Niall Madden (personal webpage)

Dr Niall Madden

Senior Lecturer (Associate Professor)
School of Mathematical and Statistical Sciences,
University of Galway, Ireland.

ORCID: ORCID iD
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orcid.org/0000-0002-4327-4234
University of Galway Profile and Google Scholar profile

About me

I am a Senior Lecturer (Associate Professor) in Mathematics, in the School of Mathematical and Statistical Sciences, at the University of Galway (formerly called NUI Galway). My research is in the area of numerical analysis, particularly finite element and finite difference methods for differential equations. My teaching covers a broad range of undergraduate and graduate modules in theoretical and computational mathematics. I contribute to the community at University of Galway, and broader mathematical community, in various ways including, at present, as Head of Mathematics, May 2023-May 2025 (excluding July- December 2023). I'm an associate editor for Numerical Algorithms (Springer), and I was one of the local of ILAS 2022: the 24th Conference of the International Linear Algebra Society which was held here in Galway in June 2022.

Research

Finite Elements ◉ Finite Differences ○ PDEs ◌ Singularly Perturbed Problems ◍ Boundary and Interior Layers ◎ Numerical Linear Algebra ● Preconditioners ◐ Sparse Grids ◑ Mesh Adaptivity ◒ Software

I work in Numerical Analysis and Computational Mathematics. I am particularly interested in the design and analysis of novel discretizations and/or linear solvers for singularly perturbed differential equations, and in the application of novel methods in numerical modelling.

Affiliations: The de Brún Centre for Mathematics, The Stokes Applied Mathematics Cluster, and the The Ryan Institute

Publications

Naresh M. Chadha, Nanda Poddar, Niall Madden, Kajal Kumar Mondal. Numerical Modelling of Dispersion of Suspended Particles in a Turbulent Open Channel Flow: A Fitted Operator Approach. Emerging Trends in Mathematical Sciences and Computing. 2024. doi.org/10.52305/VTTP1252".
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).
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
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
Scott P. MacLachlan, Niall Madden, Thái Anh Nhan. A Boundary-Layer Preconditioner for Singularly Perturbed Convection Diffusion. SIAM J. Matrix Anal. Appl. 43 (2022), no. 2, 561–583. https://doi.org/10.1137/21M1443297. arXiv: arxiv.org/abs/2108.13468.
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.
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: osf.io/dpexh/.

Full list

Presentations

[Conference] BAIL 2024: International Conference on Boundary and Interior Layers. A Coruña, Spain. 10-14 June, 2024.
[Seminar] Mathematical Sciences Seminar Series, University College Cork. 18 April 2024
[Colloquium] Department of Mathematics and Statistics, Memorial University of Newfoundland. 15 October, 2023.
[Workshop] New Directions in Applied Linear Algebra, Banff, 27 Aug - 1 Sep, 2023.
[Conference] 29th Biennial Numerical Analysis Conference Strathclyde, 27-30 June 2023.
[Workshop] 19th Workshop on Numerical Methods for Problems with Layer Phenomena, 25-27 May 2023, Prague.
[Conference] 2022 Annual Meeting of the Irish Mathematical Society,. 1-2 September, TU Dublin
[Conference] 24th Conference of the International Linear Algebra Society, 20-24 June, 2022, NUI Galway. (Local co-organiser of the conference, organised a mini-symposium on Numerical linear algebra for PDEs, and gave a talk.
[Workshop] 18th Workshop on Numerical Methods for Problems with Layer Phenomena. 24-26 March, 2022, Hagen.

Full list

Team (past and present)

Róisín Hill. PhD 2022. Funding: Irish Research Council.
Faiza Alssaedi. PhD 2021. Funding: NUI Galway and Government of Libya.
Thái Anh Nhan PhD 2015, and MSc 2011. Funding: Irish Research Council, and Science Foundation Ireland.
Stephen Russell. PhD 2016, and MSc 2012. Funding: NUI Galway.

Teaching

Academic Year 2023/2024

Semester 1

On sabbatical

Semester 2

MA378: Numerical Analysis 2
CS319: Scientific Computing

[My teaching contributions in previous years.]

Contributions and Leadership

May 2023-Apr 2025: Head of Discipline Mathematics, School of Mathematical and Statistical Sciences, University of Galway.
Jan-Jun 2022: Head of Discipline Mathematics (interim), School of Maths, University of Galway.
2016-present: Associate Editor for Numerical Algorithms (Springer).
May 2019-Jun 2023: Director of Equality Diversity and Inclusion, School of Mathematical and Statistical Sciences, and member of the EDI committee of the College of Science and Engineering.
University of Galway SIAM Chapter: Faculty Advisor.

News

I'm organising the 21th Workshop on Numerical Methods for Problems with Layer Phenomena at University of Galway, 24-25 of April, 2025.
[Jan 2024] I'm back at University of Galway, and again heading the Mathematics discipline, as well as teaching MA378 (Numerical Analysis 2) and CS319 (Scientific Computing) in Semester 2 of 2023/2024.
[Sep 2023] For the Fall semester of 2023/2024, I am on sabbatical, and am a visiting scientist at the Department of Mathematics and Statistics, Memorial University, St. John's, Newfoundland.
[Aug 2023] I participated in New Directions in Applied Linear Algebra BIRS, Banff.
[June 2023] For several years, until June 2023, I chaired the School of Mathematical and Statistical Science's Equality, Diversity and Inclusion committee.
[June 2022] I am one of the local organisers of ILAS 2022: the 24th Conference of the International Linear Algebra Society here in Galway in June 2022 (postponed from 2020). As part of the conference, I am organising a mini-symposium on Numerical Linear Algebra for PDEs.
[Sep 2021] I chaired our School's Self-Assessment Team (SAT) which submitted a successful application for an Athena SWAN Bronze Award.
[Apr 2020] I participated in the 17th Workshop on Numerical Methods for Problems with Layer Phenomena Limerick, 6-7 April, which is dediated to the memory of the late Piet Hemker.

Contact

Email: Niall.Madden@UniversityOfGalway.ie
Office: ADB-1013, Arás de Brún
Phone: (353) 91 493803 (office)

Postal address:

School of Mathematical and Statistical Sciences
Arás de Brún
University of Galway
University Rd.
Galway
Ireland H91 TK33