Alan Hegarty

Alan Hegarty serves as Associate Professor in the Department of Mathematics and Statistics at the University of Limerick, concurrently holding membership in the Centre for Research Training in Foundations of Data Science and the Mathematics Applications Consortium for Science and Industry (MACSI), which drives industry-academic partnerships in mathematical modeling.

His academic credentials include a B.A. in Mathematics from Dublin University (1979), M.Sc. from Dublin (1982), and Ph.D. from Dublin (1986), establishing foundational expertise in computational mathematics.

Dr. Hegarty's research specializes in numerical solutions for singular perturbation problems, with pioneering work in adaptive mesh methods and moving mesh techniques to resolve boundary layer phenomena. His methodologies address critical challenges in convection-diffusion systems and elliptic equations where conventional numerical approaches fail, employing specialized finite difference and finite element schemes on layer-adapted meshes to ensure stability and accuracy across thin transitional regions.

Analysis of his 2020-2024 publications reveals consistent advancement in algorithmic precision for singularly perturbed systems, particularly through higher-order methods for elliptic problems and extensions to smooth domains. This trajectory demonstrates evolving sophistication in handling characteristic boundary layers and convection-dominated flows, with strong emphasis on achieving uniform convergence through fitted meshes and Shishkin-type adaptations.

No scientific awards were documented in the provided materials.

He actively supervises PhD candidates as indicated by his recruitment status and 52 cumulative research outputs, with funding channeled through MACSI's industry collaborations and the Centre for Research Training. These frameworks support applied mathematical research addressing real-world industrial challenges through consortium-based projects.

Within MACSI and the Centre for Research Training, Hegarty contributes to interdisciplinary teams developing data-driven solutions where singular perturbation methods interface with modern data science applications, particularly in fluid dynamics modeling and industrial process optimization.