Publications of Paul A. Farrell
Books
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin,
Robust Computational Techniques for Boundary Layers,
CRC Press, Catalog Number: C1925,
ISBN: 1584881925, No of pages: 275
Publication Date: 03/22/00
Papers
 Numerical results for singularly perturbed linear and
quasilinear
differential equations using a coarse grid, in Proceedings of
First
International Conference on Computational and Asymptotic Methods
for Boundary and Interior Layers (BAIL I), (with A. F. Hegarty, J.
J. H.
Miller, M. J. O'Reilly, and A. A. Sloane), Boole Press, Dublin, pp.
275280
(1980), MR 81m:65132.
 A uniformly convergent difference scheme for turning point
problems,
in Proceedings of First International Conference on Computational
and
Asymptotic Methods for Boundary and Interior Layers (BAIL I), Boole
Press,
pp. 270274 (1980). MR 82b:65069
 Sufficient conditions for the uniform convergence of
difference
schemes
for singularly perturbed turning and nonturning point problems,
in
Proceedings of Second International Conference on Computational and
Asymptotic Methods for Boundary and Interior Layers (BAIL II), Boole
Press,
Dublin, pp. 230235 (1982), MR 85d:65004.

A family of uniformly convergent schemes for a singularly
perturbed
equation
in conservation form, in Proceedings of Third International
Conference
on Computational and Asymptotic Methods for Boundary and Interior
Layers
(BAIL III), Boole Press Conf. Ser., 6,
Boole Press, Dublin, pp 203208 (1984), MR 86d:65096

Criteria for Uniform Convergence, in Proc. of the
Fourth
International Conference on Computational and Asymptotic Methods for
Boundary and Interior Layers (BAIL IV), Novosibirsk, U.S.S.R.,
Boole Press Conf. Ser., 8, Boole Press,
Dublin pp. 286291 (1986), MR 89m:65073

Uniform and optimal schemes for stiff initial value
problems,
Comput. Math. Applic. , 13(12),
pp 925936 (1987), MR 88g:65064
 Sufficient conditions for uniform convergence of a class
of difference schemes
for a singularly perturbed problem, IMA J. Numer. Anal., 7(4),
pp 459472 (1987) MR 90h:65130
 Sufficient conditions for the uniform convergence of a
difference
scheme
for a singularly perturbed turning point problem,
SIAM J. Numer. Anal. , 25(3), pp 618643 (1988), MR
89g:65100

Approximation of Uniformly Convergent Schemes,
in Proc. of Fifth International Conference on Boundary and
Interior Layers  Computational and Asymptotic Methods (BAIL V) ,
Shanghai, Boole Press Conf. Ser., 12, Boole Press,
Dublin, pp. 121126 (1988) MR 90b:65156

A Uniform Convergence Result for a Turning Point Problem,
( with E.C. Gartland ),
Proc. of Fifth International Conference on Boundary and
Interior Layers  Computational and Asymptotic Methods (BAIL V) ,
Shanghai, Boole Press Conf. Ser., 12,
Boole Press, Dublin, pp. 127132 (1988), (Invited)
MR 89j:65008/CMP 21 10

Iterative Methods for the Solution of Linear Systems
arising from
Singularly Perturbed Systems,
 Flow Conforming Iterative Methods for Convection Dominated
Flows,
IMACS Ann. Comput. Appl. Math., 1.2,
Baltzer, Basel, pp 681686 (1989) MR 91g:65181
 Analytic Estimates and Uniform Numerical Methods for Multiple Boundary Turning Point
Problems
(with R. Vulanovic) , in Numerical Methods in Singular
Perturbation Problems, Proc. of ISAM'91, pp. 3338,
Dresden, (1991).
 Limiting Distributions of Some Circuit Switched
Nonhierarchical
Networks , (with H. Peyravi, K. Khan)
 On the ScharfetterGummel Discretization for
DriftDiffusion Continuity Equations, (with E.C. Gartland, Jr.),
in ``Computational Methods for Boundary and Interior
Layers in Several Dimensions'', J.J.H. Miller, ed., pp. 5179,
Boole Press, Dublin, Ireland, (1991). CMP 92 08
 LU Decomposition on a Shared Memory Multiprocessor
(with A. Ruttan), in Proc. of
13 IMACS World Congress, Dublin, Ireland, pp. 718719
(1991).
 On the Determination of the Order of Uniform Convergence
(with A. Hegarty), in Proc. of
13th IMACS World Congress, Dublin, Ireland, pp. 501502
(1991).
 On Blocking Distribution of NonHierarchical Networks
(with K. Khan, H. Peyravi), First Inter. Conf. on Comp.
Applic. in Sc., Tech. and Med., Isfahan, Iran, pp. 8292, (1991)
 Analysis of Multiple Turning Point Problems
(with R. Vulanovic), Rad. Mat., 8(1) (1992)
 Finite Difference Minimization of the Landau  de Gennes
Free Energy for Liquid Crystals in Ellipsoidal Regions,
(with A. Ruttan), in ALCOM Symposium  Liquid Crystals:
Surfaces and Finite Size Effects, pp. 5156, (1992)

