved estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations'. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 3 (3):417-423 [Details]
	(2003)	'A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems' Madden, N,Stynes, M (2003) 'A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems'. Ima Journal Of Numerical Analysis, 23 :627-644 [Details]
	(1997)	'Efficient generation of oriented meshes for solving convection-diffusion problems' Madden, N,Stynes, M (1997) 'Efficient generation of oriented meshes for solving convection-diffusion problems'. International Journal For Numerical Methods In Engineering, 40 :565-576 [Details]
	(1996)	'Linear enhancements of the streamline diffusion method for convection-diffusion problems' Madden, N,Stynes, M (1996) 'Linear enhancements of the streamline diffusion method for convection-diffusion problems'. Computers & Mathematics With Applications, 32 :29-42 [Details]

Book Chapters

	Year	Publication
	(2020)	'First-Order System Least Squares Finite-Elements for Singularly Perturbed Reaction-Diffusion Equations' James H. Adler, Scott MacLachlan, Niall Madden (2020) 'First-Order System Least Squares Finite-Elements for Singularly Perturbed Reaction-Diffusion Equations' In: LSSC 2019: Large-Scale Scientific Computing. :3-14 Cham: Springer. [DOI] [Details]
	(2017)	'Applying a Patched Mesh Method to Efficiently Solve a Singularly Perturbed Reaction-Diffusion Problem' José Luis Gracia, Niall Madden, Thái Anh Nhan (2017) 'Applying a Patched Mesh Method to Efficiently Solve a Singularly Perturbed Reaction-Diffusion Problem' In: Modeling, Simulation and Optimization of Complex Processes HPSC 2015. :41-54 Cham: Springer. [DOI] [Details]
	(2015)	'A Multiscale Sparse Grid Technique for a Two-Dimensional Convection-Diffusion Problem with Exponential Layers' Russell, S., Madden, N. (2015) 'A Multiscale Sparse Grid Technique for a Two-Dimensional Convection-Diffusion Problem with Exponential Layers' In: Boundary and interior layers, computational and asymptotic methods—BAIL 2014. :245-255 Cham: Springer. [DOI] [Details]
	(2015)	'Cholesky Factorisation of Linear Systems Coming from Finite Difference Approximations of Singularly Perturbed Problems' Nhan, T.A., Madden, N. (2015) 'Cholesky Factorisation of Linear Systems Coming from Finite Difference Approximations of Singularly Perturbed Problems' In: Boundary and interior layers, computational and asymptotic methods—BAIL 2014. :209-220 Cham: Springer. [DOI] [Details]
	(2013)	'hp Finite Element Methods for Fourth Order Singularly Perturbed Boundary Value Problems' Xenophontos, Christos; Melenk, Markus; Madden, Niall; Oberbroeckling, Lisa; Panaseti, Pandelitsa; Zouvan; Antri . (2013) 'hp Finite Element Methods for Fourth Order Singularly Perturbed Boundary Value Problems' In: Lecture Notes In Computer Science. :532-539 Heidelberg: Springer. [DOI] [Details]
	(2011)	'Improved mathematical and numerical modelling of dispersion of a solute from a continuous source' Niall Madden and Kajal Kumar Mondal (2011) 'Improved mathematical and numerical modelling of dispersion of a solute from a continuous source' In: Lecture Notes In Computational Science And Engineering. :177-185 Heidelberg: Springer. [DOI] [ARAN Link] [Details]
	(2011)	'A two-weight scheme for a time-dependent advection-diffusion problem' Chadha, Naresh M. and Madden, Niall (2011) 'A two-weight scheme for a time-dependent advection-diffusion problem' In: BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods. :99-108 Heidelberg: Springer. [DOI] [Details]
	(2009)	'A Schwarz technique for a system of reaction diffusion equations with differing parameters' Stephens, Meghan and Madden, Niall (2009) 'A Schwarz technique for a system of reaction diffusion equations with differing parameters' In: BAIL 2008 - Boundary and Interior Layers. :247-255 Berlin: Springer. [DOI] [Details]

