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Dr. Alan Hegarty

Biography

B.A. (Mathematics) Dublin University 1979 M.Sc., Dublin, 1982 Ph.D. Dublin, 1986

Research Interests

Numerical solution of singular perturbation problems. Special mesh methods. Adaptive and moving mesh methods.

Publications

Books

2009

BAIL 2008 - Boundary and Interior Layers, Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Limerick, July 2008, Lecture Notes in Computational Science and Engineering, 69
Hegarty, AF; Kopteva, N; O'Riordan, E; Stynes, M (Eds)
(2009) BAIL 2008 - Boundary and Interior Layers, Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Limerick, July 2008, Lecture Notes in Computational Science and Engineering, 69
(Ed.) Berlin Heidelberg : Springer Berlin Heidelberg

2000

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 Boca raton, Florida

Book Chapters

1993

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.
In Applications of Advanced Computational Methods for Boundary and Interior Layers;

Peer Reviewed Journals

2017

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
In Advances In Computational Mathematics; pp. 885-909
DOI: 10.1007/s10444-016-9510-z

2009

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.
In Faseb Journal; pp. 818.7-818.7-818.7-818.7
DOI: 10.1096/fj.1530-6860

2004

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
In Journal Of Computational And Applied Mathematics; pp. 133-151
DOI: 10.1016/j.cam.2003.09.033

2004

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
In Mathematical And Computer Modelling; pp. 1375-1392
DOI: 10.1016/j.mcm.2005.01.025

2003

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
In International Journal For Numerical Methods In Fluids; pp. 937-951
DOI: 10.1002/fld.511

2003

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.
In Computational Methods In Applied Mathematics; pp. 373-386

2003

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
In International Journal For Numerical Methods In Fluids; pp. 915-936
DOI: 10.1002/fld.536

2003

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
In International Journal For Numerical Methods In Fluids; pp. 895-902
DOI: 10.1002/fld.573

2003

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
In Journal Of Computational And Applied Mathematics; pp. 221-238
DOI: 10.1016/S0377-0427(02)00913-5

2003

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
In Applied Numerical Mathematics; pp. 353-365
DOI: 10.1016/S0168-9274(02)00225-8

2003

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
In Computer Methods In Applied Mechanics And Engineering; pp. 3673-3687
DOI: 10.1016/S0045-7825(03)00369-4

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
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
In Applied Numerical Mathematics; pp. 143-149
DOI: 10.1016/S0168-9274(01)00073-3

2001

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
In Numerical Analysis And Its Applications; Err:511(Ed.) pp. 723-731

2001

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
In Lecture Notes In Computer Science; pp. 723-731

2001

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
In Numerical Analysis And Its Applications; Err:511(Ed.) pp. 292-303

2001

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
In Numerical Analysis And Its Applications; Err:511(Ed.) pp. 18-26

1997

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
In Cwi Quarterly; pp. 235-289

1995

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
In Journal Of Computational Physics; pp. 47-54
DOI: 10.1006/jcph.1995.1043

1995

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
In International Journal Of Numerical Methods For Heat & Fluid Flow; pp. 131-140
DOI: 10.1108/EUM0000000004115

1995

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
In Communications In Numerical Methods In Engineering; pp. 435-441
DOI: 10.1002/cnm.1640110508

1994

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
In Communications In Numerical Methods In Engineering; pp. 297-302
DOI: 10.1002/cnm.1640100404

1994

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.
In J. Numerical Mathematics; pp. 65-74

1993

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
In Journal Of Computational Physics; pp. 24-32
DOI: 10.1006/jcph.1993.1050

Conference Publications

2012

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)
In British Journal of Surgery; J.J.H. Miller(Ed.) pp. 67-68

2009

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
pp. 1469-1471

2009

Lecture Notes in Computational Science and Engineering
Hegarty A.F., Gonzalez M., Thomas S.R.
(2009) Lecture Notes in Computational Science and Engineering
pp. 153-161
DOI: 10.1007/978-3-642-00605-0_11

2009

AIP Conference Proceedings
Gonzalez M.T., Hegarty A.F., Thomas S.R.
(2009) AIP Conference Proceedings
pp. 1469-1471
DOI: 10.1063/1.3241372

2006

BAIL 2006
Hegarty,A.F., Sikwila, S., Shiskin, G.I.
(2006) BAIL 2006
G. Lube, G.Rapin(Ed.) pp. *-*

2006

BAIL 2006
Branley, D., Hegarty, A.F., Purtill, H., Shishkin, G.I.
(2006) BAIL 2006
G. Lube, G. Rapin(Ed.) pp. *-*

2005

Biennial Numerical Analysis Conference
Sikwila, S., Hegarty, A.F. and Shishkin, G.I.
(2005) Biennial Numerical Analysis Conference
*(Ed.) pp. *-*

2005

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
*(Ed.) pp. *-*

2004

BAIL 2004
Ansari, A.R., Hegarty, A.F. and Shishkin, G.I.
(2004) BAIL 2004
*(Ed.) pp. *-*

2004

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
Ansari, A.R., Hegarty, A.F. and Shishkin, G.I.(Ed.) pp. 52-58

2004

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
Ansari, A.R., Hegarty, A.F. and Shishkin, G.I.(Ed.) pp. 70-75

2004

BAIL 2004
Sikwila, S., Hegarty, A.F. and Shishkin, G.I.
(2004) BAIL 2004
*(Ed.) pp. *-*

2002

BAIL 2002
Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O'Riordan, E. and Shishkin. G.I.
(2002) BAIL 2002
S.Wang(Ed.) pp. 115-120

2002

BAIL 2002
Ansari, A.R. and Hegarty, A.F.
(2002) BAIL 2002
*(Ed.) pp. 43-48

2001

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
*(Ed.) pp. *-*

2001

Eccomas Computational Fluid Dynamics Conference
Ansari A.R., Hegarty A.F. and Shishkin G.I.
(2001) Eccomas Computational Fluid Dynamics Conference
*(Ed.) pp. *-*

1999

International Seminar on Applied Mathematics '91
O'Riordan E., Hegarty A.F. and Stynes M.
(1999) International Seminar on Applied Mathematics '91
H.-G. Roos, A. Felgenhauer, L. Angermann(Ed.) pp. 91-96

1995

Meeting on Singular Perturbation Problems
Hegarty A.F.
(1995) Meeting on Singular Perturbation Problems
*(Ed.) pp. *-*

1995

September Meeting, Irish Mathematical Society
Hegarty, A.F.
(1995) September Meeting, Irish Mathematical Society
*(Ed.) pp. *-*

1992

BAIL VI
HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI
(1992) BAIL VI
pp. 67-68

1991

13th IMACS World Congress
Farrell P.A. and Hegarty A.F.
(1991) 13th IMACS World Congress
R. Vichnevetsky and J.J.H. Miller(Ed.) pp. 501-502

1991

13th IMACS World Congress
Hegarty A.F., Miller J.J.H., O'Riordan E. and Shishkin G.I.
(1991) 13th IMACS World Congress
R. Vichnevetsky and J.J.H. Miller(Ed.) pp. 503-504

1986

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)
J.J.H. Miller and Novikov(Ed.) pp. 314-319

1982

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)
J.J.H. Miller(Ed.) pp. 263-268

1980

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)
J.J.H. Miller(Ed.) pp. 301-305

1980

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)
J.J.H. Miller(Ed.) pp. 275-280