Minimization of the Landau  de Gennes
Free Energy for Liquid Crystals in Rectangular Geometries,
(with E.C. Gartland, A. Ruttan, R.R. Zeller), in
Proceedings of the ALCOM Symposium:
Nonlinear Optics of Liquid Crystals, Polymers and Ordered Fluids,
pp. 5762, (1992)

Solution of Singular Perturbation Problems via the Domain
Decomposition Method on Serial and Parallel Computers,
(with I.P. Boglaev, V.V. Sirotkin),
Proc. of Sixth International Conference on Boundary and
Interior Layers  Computational and Asymptotic Methods (BAIL VI),
Front Range Press, Copper Mountain, pp. 9293, (1992)
 Parallel LU Decomposition of Upper Hessenberg Matrices
(with J. Buoni, A. Ruttan), Comput. & Appl. Math. I,
pp. 6170, (1992)
 Finite Difference Minimization of the Landau  de Gennes
Free Energy for Liquid Crystals in Rectangular Regions,
(with A. Ruttan, R.R. Zeller), Comput. & Appl. Math. I,
pp. 137146, (1992)

Limiting Distribution of the Blocking Probability
for Circuitswitched Networks (with K. Khan, H. Peyravi),
Computers Elect. Engng., 19(3), pp. 231244 (1993)

Solution of the LandaudeGennes Equations of Liquid
Crystal Physics on a SIMD Computer,
(with A. Ruttan, R.R. Zeller), Proc. of
Sixth SIAM Conference on Parallel Processing for Scientific Computing,
Volume 1, R. Sinovec, D. Keys, M. Leuze, L. Petzold, D. Reed, eds.,
pp. 266269 (1993)

Numerical Solution of Nonlinear Singular Perturbation
Problems
Modeling Chemical Reactions, (with R. Vulanovic, P. Lin),
in ``Applications of Advanced Computational Methods for
Boundary and Interior
Layers'', J.J.H. Miller, ed., Boole Press, Dublin, Ireland,
pp. 192213 (1993)

Application of Multigrid Methods to the Solution of Liquid
Crystal Equations on a SIMD Computer (with A. Ruttan, R.R. Zeller),
 in the informal electronic Proceedings of the
Sixth Copper Mountain Conference on Multigrid Methods,
15 pages (1993)
 Sixth Copper Mountain Conference on Multigrid
Methods, NASA Conference Publication 3224, Part 1,
N. Duane Melson, T.A. Manteuffel, S.F. McCormick eds.,
pp 191206 (1993)

Continuous and Numerical Analysis of a Multiple
Boundary Turning Point Problem (with R. Vulanovic)
SIAM J. Numer. Anal., 30(5), pp 14001418 (1993)

An Algorithms for LU Decomposition on a Shared Memory
Multiprocessor, (with J. Buoni, A. Ruttan),
Parallel Computing, 19, pp. 925937 (1993).

Computation of the Exact Limiting Distribution for the
Blocking Probability in Network Models, (with H. Peyravi, K. Khan)
Inter. Congress on Comput. Meth. in Eng., Shiraz, Iran, pp. 3542,
(1993)

Parallel Domain Decomposition Methods for Semilinear Singularly
Perturbed Differential Equations,
(with I.P. Boglaev, V.V. Sirotkin),
Computational Fluid Dynamics Journal, 2, no. 4,
pp 423434 (1994).
 On the Design of Piecewise Uniform Meshes for Solving
AdvectionDominated Transport Equations to a Prescribed
Accuracy
(with A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shiskin),
Procs. 10th GAMM Seminar, Kiel, Jan 1416, 1994,
Notes on Numerical Fluid Mechanics, vol. 49, pp. 86 95,
Vieweg, (1995).