Conference Publications

	Year	Publication
	(2012)	*23rd Irish Artificial Intelligence and Cognitive Science Conference* Catherine G. Enright, Michael G. Madden, Niall Madden, John G. Laffey (2012) Modelling the Individual Patient 23rd Irish Artificial Intelligence and Cognitive Science Conference [Details]
	(2010)	*BIOSIGNALS 2010: PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON BIO-INSPIRED SYSTEMS AND SIGNAL PROCESSING* Enright, CG;Madden, MG;Russell, S;Aleks, N;Manley, G;Laffey, J;Harte, B;Mulvey, A;Madden, N (2010) MODELLING GLYCAEMIA IN ICU PATIENTS A Dynamic Bayesian Network Approach BIOSIGNALS 2010: PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON BIO-INSPIRED SYSTEMS AND SIGNAL PROCESSING , pp.452-459 [Details]
	(2012)	*APPLICATIONS OF MATHEMATICS 2012* Madden, N;Stynes, M (2012) A CURIOUS PROPERTY OF OSCILLATORY FEM SOLUTIONS OF ONE-DIMENSIONAL CONVECTION-DIFFUSION PROBLEMS APPLICATIONS OF MATHEMATICS 2012 , pp.188-196 [Details]
	(2015)	*BOUNDARY AND INTERIOR LAYERS, COMPUTATIONAL AND ASYMPTOTIC METHODS - BAIL 2014* Nhan, TA;Madden, N (2015) Cholesky Factorisation of Linear Systems Coming from Finite Difference Approximations of Singularly Perturbed Problems BOUNDARY AND INTERIOR LAYERS, COMPUTATIONAL AND ASYMPTOTIC METHODS - BAIL 2014 , pp.209-220 [DOI] [Details]
	(2015)	*BOUNDARY AND INTERIOR LAYERS, COMPUTATIONAL AND ASYMPTOTIC METHODS - BAIL 2014* Russell, S;Madden, N (2015) A Multiscale Sparse Grid Technique for a Two-Dimensional Convection-Diffusion Problem with Exponential Layers BOUNDARY AND INTERIOR LAYERS, COMPUTATIONAL AND ASYMPTOTIC METHODS - BAIL 2014 , pp.245-255 [DOI] [Details]
	(2016)	*APPLIED NUMERICAL MATHEMATICS* Panaseti, P;Zouvani, A;Madden, N;Xenophontos, C (2016) A C-1-conforming hp finite element method for fourth order singularly perturbed boundary value problems APPLIED NUMERICAL MATHEMATICS , pp.81-97 [DOI] [Details]
	(2012)	*APPLICATIONS OF MATHEMATICS 2012* Niall Madden and Martin Stynes (2012) A curious property of oscillatory FEM solutions of one-dimensional convection-diffusion problems . In: J. Brandts, J. Chleboun, S. Korotov, K. Segeth, J. Šístek & T. Vejchodský eds. APPLICATIONS OF MATHEMATICS 2012 Prague, , 02-MAY-12 - 05-MAY-12 , pp.188-196 [Details]
	(2011)	*Proc. 13th Conference on Artificial Intelligence in Medicine* Catherine G. Enright; Michael G. Madden; Niall Madden; John G. Laffey (2011) Clinical Time Series Data Analysis Using Mathematical Models and DBNs . In: Mor Peleg and Nada Lavrac and Carlo Combi eds. Proc. 13th Conference on Artificial Intelligence in Medicine Slovenia, , pp.159-168 [Details]
	(2010)	*BIOSIGNALS 2010: PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON BIO-INSPIRED SYSTEMS AND SIGNAL PROCESSING* Enright, C.G.; Madden, M.G.; Russell, S., Aleks, N.; Manley, G.; Laffey, J.; Harte, B.; Mulvey, A.; Madden, N.; Fred, A.; Filipe, J.; Gamboa, H. (2010) Modelling Glycaemia in ICU Patients - A Dynamic Bayesian Network Approach BIOSIGNALS 2010: PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON BIO-INSPIRED SYSTEMS AND SIGNAL PROCESSING , pp.452-459 [Details]
	(2005)	*20th International Workshop on Statistical Modelling* Newell, J.; Einbeck, J.; Madden, N.; McMillan, K. (2005) Model free endurance markers based on the second derivative of blood lactate curves . In: A.R. Francis, K.M. Matawie, A. Oshlack, and G.K. Smyth eds. 20th International Workshop on Statistical Modelling Sydney, Australia, , 10-JUL-05 - 15-JUL-05 , pp.357-364 [Details]
	(1997)	*Coastal Dynamics '97* Madden N.; Stynes M.; Thomas, G.P. (1997) On the development of complete flow models for wave-current interactions . In: Edward B. Thornton eds. Coastal Dynamics '97 Plymouth, , pp.405-415 [Details]

