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Mathematics, Statistics & Applied Mathematics
Dr Niall Madden
BSc, MSc, PhD
Contact Details
Lecturer Above The Bar

ADB1013
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics
T: 091493803
E: Niall.Madden@NUIGalway.ie
W: http://www.maths.nuigalway.ie/~niall

ADB1013
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics
T: 091493803
E: Niall.Madden@NUIGalway.ie
W: http://www.maths.nuigalway.ie/~niall
Biography
Research Interests
Research Projects
Project  Start Date  End Date  

IRCSET EMBARK POSTGRAD MULTIGRID METHODS FOR SINGULARLY PERTURBED PROBLEMS (ANH THAI NHAN) RS/2011/179 NIALL MADDEN  01SEP11  31AUG15  
SFI RFP NUMERICAL MODELLING OF ADVECTIONDIFFUSION  01SEP08  01NOV12  
IRCSET EMBARK 04 MEGHAN STEPHENS MADDEN  01SEP04  30APR09  
MF2005 FAST PARALLEL SOLVERS N MADDEN  01NOV05  19JUN09  
MF2003 MF 89 03 M NIALL MADDEN  01JAN04  28FEB07 
Peer Reviewed Journals
Year  Publication  

(2016)  'An optimal timestepping algorithm for unsteady advectiondiffusion problems'
Chadha, NM,Madden, N (2016) 'An optimal timestepping algorithm for unsteady advectiondiffusion problems'. Journal Of Computational And Applied Mathematics, 294 :5777 [DOI] [Details] 

(2016)  'A C1conforming hp Finite Element Method for fourth order singularly perturbed boundary value problems'
P. Panaseti, A. Zouvani, N. Madden and C. Xenophontos (2016) 'A C1conforming hp Finite Element Method for fourth order singularly perturbed boundary value problems'. Applied Numerical Mathematics, 104 :8197 [DOI] [Details] 

(2015)  'A multiscale sparse grid finite element method for a twodimensional singularly perturbed reactiondiffusion problem'
Madden, N,Russell, S (2015) 'A multiscale sparse grid finite element method for a twodimensional singularly perturbed reactiondiffusion problem'. Advances In Computational Mathematics, 41 :9871014 [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):22252254 [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 :323342 [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'. Lecture Notes In Computer Science, 8236 :532539 [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):1123 [ARAN Link] [Details] 

(2011)  'A twoweight scheme for a timedependent advectiondiffusion problem'
Naresh M. Chadha and Niall Madden (2011) 'A twoweight scheme for a timedependent advectiondiffusion problem'. Lecture Notes In Computational Science And Engineering, 85 :99108 [DOI] [ARAN Link] [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'. Lecture Notes In Computational Science And Engineering, 81 :177185 [ARAN Link] [Details] 

(2010)  'ANALYSIS OF AN ALTERNATING DIRECTION METHOD APPLIED TO SINGULARLY PERTURBED REACTIONDIFFUSION PROBLEMS'
Linss, T,Madden, N (2010) 'ANALYSIS OF AN ALTERNATING DIRECTION METHOD APPLIED TO SINGULARLY PERTURBED REACTIONDIFFUSION PROBLEMS'. International Journal Of Numerical Analysis And Modeling, 7 :507519 [Details] 

(2009)  'A ParameterUniform Schwarz Method for a Coupled System of Reaction Diffusion Equations'
Stephens, M., Madden, N. (2009) 'A ParameterUniform Schwarz Method for a Coupled System of Reaction Diffusion Equations'. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 230 (2):360370 [DOI] [Details] 

(2009)  'A twoscale sparse grid method for a singularly perturbed reactiondiffusion problem in two dimensions'
Liu, F,Madden, N,Stynes, M,Zhou, AH (2009) 'A twoscale sparse grid method for a singularly perturbed reactiondiffusion problem in two dimensions'. Ima Journal Of Numerical Analysis, 29 :9861007 [DOI] [Details] 

(2009)  'A Schwarz technique for a system of reaction diffusion equations with differing parameters'
Stephens, M., Madden, N. (2009) 'A Schwarz technique for a system of reaction diffusion equations with differing parameters'. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING, 69 :247255 [Details] 

(2009)  'Layeradapted meshes for a linear system of coupled singularly perturbed reactiondiffusion problems'
Linss, T,Madden, N (2009) 'Layeradapted meshes for a linear system of coupled singularly perturbed reactiondiffusion problems'. Ima Journal Of Numerical Analysis, 29 :109125 [DOI] [Details] 

