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Computational Mathematics and High-Performance Computing

Computational Mathematics and High-Performance Computing

Computational mathematics involves the application of computers to mathematics.  At a fundamental level, computational mathematics is about the development and analysis of algorithms.

An algorithm is a process or set of rules to be followed in calculations or other problem-solving operations.  Because of the step-like and rule-based nature of algorithms, they are readily implemented on computers, which gives computational mathematics great power and scope.  Computer algorithms are to be found in all areas of modern life, from wireless communication to internet search.  

Computational mathematics in the School of Mathematics and Statistics has many focal points.  Some of our researchers are involved in the fundamental mathematical theories that underpin wireless communication and internet cryptography, while others are involved in the development of simulation algorithms, which are computer models of complex phenomena in Mathematical Biology, Fluid Mechanics, and General Relativity.  What unites these different researchers is the focus on developing and understanding the relevant algorithms form a first-principles approach, as well as the implementation of these algorithms on high-performance computer platforms, such as (opens in a new window)ICHEC, (opens in a new window)ARCHER, and (opens in a new window)PRACE.  The machines used by our researchers frequently feature in the world’s top 500 supercomputers on (opens in a new window)top500.org


(opens in a new window)Dr Graham Benham
Research Interests:
Environmental fluid dynamics, flow in porous media, carbon capture and storage, water waves, wave-body interactions, mathematics of rowing and cycling, industrial mathematics

Assoc Prof Miguel Bustamante 
Research Interests: Fluid Dynamics and Turbulence, Nonlinear PDEs, Hamiltonian Methods and Integrable Systems

(opens in a new window)Dr Áine Byrne
Research Interests:  Dynamical systems, mathematical neuroscience, biological systems and bifurcation theory

Dr Michelle Carey
Research Interests: Functional Data Analysis, Differential Equations, Financial instruments, Biological systems and Climatology

Prof Frederic Dias
Research Interests: Partial Differential Equations, Free-surface Flows, Wave energy

(opens in a new window)Dr James Herterich
Research Interests: oceanographic and geophysical flows, fluid-structure interaction, industrial mathematics

(opens in a new window)Assoc Prof Marcus Greferath
Research Interests: Discrete mathematics, abstract algebra, geometry, computer science

Prof Gary McGuire
Research Interests: Finite Mathematics, Coding, Cryptography, Computation, Algebraic Number Theory, Algebraic Geometry

Dr Lennon Ó'Náraigh
Research Interests: Two-Phase Flows, Turbulence, Stability Theory, High-Performance Computing

Prof Adrian Ottewill
Research Interests: ‌General relativity, Quantum field theory in curved space-time

Dr Conor Sweeeny
Research Interests‌: Probabilistic forecasting, weather and climate modelling, renewable energy

Dr Barry Wardell
Research Interests: General Relativity, Gravitational Waves, Black Holes, Cosmic Strings, High-performance Computing

Group Contact (Email): (opens in a new window)Assoc Prof Miguel Bustamante

UCD School of Mathematics and Statistics

Room S3.04, Science Centre South, University College Dublin, Belfield, Dublin 4, Ireland.