Edited Books

	Year	Publication
	(2003)	The Second Irish Conference on the Mathematical Foundations of Computer Science and Information Technology (MFCSIT 2002). Sharon Flynn, Ted Hurley, Micheal Mac an Airchinnigh, Niall Madden, Michael McGettrick, Michel Schellekens and Anthony Seda (Ed.). (2003) The Second Irish Conference on the Mathematical Foundations of Computer Science and Information Technology (MFCSIT 2002) The Second Irish Conference on the Mathematical Foundations of Computer Science and Information Technology (MFCSIT 2002). x: Electronic Notes in Theoretical Computer Science (Elsevier). [DOI] [Details]

Conference Contributions

	Year	Publication
	(2017)	27th Biennial Numerical Analysis Conference, Koptena, N., Linss, T., Madden, N. (2017) Mini-symposium organiser: Advances in the robust solution of singularly perturbed differential equations. [Co-chaired Session], 27th Biennial Numerical Analysis Conference, Glasgow , 27-JUN-17 - 30-JUN-17. [Details]
	(2017)	The SIAM UKIE National Student Chapter Conference, The NUI Galway SIAM Chapter (2017) Annual meeting of UK and Ireland Student Chapters of the Society for Industrial and Applied Mathematics. [Conference Organising Committee Member], The SIAM UKIE National Student Chapter Conference, Galway , 26-MAY-17. [Details]
	(2017)	14th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, Niall Madden (2017) Main Organiser. [Conference Organising Committee Chairperson], 14th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, NUI Galway , 06-APR-17 - 07-APR-17. [Details]
	(2016)	2016 AARMS-CRM Workshop on Numerical Analysis of Singularly Perturbed Differential Equations, Niall Madden (2016) Plenary lecture: Sparse grid methods for reaction-diffusion problems in two and three dimensions. [Invited Oral Presentation], 2016 AARMS-CRM Workshop on Numerical Analysis of Singularly Perturbed Differential Equations, Halifax Canada , 27-JUL-16 - 29-JUL-16. [Details]
	(2016)	2016 AARMS-CRM Workshop on Numerical Analysis of Singularly Perturbed Differential Equations, Niall Madden (2016) Short Course: Numerical Methods for Singularly Perturbed Problems. [Invited Oral Presentation], 2016 AARMS-CRM Workshop on Numerical Analysis of Singularly Perturbed Differential Equations, Halifax, NS , 25-JUL-16 - 29-JUL-16. [Details]
	(2016)	The 14th European Finite Element Fair, Niall Madden (2016) A balanced first-order system Petrov-Galerkin method for a singularly perturbed PDE. [Oral Presentation], The 14th European Finite Element Fair, Universiatät Bonn , 20-MAY-16 - 21-MAY-16. [Details]
	(2015)	26th Biennial Numerical Analysis Conference, Niall Madden (2015) A balanced-norm finite element method for singularly perturbed problems. [Oral Presentation], 26th Biennial Numerical Analysis Conference, University of Strathclyde , 23-JUN-15 - 26-JUN-15. [Details]
	(2015)	26th Biennial Numerical Analysis Conference, Madden, N; Stynes M. (2015) Mini-symposium organiser: Singularly perturbed differential equations. [Co-chaired Session], 26th Biennial Numerical Analysis Conference, Glasgow , 23-JUN-15 - 26-JUN-15. [Details]
	(2015)	12th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, Niall Madden (2015) A balanced first-order system Petrov-Galerkin discretization for a reaction-diffusion problem on a fitted mesh. [Oral Presentation], 12th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, TU Dresden , 09-APR-15 - 10-APR-15. [Details]
	(2014)	Joint Symposium Irish Mechanics Society and the Irish Society for Scientific Engineering & Computation (ISSEC), Niall Madden (2014) Sparse grid finite element methods for boundary layers problems. [Oral Presentation], Joint Symposium Irish Mechanics Society and the Irish Society for Scientific Engineering & Computation (ISSEC), NUI Galway , 08-DEC-14 - 09-DEC-14. [Details]
	(2014)	2nd Irish Linear Algebra and Matrix Theory Meeting, Niall Madden (2014) Linear solvers for a singularly perturbed problem. [Invited Oral Presentation], 2nd Irish Linear Algebra and Matrix Theory Meeting, University College Dublin , 29-AUG-14 - 29-AUG-14. [Details]
	(2014)	11th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, Niall Madden (2014) A first-order system Petrov-Galerkin discretization for solving a reaction-diffusion problem. [Oral Presentation], 11th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, Novi Sad, Serbia , 20-MAR-14 - 21-MAR-14. [Details]