(2008)  'A parameterrobust numerical method for a system of reactiondiffusion equations in two dimensions'
Kellogg, RB,Madden, N,Stynes, M (2008) 'A parameterrobust numerical method for a system of reactiondiffusion equations in two dimensions'. Numerical Methods For Partial Differential Equations, 24 :312334 [DOI] [Details] 

(2007)  'Parameter uniform approximations for timedependent reactiondiffusion problems'
Linss, T,Madden, N (2007) 'Parameter uniform approximations for timedependent reactiondiffusion problems'. Numerical Methods For Partial Differential Equations, 23 :12901300 [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 reactiondiffusion problems in one dimension'
Kopteva, N,Madden, N,Stynes, M (2005) 'Grid equidistribution for reactiondiffusion problems in one dimension'. Numerical Algorithms, 40 :305322 [DOI] [Details] 

(2004)  'Accurate solution of a system of coupled singularly perturbed reactiondiffusion equations'
Linss, T,Madden, N (2004) 'Accurate solution of a system of coupled singularly perturbed reactiondiffusion equations'. Computing, 73 :121133 [DOI] [Details] 

(2004)  'A finite element analysis of a coupled system of singularly perturbed reactiondiffusion equations'
Linss, T,Madden, N (2004) 'A finite element analysis of a coupled system of singularly perturbed reactiondiffusion equations'. Applied Mathematics And Computation, 148 :869880 [DOI] [Details] 

(2003)  'An improved error estimate for a numerical method for a system of coupled singularly perturbed reactiondiffusion equations'
Linss, Torsten and Madden, Niall (2003) 'An improved error estimate for a numerical method for a system of coupled singularly perturbed reactiondiffusion equations'. Comput. Methods Appl. Math, 3 (3):417423 [DOI] [Details] 

(2003)  'An improved estimate for a numerical method for a system of coupled singularly perturbed reactiondiffusion equations'
Linss, T., Madden, N. (2003) 'An improved estimate for a numerical method for a system of coupled singularly perturbed reactiondiffusion equations'. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 3 (3):417423 [Details] 

(2003)  'A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reactiondiffusion problems'
Madden, N,Stynes, M (2003) 'A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reactiondiffusion problems'. Ima Journal Of Numerical Analysis, 23 :627644 [Details] 

(1997)  'Efficient generation of oriented meshes for solving convectiondiffusion problems'
Madden, N,Stynes, M (1997) 'Efficient generation of oriented meshes for solving convectiondiffusion problems'. International Journal For Numerical Methods In Engineering, 40 :565576 [Details] 

(1996)  'Linear enhancements of the streamline diffusion method for convectiondiffusion problems'
Madden, N,Stynes, M (1996) 'Linear enhancements of the streamline diffusion method for convectiondiffusion problems'. Computers & Mathematics With Applications, 32 :2942 [Details] 
Book Chapters
Year  Publication  

(2011)  'Improved mathematical and numerical modelling of dispersion of a solute from a continuous source'
Madden, Niall and Mondal, Kajal Kumar (2011) 'Improved mathematical and numerical modelling of dispersion of a solute from a continuous source' In: Springer, Heidelberg. [Details] 

(2011)  'A twoweight scheme for a timedependent advectiondiffusion problem'
Chadha, Naresh M. and Madden, Niall (2011) 'A twoweight scheme for a timedependent advectiondiffusion problem' In: Springer, Heidelberg. [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: Springer, Berlin. [Details] 
Conference Publications
Year  Publication  

(2012)  APPLICATIONS OF MATHEMATICS 2012
Niall Madden and Martin Stynes (2012) A curious property of oscillatory FEM solutions of onedimensional convectiondiffusion problems . In: J. Brandts, J. Chleboun, S. Korotov, K. Segeth, J. Šístek & T. Vejchodský eds. APPLICATIONS OF MATHEMATICS 2012 Prague, , 02MAY12  05MAY12 , pp.188196 [Details] 

(2011)  Proc. 13th Conference on Artificial Intelligence in Medicine
Catherine G. Enright, Michael G. Madden, Niall Madden, and John G. Laffey (2011) Clinical Time Series Data Analysis Using Mathematical Models and DBNs Proc. 13th Conference on Artificial Intelligence in Medicine Slovenia, [Details] 

(2011)  AIME
Catherine G. Enright and Michael G. Madden and Niall Madden and John G. Laffey (2011) Clinical Time Series Data Analysis Using Mathematical Models and DBNs . In: Mor Peleg and Nada Lavrac and Carlo Combi eds. AIME , pp.159168 [Details] 

