Photo of  Niall from 2018

Dr Niall Madden

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

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.


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


  • 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. (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.
  • 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. arXiv:
  • 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:

Full list


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.


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.



Postal address:

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