	(2014)	Irish Mathematical Student Association Annual Meeting, Niall Madden (2014) An introduction to the numerical solution of singularly perturbed differential equations. [Invited Lecture], Irish Mathematical Student Association Annual Meeting, NUI Maynooth , 07-MAR-14 - 09-MAR-14. [Details]
	(2014)	Singularly perturbed differential equations are difficult to solve numerically, except when they are not, Niall Madden (2014) The annual meeting of SIAM UKIE, the UK & Republic of Ireland section of SIAM. [Invited Oral Presentation], Singularly perturbed differential equations are difficult to solve numerically, except when they are not, University College London , 09-JAN-14 - 09-JAN-14. [Details]
	(2013)	25th Biennial Numerical Analysis Conference, Niall Madden (2013) A boundary layer preconditioner for a singularly perturbed problem. [Oral Presentation], 25th Biennial Numerical Analysis Conference, Strathclyde, UK , 25-JUN-13 - 26-JUL-13. [Details]
	(2013)	10th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, Niall Madden (2013) Robust solution of singularly perturbed problems using multigrid methods. [Oral Presentation], 10th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, Larnaca, Cyprus , 23-MAY-13 - 24-MAY-13. [Details]
	(2012)	1st Irish Linear Algebra and Matrix Theory Meeting, Niall Madden and Rachel Quinlan (2012) 1st Irish Linear Algebra and Matrix Theory Meeting. [Conference Organising Committee Member], 1st Irish Linear Algebra and Matrix Theory Meeting, NUI Galway , 08-DEC-12 - 08-DEC-12. [Details]
	(2012)	6th de Brún Workshop on Linear Algebra and Matrix Theory, Niall Madden and Rachel Quinlan (2012) 6th de Brún Workshop on Linear Algebra and Matrix Theory. [Conference Organising Committee Member], 6th de Brún Workshop on Linear Algebra and Matrix Theory, NUI Galway , 03-DEC-12 - 07-DEC-12. [Details]
	(2012)	School of Mathematics, Statistics and Applied Mathematics Research Day, Madden, N; Stynes M. (2012) Post-processing of one-dimensional finite element solutions to convection-diffusion problems. [Invited Oral Presentation], School of Mathematics, Statistics and Applied Mathematics Research Day, NUI Galway , 02-APR-12 - 02-APR-12. [Details]
	(2012)	BAIL: International Conference on Boundary and Interior Layers-- Computational and Asymptotic Methods, Niall Madden (2012) A Schwarz-type method for a coupled system of singularly perturbed problems. [Oral Presentation], BAIL: International Conference on Boundary and Interior Layers-- Computational and Asymptotic Methods, POSTECH, Korea , 06-FEB-12 - 10-FEB-12. [Details]
	(2011)	Numerical Analysis for Singularly Perturbed Problems, Niall Madden (2011) Linear Solvers for Singularly Perturbed Problems. [Oral Presentation], Numerical Analysis for Singularly Perturbed Problems, TU Dresden , 16-NOV-11 - 18-NOV-11. [Details]
	(2011)	ICIAM: 7th International Congress on Industrial and Applied Mathematics, Niall Madden and Naresh Chadha (2011) Improved Numerical Modelling of Dispersion of Pollutants in Tidal Regions. [Oral Presentation], ICIAM: 7th International Congress on Industrial and Applied Mathematics, Vancouver , 18-JUL-11 - 22-JUL-11. [Details]
	(2011)	Numerical Methods for Incompressible Fluid Flow, Niall Madden and Naresh Chadha (2011) Numerical Simulation of an Advection Diffusion Problem in Tidal Regions. [Invited Oral Presentation], Numerical Methods for Incompressible Fluid Flow, University of British Columbia , 14-JUL-11 - 16-JUL-11. [Details]
	(2010)	Numerical Solutions of Partial Differential Equations: Novel Discretization Techniques, Niall Madden (2010) Computational aspects of a two-scale finite element method for singularly perturbed problem. [Poster Presentation], Numerical Solutions of Partial Differential Equations: Novel Discretization Techniques, University of Minnesota , 01-NOV-10 - 05-NOV-10. [Details]
	(2010)	Computing with Uncertainty: Mathematical Modeling, Numerical Approximation and Large Scale Optimization of Complex Systems, Niall Madden (2010) Derivation of DBN Structure from Expert Knowledge in the Form of Systems of ODEs. [Poster Presentation], Computing with Uncertainty: Mathematical Modeling, Numerical Approximation and Large Scale Optimization of Complex Systems, University of Minnesota , 18-OCT-10 - 22-OCT-10. [Details]
	(2010)	BAIL - Boundary and Interior Layers, Mondol, K.K; Madden N. (2010) A computational study of a fluid flow problem featuring an interior layer. [Oral Presentation], BAIL - Boundary and Interior Layers, Zaragoza, Spain , 05-JUL-10 - 09-JUL-10. [Details]

