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

  1. Numerical results for singularly perturbed linear and quasi-linear 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. 275-280 (1980), MR 81m:65132.
  2. 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. 270-274 (1980). MR 82b:65069
  3. Sufficient conditions for the uniform convergence of difference schemes for singularly perturbed turning and non-turning point problems, in Proceedings of Second International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL II), Boole Press, Dublin, pp. 230-235 (1982), MR 85d:65004.
  4. 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 203-208 (1984), MR 86d:65096
  5. 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. 286-291 (1986), MR 89m:65073
  6. Uniform and optimal schemes for stiff initial value problems, Comput. Math. Applic. , 13(12), pp 925-936 (1987), MR 88g:65064
  7. Sufficient conditions for uniform convergence of a class of difference schemes for a singularly perturbed problem, IMA J. Numer. Anal., 7(4), pp 459-472 (1987) MR 90h:65130
  8. Sufficient conditions for the uniform convergence of a difference scheme for a singularly perturbed turning point problem, SIAM J. Numer. Anal. , 25(3), pp 618-643 (1988), MR 89g:65100
  9. 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. 121-126 (1988) MR 90b:65156
  10. 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. 127-132 (1988), (Invited) MR 89j:65008/CMP 21 10
  11. Iterative Methods for the Solution of Linear Systems arising from Singularly Perturbed Systems,
  12. Flow Conforming Iterative Methods for Convection Dominated Flows, IMACS Ann. Comput. Appl. Math., 1.2, Baltzer, Basel, pp 681-686 (1989) MR 91g:65181
  13. 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. 33-38, Dresden, (1991).
  14. Limiting Distributions of Some Circuit Switched Nonhierarchical Networks , (with H. Peyravi, K. Khan)
  15. On the Scharfetter-Gummel Discretization for Drift-Diffusion Continuity Equations, (with E.C. Gartland, Jr.), in ``Computational Methods for Boundary and Interior Layers in Several Dimensions'', J.J.H. Miller, ed., pp. 51-79, Boole Press, Dublin, Ireland, (1991). CMP 92 08
  16. LU Decomposition on a Shared Memory Multiprocessor (with A. Ruttan), in Proc. of 13 IMACS World Congress, Dublin, Ireland, pp. 718-719 (1991).
  17. On the Determination of the Order of Uniform Convergence (with A. Hegarty), in Proc. of 13th IMACS World Congress, Dublin, Ireland, pp. 501-502 (1991).
  18. On Blocking Distribution of Non-Hierarchical Networks (with K. Khan, H. Peyravi), First Inter. Conf. on Comp. Applic. in Sc., Tech. and Med., Isfahan, Iran, pp. 82-92, (1991)
  19. Analysis of Multiple Turning Point Problems (with R. Vulanovic), Rad. Mat., 8(1) (1992)
  20. 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. 51-56, (1992)
  21. 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. 57-62, (1992)
  22. 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. 92-93, (1992)
  23. Parallel LU Decomposition of Upper Hessenberg Matrices (with J. Buoni, A. Ruttan), Comput. & Appl. Math. I, pp. 61-70, (1992)
  24. 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. 137-146, (1992)
  25. Limiting Distribution of the Blocking Probability for Circuit-switched Networks (with K. Khan, H. Peyravi), Computers Elect. Engng., 19(3), pp. 231-244 (1993)
  26. Solution of the Landau-de-Gennes 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. 266-269 (1993)
  27. Numerical Solution of Non-linear 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. 192-213 (1993)
  28. Application of Multigrid Methods to the Solution of Liquid Crystal Equations on a SIMD Computer (with A. Ruttan, R.R. Zeller),
  29. Continuous and Numerical Analysis of a Multiple Boundary Turning Point Problem (with R. Vulanovic) SIAM J. Numer. Anal., 30(5), pp 1400-1418 (1993)
  30. An Algorithms for LU Decomposition on a Shared Memory Multiprocessor, (with J. Buoni, A. Ruttan), Parallel Computing, 19, pp. 925-937 (1993).
  31. 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. 35-42, (1993)
  32. Parallel Domain Decomposition Methods for Semi-linear Singularly Perturbed Differential Equations, (with I.P. Boglaev, V.V. Sirotkin), Computational Fluid Dynamics Journal, 2, no. 4, pp 423-434 (1994).
  33. On the Design of Piecewise Uniform Meshes for Solving Advection-Dominated 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 14--16, 1994, Notes on Numerical Fluid Mechanics, vol. 49, pp. 86 -95, Vieweg, (1995).
  34. 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. 71-97, (1995)
  35. 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. 1-7, 1996.
  36. 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. 183-194, (1996)
  37. 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. 1135-1149.
  38. 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. 273-290, (1996)
  39. On the Non-existence of epsilon-Uniform Finite Difference Methods on Uniform Meshes for Semilinear Two-point Boundary Value Problems, (with J.J.H. Miller, E. O'Riordan, G.I. Shishkin) Math. Comp., 67 no. 222, Apr 1998, pp. 603-617. preprint
  40. 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 1--7.
  41. 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. 71-78.
  42. Paul A. Farrell, Hong Ong, Communication Performance over a Gigabit Network, 19th IEEE International Performance, Computing, and Communications Conference -- IPCCC 2000, pp. 181--189, 2000.
  43. 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 145--149. (2000) (invited poster)
    Local version
  44. Paul A. Farrell, Hong Ong, Arden Ruttan, Modeling liquid crystal structures on an SMP workstation cluster, in the Proceedings of CC-TEA'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.
  45. 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 353--362.
    Local version
  46. 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 Convection-Dominated and Singularly Perturbed Problems", L.G. Vulkov, J.J.H. Miller, G.I. Shishkin eds., Nova Science Publishers, Inc., New York, USA, 2000, pp 23--32.
  47. P.A. Farrell, G.I. Shishkin, Schwartz Methods for Singularly Perturbed Convection-Diffusion Problems, In: "Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems", L.G. Vulkov, J.J.H. Miller, G.I. Shishkin eds., Nova Science Publishers, Inc., New York, USA, 2000, pp 33--42.
  48. 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.
  49. G.I. Shishkin, P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E.O'Riordan. On Reynolds-uniform numerical methods, in parabolic boundary layer regions, for Prandtl's problems, in Proc. of the 3rd International Conference FDS2000, Sept. 1-4, 2000, Palanga, Lithuania, Finite difference schemes: theory and applications, R. Ciegis, A. Samarskii and M. Sapagovas (Eds.), IMI, Vilnius, 2000, pp. 215-225
  50. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan and G.I. Shishkin, Parameter-uniform 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. 292-303. preprint
  51. G.I. Shishkin, P.A. Farrell, A.F. Hegarty, J.J.H. Miller and E. O'Riordan. 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: 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. 723-731.
  52. P.A. Farrell, E. O'Riordan, J.J.H. Miller, G.I. Shishkin. Parameter-uniform fitted mesh method for quasilinear differential equations with boundary layers. Computational Methods in Applied Mathematics, 2001, 1 (2), 154-172.
  53. 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. 132--141, Springer-Verlag, 2001. %2002
  54. P.A.Farrell, A.F.Hegarty, J.J.H. Miller , E. O'Riordan and G.I. Shishkin, 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, Appl. Num. Math., Vol 40 /1-4, pp. 143--149.
  55. P.A. Farrell, P.W. Hemker, G.I. Shishkin, L.P. Shishkina, Iterative Domain Decomposition Methods for Singularly Perturbed Nonlinear Convection-Duffusion Equations, pp 121--126, Proceedings of BAIL2002, Perth, Australia, 2002.
  56. 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,
  57. Paul A. Farrell, Hong Ong, Factors Involved in the Performance of Computations on Beowulf Clusters, ETNA - Electronic Transactions in Numerical Analysis, 15, pp. 211-224, 2003.
  58. Yang-Ming Zhu, Paul A. Farrell, Vector Grouping Algorithm for Liquid Crystal Tensor Field Visualization, Liquid Crystals, 29(10), pp. 1259 - 1264, 2002. preprint
  59. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan and G.I. Shishkin, Computing realistic Reynolds-uniform 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. 895-902, (2003)
  60. 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. 915-936, (2003)
  61. 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)
  62. P.A.Farrell, A.F.Hegarty, J.J.H. Miller, E. O'Riordan and G.I. Shishkin, Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient, Mathematical and Computer Modelling, 40, pp. 1375-1392, (2004)
  63. P.A. Farrell, E. O'Riordan, G.I. Shishkin, A class of singularly perturbed semilinear differential equations with interior layers, Math. Comp., 74, 2005, 1759-1776
  64. Dan Bennett, Paul A. Farrell, Experiences Instrumenting a Distributed Molecular Dynamics Program, Proceedings of PACISE'O6, pp 45 - 50 (2006)
  65. 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 451--457, (2006)
  66. 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 472--477, (2006)
  67. Paul A. Farrell, Hong Ong, Arden Ruttan, Yang-Ming 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. 83--91, 2007
  68. 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).
  69. P.A. Farrell, E. O'Riordan, G.I. Shishkin, A class of singularly perturbed quasilinear differential equations with interior layers, Math. Comp. 78 (2009), 103-127. preprint
  70. 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), 141-151. preprint
  71. Dan Bennett, Paul Farrell, and Arden Ruttan, An Extensible Parameter Viewer for CUMULVS, Proceedings of PACISE 20O9, 10-15, (2009)
  72. 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)
  73. 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

