Dr. Alan Hegarty
Biography
B.A. (Mathematics) Dublin University 1979 M.Sc., Dublin, 1982 Ph.D. Dublin, 1986Research Interests
Numerical solution of singular perturbation problems. Special mesh methods. Adaptive and moving mesh methods.Peer Reviewed Journals
Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain
Hegarty, AF,O'Riordan, E (2017) Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain. Advances In Computational Mathematics :885-909
A shunted model of renal inner medulla with pre-bend transitions: Comparison with multi-nephron models.
Gonzalez M, Thomas SR, Hegarty AF (2009) A shunted model of renal inner medulla with pre-bend transitions: Comparison with multi-nephron models.. Faseb Journal :818.7-818.7-818.7-818.7
Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient
Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (2004) Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient. Mathematical And Computer Modelling :1375-1392
Singularly perturbed convection-diffusion problems with boundary and weak interior layers
Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (2004) Singularly perturbed convection-diffusion problems with boundary and weak interior layers. Journal Of Computational And Applied Mathematics :133-151
Numerical techniques for flow problems with singularities
Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (2003) Numerical techniques for flow problems with singularities. International Journal For Numerical Methods In Fluids :915-936
Computing realistic Reynolds-uniform error bound's for discrete derivatives of flow velocities in the boundary layer for Prandtl's problem
Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (2003) Computing realistic Reynolds-uniform error bound's for discrete derivatives of flow velocities in the boundary layer for Prandtl's problem. International Journal For Numerical Methods In Fluids :895-902
A note on fitted operator methods for a laminar jet problem
Ansari, AR; Hegarty, AF; Shishkin, GI (2003) A note on fitted operator methods for a laminar jet problem. Applied Numerical Mathematics :353-365
Numerical solution of a convection diffusion problem with Robin boundary conditions
Ansari, AR; Hegarty, AF (2003) Numerical solution of a convection diffusion problem with Robin boundary conditions. Journal Of Computational And Applied Mathematics :221-238
A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes
Ansari, AR; Hegarty, AF (2003) A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes. Computer Methods In Applied Mechanics And Engineering :3673-3687
Parameter-uniform numerical methods for a laminar jet problem
Ansari, AR; Hegarty, AF; Shishkin, GI (2003) Parameter-uniform numerical methods for a laminar jet problem. International Journal For Numerical Methods In Fluids :937-951
Numerical solution of a rimming flow problem using a moving mesh method.
Hegarty, AF;O'Brien, SB; Sikwila, S (2003) Numerical solution of a rimming flow problem using a moving mesh method.. Computational Methods In Applied Mathematics :373-386
An experimental technique for computing parameter-uniform error estimates for numerical solutions of singular perturbation problems, with an application to Prandtl's problem at high Reynolds number
Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (2002) An experimental technique for computing parameter-uniform error estimates for numerical solutions of singular perturbation problems, with an application to Prandtl's problem at high Reynolds number. Applied Numerical Mathematics :143-149
On a necessary requirement for re-uniform numerical methods to solve boundary layer equations for flow along a flat plate
Shishkin, GI; Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E (2001) On a necessary requirement for re-uniform numerical methods to solve boundary layer equations for flow along a flat plate. Numerical Analysis And Its Applications :723-731
Parameter-uniform numerical methods for a class of singularly perturbed problems with a Neumann boundary condition
Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (2001) Parameter-uniform numerical methods for a class of singularly perturbed problems with a Neumann boundary condition. Numerical Analysis And Its Applications :292-303
A parameter robust method for a problem with a symmetry boundary layer
Ansari, AR; Hegarty, AF; Shishkin, GI (2001) A parameter robust method for a problem with a symmetry boundary layer. Numerical Analysis And Its Applications :18-26
On a necessary requirement for re-uniform numerical methods to solve boundary layer equations for flow along a flat plate
Shishkin, GI; Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E (2001) On a necessary requirement for re-uniform numerical methods to solve boundary layer equations for flow along a flat plate. Lecture Notes In Computer Science :723-731
Numerical results for advection-convection problems on fitted meshes
Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (1997) Numerical results for advection-convection problems on fitted meshes. Cwi Quarterly :235-289
SPECIAL MESHES FOR FINITE-DIFFERENCE APPROXIMATIONS TO AN ADVECTION-DIFFUSION EQUATION WITH PARABOLIC LAYERS
HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI (1995) SPECIAL MESHES FOR FINITE-DIFFERENCE APPROXIMATIONS TO AN ADVECTION-DIFFUSION EQUATION WITH PARABOLIC LAYERS. Journal Of Computational Physics :47-54
NUMERICAL RESULTS FOR ADVECTION-DOMINATED HEAT-TRANSFER IN A MOVING FLUID WITH A NON-SLIP BOUNDARY-CONDITION
HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI (1995) NUMERICAL RESULTS FOR ADVECTION-DOMINATED HEAT-TRANSFER IN A MOVING FLUID WITH A NON-SLIP BOUNDARY-CONDITION. International Journal Of Numerical Methods For Heat & Fluid Flow :131-140
ON A NOVEL MESH FOR THE REGULAR BOUNDARY-LAYERS ARISING IN ADVECTION-DOMINATED TRANSPORT IN 2 DIMENSIONS
HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI (1995) ON A NOVEL MESH FOR THE REGULAR BOUNDARY-LAYERS ARISING IN ADVECTION-DOMINATED TRANSPORT IN 2 DIMENSIONS. Communications In Numerical Methods In Engineering :435-441
USE OF CENTRAL-DIFFERENCE OPERATORS FOR SOLUTION OF SINGULARLY PERTURBED PROBLEMS
HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI (1994) USE OF CENTRAL-DIFFERENCE OPERATORS FOR SOLUTION OF SINGULARLY PERTURBED PROBLEMS. Communications In Numerical Methods In Engineering :297-302
Special numerical methods for convection-dominated laminar flows at arbitrary Reynolds number.
Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (1994) Special numerical methods for convection-dominated laminar flows at arbitrary Reynolds number.. J. Numerical Mathematics :65-74
A COMPARISON OF UNIFORMLY CONVERGENT DIFFERENCE-SCHEMES FOR 2-DIMENSIONAL CONVECTION DIFFUSION-PROBLEMS
HEGARTY, AF; ORIORDAN, E; STYNES, M (1993) A COMPARISON OF UNIFORMLY CONVERGENT DIFFERENCE-SCHEMES FOR 2-DIMENSIONAL CONVECTION DIFFUSION-PROBLEMS. Journal Of Computational Physics :24-32
Books
Robust Computational Techniques for Boundary Layers
Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (2000) Robust Computational Techniques for Boundary Layers. Boca raton, Florida : Chapman & Hall/CRC
Book Chapters
Key to the computation of the transfer of a substance by convection-diffusion in a laminar fluid.
Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI (1993) Key to the computation of the transfer of a substance by convection-diffusion in a laminar fluid.. Applications of Advanced Computational Methods for Boundary and Interior Layers
Edited Books
Other Journals
Conference Publications
6th International Conference on Boundary and Interior Layers (BAIL VI)
Hegarty A.F., Miller J.J.H., O'Riordan E. and Shishkin G.I.,Menakuru, S.,Ahmed, J.,Larvin, M.,Leeder, P. (2012) 6th International Conference on Boundary and Interior Layers (BAIL VI). British Journal of Surgery :67-68
Lecture Notes in Computational Science and Engineering
Hegarty A.F., Gonzalez M., Thomas S.R. (2009) Lecture Notes in Computational Science and Engineering. :153-161
AIP Conference Proceedings
Gonzalez M.T., Hegarty A.F., Thomas S.R. (2009) AIP Conference Proceedings. :1469-1471
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2
Gonzalez, MT; Hegarty, AF; Thomas, SR (2009) NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2. :1469-1471
BAIL 2006
Hegarty,A.F., Sikwila, S., Shiskin, G.I. (2006) BAIL 2006. :*-*
BAIL 2006
Branley, D., Hegarty, A.F., Purtill, H., Shishkin, G.I. (2006) BAIL 2006. :*-*
Biennial Numerical Analysis Conference
Sikwila, S., Hegarty, A.F. and Shishkin, G.I. (2005) Biennial Numerical Analysis Conference. :*-*
2nd International Conference, Computational Methods in Applied Mathematics
Sikwila, S., Hegarty, A.F. and Shishkin, G.I. (2005) 2nd International Conference, Computational Methods in Applied Mathematics. :*-*
3rd Annual Workshop on Numerical Methods for Problems with Layer Phenomena
Sikwila, S., Hegarty, A.F. and Shishkin, G.I., (2004) 3rd Annual Workshop on Numerical Methods for Problems with Layer Phenomena. :52-58
3rd Annual Workshop on Numerical Methods for Problems with Layer Phenomena
Ansari, A.R., Hegarty, A.F. and Shishkin, G.I. (2004) 3rd Annual Workshop on Numerical Methods for Problems with Layer Phenomena. :70-75
BAIL 2004
Sikwila, S., Hegarty, A.F. and Shishkin, G.I. (2004) BAIL 2004. :*-*
BAIL 2004
Ansari, A.R., Hegarty, A.F. and Shishkin, G.I. (2004) BAIL 2004. :*-*
BAIL 2002
Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O'Riordan, E. and Shishkin. G.I. (2002) BAIL 2002. :115-120
BAIL 2002
Ansari, A.R. and Hegarty, A.F. (2002) BAIL 2002. :43-48
Eccomas Computational Fluid Dynamics Conference
Ansari A.R., Hegarty A.F. and Shishkin G.I. (2001) Eccomas Computational Fluid Dynamics Conference. :*-*
Eccomas Computational Fluid Dynamics Conference
Farrell P.A., Hegarty A.F., Miller J.J.H., O'Riordan E. and Shishkin G.I. (2001) Eccomas Computational Fluid Dynamics Conference. :*-*
International Seminar on Applied Mathematics '91
O'Riordan E., Hegarty A.F. and Stynes M. (1999) International Seminar on Applied Mathematics '91. :91-96
September Meeting, Irish Mathematical Society
Hegarty, A.F. (1995) September Meeting, Irish Mathematical Society. :*-*
Meeting on Singular Perturbation Problems
Hegarty A.F. (1995) Meeting on Singular Perturbation Problems. :*-*
BAIL VI
HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI (1992) BAIL VI. :67-68
13th IMACS World Congress
Farrell P.A. and Hegarty A.F. (1991) 13th IMACS World Congress. :501-502
13th IMACS World Congress
Hegarty A.F., Miller J.J.H., O'Riordan E. and Shishkin G.I. (1991) 13th IMACS World Congress. :503-504
Fourth International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL IV)
Hegarty, A.F. (1986) Fourth International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL IV). :314-319
Second International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL II)
Hegarty, A.F. (1982) Second International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL II). :263-268
First International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL I)
Farrell P.A., Hegarty A.F., Miller J.J.H., O'Reilly M.J. and Sloane A.A. (1980) First International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL I). :275-280
First International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL I)
Hegarty A.F., Miller J.J.H. and O'Riordan E. (1980) First International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL I). :301-305