Discrete Approximations for Singularly Perturbed Boundary Problems
with Parabolic Layers I (with P.W. Hemker, G.I.
Shishkin),
J. of Computational Mathematics, 14, no. 1, pp. 7197, (1995)
 A Numerical Method for Eigenvalue Problems in
Modelling Liquid Crystals, (with J. Baglama, D. Calvetti, L.
Reichel,
A. Ruttan), Proc. of Copper Mountain Conf. on Iterative Methods, pp.
17,
1996.

Discrete Approximations for Singularly Perturbed Boundary Problems
with Parabolic Layers II (with P.W. Hemker, G.I.
Shishkin),
J. of Computational Mathematics, 14, no. 2, pp. 183194, (1996)

A Uniformly Convergent Finite Difference Scheme for a
Singularly Perturbed Semilinear Equation ,
(with J.J.H. Miller, E. O'Riordan, G.I. Shishkin),
SIAM J. Numer. Anal., 33, no. 3, (1996), pp. 11351149.

Discrete Approximations for Singularly Perturbed Boundary Problems
with Parabolic Layers III (with P.W. Hemker, G.I. Shishkin),
J. of Computational Mathematics, 14, no. 3, pp. 273290, (1996)

On the Nonexistence of epsilonUniform Finite Difference
Methods on Uniform Meshes for Semilinear Twopoint Boundary
Value Problems,
(with J.J.H. Miller, E. O'Riordan, G.I. Shishkin)
Math. Comp., 67 no. 222, Apr 1998, pp. 603617.
preprint

On the Convergence of Iterative Methods for Linear Systems
arising from Singularly Perturbed Equations, (with G.I.
Shishkin),
Proc. Copper Mountain Conf. on Iterative Methods, 1998, pp 17.
 On a Fitted Operator Technique for Singular Perturbation
Equations
(with A. Hegarty, J.J.H. Miller, E.O'Riordan, G.I. Shishkin),
Finite Difference Methods: Theory and Applications,
A.A. Samarskii, L.G. Vulkov and P.N. Vabishchevich eds.,
in Series on Physical Sciences and Engineering Sciences,
Mathematics and Statistics,
Nova Science, N.Y., 1999, pp. 7178.
 Paul A. Farrell, Hong Ong,
Communication Performance over a Gigabit Network,
19th IEEE International Performance,
Computing, and Communications Conference  IPCCC 2000, pp.
181189, 2000.
 Dan Bennett, Paul A. Farrell, Michael A. Lee, Arden Ruttan,
A Low Cost Commodity Based System for Group Viewing of 3d Images,
Proceedings of VDE2000, Visualization Development
Environments 2000, pp 145149. (2000) (invited poster)
Local
version
 Paul A. Farrell, Hong Ong, Arden Ruttan,
Modeling liquid crystal structures on an SMP workstation
cluster, in the Proceedings of CCTEA'2000 
The 2000 International Workshop on Cluster Computing 
Technologies, Environments, and Applications (sponsored by
IEEE Task Force on Cluster Computing), 6 pages, numbered in sessions.
 Hong Ong, Paul A. Farrell,
Performance Comparison of LAM/MPI, MPICH, and MVICH
on a Linux Cluster connected by a Gigabit Ethernet Network,
Proceedings of Linux 2000, 4th Annual Linux Showcase and Conference,
Extreme Linux Track, Atlanta, 2000, pp 353362.
Local
version
 P.A. Farrell, J.J.H. Miller, E. O'Riordan, G.I. Shishkin,
Singularly perturbed differential equations with discontinuous
source terms., In:
"Analytical and Numerical Methods for ConvectionDominated
and Singularly Perturbed Problems",
L.G. Vulkov, J.J.H. Miller, G.I. Shishkin eds., Nova Science Publishers,
Inc., New York, USA, 2000, pp 2332.
 P.A. Farrell, G.I. Shishkin,
Schwartz Methods for Singularly Perturbed ConvectionDiffusion
Problems, In:
"Analytical and Numerical Methods for ConvectionDominated
and Singularly Perturbed Problems",
L.G. Vulkov, J.J.H. Miller, G.I. Shishkin eds., Nova Science Publishers,
Inc., New York, USA, 2000, pp 3342.
 Paul A. Farrell, Hong Ong, Stephen L. Scott,
Enabling High Performance Data Transfer on Cluster Architecture,
2 pages,
Proceedings of the 2nd IEEE International Conference on
Cluster Computing (CLUSTER 2000), IEEE Computer Society, 2000.