Conference Paper

	Year	Publication
	(2006)	A parameter-robust numerical method for a coupled system of two dimensional reaction-diffusion equations. 4th Conference on Finite Difference Methods: Theory and Applications. Madden, N., Bruce, R., Kellogg, B., Stynes, M. (2006) A parameter-robust numerical method for a coupled system of two dimensional reaction-diffusion equations. 4th Conference on Finite Difference Methods: Theory and Applications. Lozenetz, Bulgaria: Conference Paper [Details]
	(2005)	Model free endurance markers based on the second derivative of blood lactate curves. 20TH IWSM, STATISTICAL SOLUTIONS TO MODERN PROBLEMS. Newell, J., Einbeck, J., Madden, N., McMillan, K. (2005) Model free endurance markers based on the second derivative of blood lactate curves. 20TH IWSM, STATISTICAL SOLUTIONS TO MODERN PROBLEMS. Swiss-Grand Resort & Spa on Bondi Beach in Sydney: Conference Paper [Details]
	(2004)	On the application of robust numerical methods to a complete flow wave-current model. Boundary and Interior Layers ONERA. Niall Madden, Martin Stynes, and Gareth Thomas (2004) On the application of robust numerical methods to a complete flow wave-current model. Boundary and Interior Layers ONERA. Conference Paper [ARAN Link] [Details]
	(2004)	On equidistribution for reaction-diffusion problems. Workshop on problems with boundary-layer phenomena. Kopteva, N., Madden, N., Stynes, M. (2004) On equidistribution for reaction-diffusion problems. Workshop on problems with boundary-layer phenomena. University of Limerick: Conference Paper [Details]

Presentation

	Year	Publication
	(2009)	An alternating direction method for a singularly perturbed reaction-diffusion problem. 23rd Biennial Conference on Numerical Analysis. Madden, N., Linss, T. (2009) An alternating direction method for a singularly perturbed reaction-diffusion problem. 23rd Biennial Conference on Numerical Analysis. University of Strathclyde: Presentation [Details]

Unpublished work

	Year	Publication
	(2012)	Robust solution of singularly perturbed problems using multigrid methods: analysis and results in one and two dimensions. MacLachlan, Scott; Madden, Niall (2012) Robust solution of singularly perturbed problems using multigrid methods: analysis and results in one and two dimensions. Unpublished work [ARAN Link] [Details]