  1. Distributed methods model liquid-crystal defects, in Scientific Computing, 27, April 1997

Technical Reports

  1. Uniformly convergent difference schemes for a stiff initial value problem. (1986)
  2. Accessing the Library Catalogue over the Campus Network, 4 pages(1990)
  3. TeX niques and Tools - a Guide to LaTeX usage and utilities, 29 pages (1990)
  4. National Internet-Accessible Library Catalogues & Databases , 34 pages (1990)
  5. Regional Internet-Accessible Library Catalogues & Databases >, 10 pages (1990)
  6. Kent State University Dissertation and Thesis Styles, 4 pages (1991)
  7. Accessing the Mathematical Reviews CD-ROM from Departmental Workstations, 7pages (1991)
  8. The Internet Gopher and some features of the MCS Kent version, 6 pages (1993)
  9. The Evolution of an Academic Network in Palestine (with Adrienne Dockrell, Yaser Doleh) 1994
  10. Evolution and Future Issues for an Academic Network in Palestine (with Adrienne Dockrell, Yaser Doleh) 1994
  11. Grid Approximations for Singularly Perturbed Boundary Problems with Parabolic Layers (with P.W. Hemker, G.I. Shiskin), Report NM-R9502, ISSN 0169-0388, CWI Amsterdam, 50 pages (1994)

farrell@mcs.kent.edu