G.I. Shishkin, P.A. Farrell, A.F. Hegarty, J.J.H. Miller,
E.O'Riordan. On Reynoldsuniform numerical methods, in parabolic
boundary layer regions, for Prandtl's problems, in Proc. of the 3rd
International Conference FDS2000, Sept. 14, 2000, Palanga,
Lithuania, Finite difference schemes: theory and applications, R.
Ciegis, A. Samarskii and M. Sapagovas (Eds.), IMI, Vilnius, 2000,
pp. 215225

P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan and
G.I. Shishkin, Parameteruniform numerical methods for
a class of singularly perturbed problems with a Neumann
boundary conditions, In: Numerical Analysis and Its
Applications: Second International Conference, NAA 2000,
Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov,
J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in
Computer Science; Vol. 1988. Springer, 2001. P. 292303.
preprint

G.I. Shishkin, P.A. Farrell, A.F. Hegarty, J.J.H. Miller
and E. O'Riordan. On a necessary requirement for
Reuniform numerical methods to solve boundary layer
equations for flow along a flat plate,
In: Numerical Analysis and Its Applications: Second
International Conference, NAA 2000, Rousse, Bulgaria,
June 2000; Revised Papers, L.Vulkov, J.Wasniewski and
P.Yalamov (Eds.) / Lecture Notes in Computer Science;
Vol. 1988. Springer, 2001. P. 723731.
 P.A. Farrell, E. O'Riordan, J.J.H. Miller, G.I. Shishkin.
Parameteruniform fitted mesh method for quasilinear differential
equations with boundary layers.
Computational Methods in Applied
Mathematics, 2001, 1 (2), 154172.
 Mark Baker, Paul A. Farrell, Hong Ong, Stephen L .Scott,
VIA Communication Performance on a Gigabit Ethernet Cluster,
Lecture Notes in Computer Science, Proceedings of EuroPar2001, Vol 2150,
pp. 132141, SpringerVerlag, 2001.
%2002
 P.A.Farrell, A.F.Hegarty, J.J.H. Miller , E. O'Riordan and
G.I. Shishkin, An experimental technique for computing
parameteruniform error estimates for numerical solutions of
singular perturbation problems, with an application to Prandtl's
problem at high Reynolds number, Appl. Num. Math., Vol 40 /14,
pp. 143149.
 P.A. Farrell, P.W. Hemker, G.I. Shishkin, L.P. Shishkina,
Iterative Domain Decomposition Methods for
Singularly Perturbed
Nonlinear
ConvectionDuffusion Equations, pp 121126,
Proceedings of BAIL2002, Perth, Australia, 2002.
 P.A.Farrell, A.F.Hegarty, J.J.H. Miller , E. O'Riordan and
G.I. Shishkin, Singularly Perturbed Convection Diffusion Problems
with Boundary and Weak Interior Layers,
 Paul A. Farrell, Hong Ong,
Factors Involved in the Performance of Computations on
Beowulf Clusters,
ETNA  Electronic Transactions in Numerical Analysis, 15, pp.
211224, 2003.
 YangMing Zhu, Paul A. Farrell,
Vector Grouping Algorithm for Liquid Crystal Tensor Field
Visualization,
Liquid Crystals, 29(10), pp. 1259  1264, 2002. preprint
 P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan and
G.I. Shishkin,
Computing realistic Reynoldsuniform error bounds for
discrete derivatives of flow velocities in the boundary layer for
Prandtl's
problem,
International Journal for Numerical Methods in Fluids,
Volume 43, No. 8. pp. 895902, (2003)
 P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I.
Shishkin,
Numerical techniques for flow problems with singularities,
International Journal for Numerical Methods in Fluids,
Volume 43, No. 8. pp. 915936, (2003)
 P.A. Farrell, E. O'Riordan, G.I. Shishkin,
Robust numerical methods for singularly perturbed
semilinear differential equations with interior layers,
Proceedings of BAIL 2004, Toulouse, France, 6 pages, (2004)
 P.A.Farrell, A.F.Hegarty, J.J.H. Miller, E. O'Riordan and
G.I. Shishkin,
Global maximum norm parameteruniform numerical
method for a singularly perturbed convectiondiffusion problem
with discontinuous convection coefficient, Mathematical and Computer
Modelling, 40, pp. 13751392, (2004)
 P.A. Farrell, E. O'Riordan, G.I. Shishkin,
A class of singularly perturbed semilinear differential equations
with interior layers, Math. Comp., 74, 2005, 17591776
 Dan Bennett, Paul A. Farrell,
Experiences Instrumenting a
Distributed Molecular Dynamics Program, Proceedings of PACISE'O6,
pp 45  50 (2006)
 Cara Stein, Daniel Bennett, Paul A. Farrell, Arden Ruttan,
A Steering and Visualization Toolkit for Distributed
Applications, The Proceedings of the 2006 International
Conference on Parallel and Distributed Processing Techniques and
Applications (PDPTA'06), pp 451457, (2006)
 Dan Bennett, Paul A. Farrell, Cara Stein,
A Chromium Based
Viewer for CUMULVS,
The Proceedings of the 2006 International Conference on Parallel
and Distributed Processing Techniques and Applications (PDPTA'06),
pp 472477, (2006)
 Paul A. Farrell, Hong Ong, Arden Ruttan, YangMing Zhu,
A
Visualization Environment
for Nematic Liquid Crystal Materials,
Proceeding of IADIS Multi Conference on Computer Science and Information
Systems, Lisbon,
Part III  Computer Graphics and Visualization, pp. 8391, 2007
 P.A. Farrell, E. O'Riordan, Examination of the performance
of robust numerical methods for singularly perturbed quasilinear
problems with interior layers., BAIL 2008, Limerick, 2 pages
(extended absract) (2008).
 P.A. Farrell, E. O'Riordan, G.I. Shishkin,
A class of singularly perturbed quasilinear differential equations
with interior layers,
Math. Comp. 78 (2009), 103127. preprint
 P.A. Farrell, E. O'Riordan, Examination of the performance
of robust numerical methods for singularly perturbed quasilinear
problems with interior layers.,
Lecture Notes in Computational Science and Engineering, 69 (2009), 141151.
preprint