(2010)  Proceedings of BIOSIGNALS2010, Part of the 3rd International Joint Conference on Biomedical Engineering Systems and Technologies
Catherine G. Enright & Michael G. Madden (NUI Galway), Stuart J. Russell & Norm Aleks (UC Berkeley), Geoffrey Manley (UCSF), John Laffey (NUI Galway), Brian Harte & Anne Mulvey (University Hospital Galway), Niall Madden (NUI Galway) (2010) Modelling Glycaemia in ICU Patients: A Dynamic Bayesian Network Approach Proceedings of BIOSIGNALS2010, Part of the 3rd International Joint Conference on Biomedical Engineering Systems and Technologies Valencia, Spain, [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  

(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 , 09JAN14  09JAN14. [Details] 

(2014)  11th Annual Workshop on Numerical Methods for Problems with Layer Phenomena,
Niall Madden (2014) firstorder system PetrovGalerkin discretization for solving a reactiondiffusion problem. [Oral Presentation], 11th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, Novi Sad, Serbia , 20MAR14  21MAR14. [Details] 

(2014)  Seminar,
Niall Madden (2014) Sparse grid finite element methods for a twodimensional reactiondiffusion problem. [Invited Lecture], Seminar, TU Dresden , 29APR14  29APR14. [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 , 07MAR14  09MAR14. [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 , 25JUN13  26JUL13. [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 , 23MAY13  24MAY13. [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 , 03DEC12  07DEC12. [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 , 08DEC12  08DEC12. [Details] 

(2012)  BAIL: International Conference on Boundary and Interior Layers Computational and Asymptotic Methods,
Niall Madden (2012) A Schwarztype 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 , 06FEB12  10FEB12. [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 , 16NOV11  18NOV11. [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 , 18JUL11  22JUL11. [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 , 14JUL11  16JUL11. [Details] 
Conference Paper
Year  Publication  

(2006)  A parameterrobust numerical method for a coupled system of two dimensional reactiondiffusion equations. 4th Conference on Finite Difference Methods: Theory and Applications.
Madden, N., Bruce, R., Kellogg, B., Stynes, M. (2006) A parameterrobust numerical method for a coupled system of two dimensional reactiondiffusion 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. SwissGrand Resort & Spa on Bondi Beach in Sydney: Conference Paper [Details] 

(2004)  On the application of robust numerical methods to a complete flow wavecurrent 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 wavecurrent model. Boundary and Interior Layers ONERA. Conference Paper [ARAN Link] [Details] 

(2004)  On equidistribution for reactiondiffusion problems. Workshop on problems with boundarylayer phenomena.
Kopteva, N., Madden, N., Stynes, M. (2004) On equidistribution for reactiondiffusion problems. Workshop on problems with boundarylayer phenomena. University of Limerick: Conference Paper [Details] 
Presentation
Year  Publication  

(2009)  An alternating direction method for a singularly perturbed reactiondiffusion problem. 23rd Biennial Conference on Numerical Analysis.
Madden, N., Linss, T. (2009) An alternating direction method for a singularly perturbed reactiondiffusion 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 reactiondiffusion 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 reactiondiffusion 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  01SEP00 /  
Association for Women in Mathematics (AWM)  https://sites.google.com/site/awmmath/home  /  
International Linear Algebra Society  http://www.ilasic.org/  /  
SIAM: Society for Industrial and Applied Mathematics  01APR00 / 
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 
Other Activities
Description  

Faculty adviser for the NUI Galway Student Chapter of SIAM 

Academic Director of Modular Programme in Science and Technology Studies 

Director of the NUI Galway Bachelor Of Science: Computer Science programme. 

Member of the NUI Galway Athena SWAN SelfAppraisal Team. 
Teaching Interests
Recent Postgraduate Students
Graduation  Name  Degree  Primary Supervisor  

2015  Nhan Anh Thai  PhD  Y  
2013  Stephen Russell  MASTERS OF SCIENCE  Y  
2011  Nhan Anh Thai  MASTERS OF SCIENCE  Y  
2009  Meghan Stephens (Mathematics)  PhD  Y 
Current Postgraduate Students (Research)
Student  Degree Type  Type  

Stephen Russell  Doctorate  Structured PhD (Science)  Supervisor  
Faiza Alssaedi  Doctorate  Structured PhD (Science)  Supervisor 
Modules Taught
Term/Year  Module Title  Module Code  Subject / Desc  

20152016  Numerical Analysis 2  MA378  Approximation theory, numerical integration, and finiteelement methods  
20152016  Numerical Analysis  MA385  Introduction to the numerical solution of problems in linear algebra and differential equations  
20152016  Scientific Computing  CS319  The solution of problems in by computational techneiques (in C++)  
20152016  Discrete Mathematics  MA284  Combinatorics and Graph Theory 