Working Paper

	Year	Publication
	(2007)	On the numerical solution of a system of M singularly perturbed reaction-diffusion equations in two dimension. 6th Annual Workshop on Numerical Methods for Problems with Layer Phenomena. Madden, N., Stynes, M. (2007) On the numerical solution of a system of M singularly perturbed reaction-diffusion equations in two dimension. 6th Annual Workshop on Numerical Methods for Problems with Layer Phenomena. University of Limerick: Working Paper [Details]

Professional Associations

Association	Function	From / To
IMS: Irish Mathematical Society		01-SEP-00 /
International Linear Algebra Society	http://www.ilasic.org/	01-SEP-14 /
SIAM: Society for Industrial and Applied Mathematics		01-APR-00 /

Committees

Committee	Function	From / To
College of Science Equality, Diversity and Inclusion	Member	01-JUL-18 /
Equality and Diversity Committee, School of Mathematical and Statistical Sciences.	Chair	01-MAR-17 /
Learning, Teaching and Assessment, School of Mathematics, Statistics and Applied Mathematics	Chair	01-SEP-16 / 31-AUG-18
NUI Galway SIAM Student Chapter	Faculty Advisor	01-SEP-14 /
Athena SWAN Institutional Self-Assessment Team	member	01-OCT-14 /
Board of the Modular Programme in Science and Technology Studies	NUI Galway Academic Director	01-NOV-13 / 01-SEP-17
Stokes Cluster for Applied Mathematics Research	Chair	01-SEP-14 / 31-AUG-17
Programme Board, B.Sc in Science - Computer Science Pathway	Co-director	01-SEP-12 /
NUI Galway Gender Equality Task Force	member	01-MAY-15 / 31-MAY-16

Education

Year	Institution	Qualification	Subject
2000	National University of Ireland, Cork	PhD	Mathematics
1996	University College Cork	Msc	Mathematics
1994	University College Galway	BSc	Computing Studies and Mathematical Science

Reviews

	Journal	Role
	Numerical Algorithms	Editoral Board
	International Journal Of Computer Mathematics	Reviewer
	Computational & Applied Mathematics	Reviewer
	Lecture Notes In Computational Science And Engineering	Reviewer
	Computational Methods In Applied Mathematics	Reviewer
	Applied Numerical Mathematics	Reviewer
	International Journal Of Computer Mathematics	Reviewer
	Journal Of Difference Equations And Applications	Reviewer
	Journal Of Applied Mathematics And Computing	Reviewer
	Journal Of Scientific Computing	Reviewer
	Applied Mathematics And Computation	Reviewer
	Advances In Computational Mathematics	Reviewer
	International Journal Of Numerical Analysis And Modeling	Reviewer
	Numerical Algorithms	Reviewer
	Numerical Methods For Partial Differential Equations	Reviewer
	Ima Journal Of Numerical Analysis	Reviewer
	Lecture Notes In Computer Science	Reviewer
	Bit Numerical Mathematics	Reviewer
	Journal Of Applied Mathematics And Computing	Reviewer

Other Activities

	Description
	Faculty adviser for the NUI Galway Student Chapter of SIAM

Teaching Interests

Mathematics, particularly computational methods and development of algorithms.

Recent Postgraduate Students

Graduation	Name	Degree	Primary Supervisor
2015	Nhan Anh Thai	PhD	Y
2016	Stephen Russell	PhD	Y
2013	Stephen Russell	MASTERS OF SCIENCE	Y
2011	Nhan Anh Thai	MASTERS OF SCIENCE	Y
2009	Meghan Stephens (Mathematics)	PhD	Y

Modules Taught

Term/Year	Module Title	Module Code	Subject / Desc
2016/2017	Numerical Analysis 1	MA385	Analysis of numerical methods for nonlinear problems, IVPs, and linear systems
2016/2017	Scientific Computing	CS319	Sicentific software development in C++
2016/2017	Numerical Analysis 2	MA378	Polynomial interpolation; splines; quadrature; finite element methods.
2016/2017	Discrete Mathematics	MA284	Enumerative combinatorics and graph theory

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Dr Niall Madden

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Mathematical and Statistical Sciences

Dr Niall Madden

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Peer Reviewed Journals

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Conference Publications

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