Dan Bennett, Paul Farrell, and Arden Ruttan,
An Extensible Parameter Viewer for CUMULVS,
Proceedings of PACISE 20O9, 1015, (2009)
 Paul A. Farrell, Hong Ong, Arden Ruttan,
Modelling Liquid Crystal Structures using MPI on a Workstation
Cluster, to appear in Proceedings of MWPP'99  Midwest Workshop
on
Parallel Processing (IEEE/ACM)
 Paul A. Farrell, Xiaodong Hu, Irina V. Lomonosov, Michael A.
Lee,
Dynamic Load Balancing Algorithm Performance in a Quantum
Monte Carlo Simulation with Random Load,
to appear in Proceedings of MWPP'99
 Midwest Workshop on Parallel Processing (IEEE/ACM)
Articles about our research
 Distributed methods model liquidcrystal defects, in
Scientific
Computing, 27, April 1997
Technical Reports
 Uniformly convergent difference schemes for a stiff initial
value
problem. (1986)
 Accessing the Library Catalogue over the Campus Network,
4 pages(1990)

TeX niques and Tools  a Guide to LaTeX usage and utilities,
29 pages (1990)

National InternetAccessible Library Catalogues & Databases ,
34 pages (1990)

Regional InternetAccessible Library Catalogues & Databases >,
10 pages (1990)

Kent State University Dissertation and Thesis Styles, 4
pages
(1991)

Accessing the Mathematical Reviews CDROM from Departmental
Workstations, 7pages (1991)

The Internet Gopher and some features of the MCS Kent version,
6 pages (1993)
 The
Evolution of an Academic Network in Palestine
(with Adrienne Dockrell, Yaser Doleh) 1994
 Evolution
and Future Issues for an Academic Network in Palestine
(with Adrienne Dockrell, Yaser Doleh) 1994

Grid Approximations for Singularly Perturbed Boundary Problems
with Parabolic Layers (with P.W. Hemker, G.I. Shiskin), Report
NMR9502,
ISSN 01690388, CWI Amsterdam, 50 pages (1994)
farrell@mcs.kent.edu