Paul A. Farrell

1.7k total citations · 1 hit paper
27 papers, 1.3k citations indexed

About

Paul A. Farrell is a scholar working on Numerical Analysis, Computational Theory and Mathematics and Computational Mechanics. According to data from OpenAlex, Paul A. Farrell has authored 27 papers receiving a total of 1.3k indexed citations (citations by other indexed papers that have themselves been cited), including 15 papers in Numerical Analysis, 11 papers in Computational Theory and Mathematics and 9 papers in Computational Mechanics. Recurrent topics in Paul A. Farrell's work include Differential Equations and Numerical Methods (15 papers), Advanced Mathematical Modeling in Engineering (10 papers) and Advanced Numerical Methods in Computational Mathematics (6 papers). Paul A. Farrell is often cited by papers focused on Differential Equations and Numerical Methods (15 papers), Advanced Mathematical Modeling in Engineering (10 papers) and Advanced Numerical Methods in Computational Mathematics (6 papers). Paul A. Farrell collaborates with scholars based in United States, Ireland and Russia. Paul A. Farrell's co-authors include G. I. Shishkin, Eugene O’Riordan, Alan F. Hegarty, John Miller, John J. H. Miller, Matthew R. Hyre, Leon R. Glicksman, Relja Vulanović, Ralph L. Webb and Hong Ong and has published in prestigious journals such as Mathematics of Computation, SIAM Journal on Numerical Analysis and SAE technical papers on CD-ROM/SAE technical paper series.

In The Last Decade

Paul A. Farrell

25 papers receiving 1.2k citations

Hit Papers

align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

Robust Computational Techniques for Boundary Layers

2000 704 citations Paul A. Farrell, Alan F. Hegarty et al. profile →

Peers

Paul A. Farrell

CTM

F.J. Lisbona Spain

J. F. B. M. Kraaijevanger Netherlands

Jozef Kačur Slovakia

Fayyaz Ahmad Spain

C. Baiocchi Italy

Vladislav N. Kovalnogov Russia

Jugal Mohapatra India

R. W. Dickey United States

Tsuan Wu Ting United States

B. Chanane Saudi Arabia

F.J. Lisbona Spain

Paul A. Farrell

451 ×0.4

373 ×0.7

CTM

72 ×0.2

517 ×1.3

75 ×0.3

Citations per year, relative to Paul A. Farrell Paul A. Farrell (= 1×) peers F.J. Lisbona

Countries citing papers authored by Paul A. Farrell

Since Specialization

Citations

This map shows the geographic impact of Paul A. Farrell's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Paul A. Farrell with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Paul A. Farrell more than expected).

Fields of papers citing papers by Paul A. Farrell

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Paul A. Farrell. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Paul A. Farrell. The network helps show where Paul A. Farrell may publish in the future.

Co-authorship network of co-authors of Paul A. Farrell

This figure shows the co-authorship network connecting the top 25 collaborators of Paul A. Farrell. A scholar is included among the top collaborators of Paul A. Farrell based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Paul A. Farrell. Paul A. Farrell is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

Farrell, Paul A., Eugene O’Riordan, & G. I. Shishkin. (2008). A class of singularly perturbed quasilinear differential equations with interior layers. Mathematics of Computation. 78(265). 103–103. 11 indexed citations

Farrell, Paul A., et al.. (2006). A Steering and Visualization Toolkit for Distributed Applications.. Parallel and Distributed Processing Techniques and Applications. 451–457. 1 indexed citations

Farrell, Paul A., Eugene O’Riordan, & G. I. Shishkin. (2005). A class of singularly perturbed semilinear differential equations with interior layers. Mathematics of Computation. 74(252). 1759–1777. 29 indexed citations

Farrell, Paul A., Alan F. Hegarty, John J. H. Miller, Eugene O’Riordan, & G. I. Shishkin. (2004). Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient. Mathematical and Computer Modelling. 40(11-12). 1375–1392. 74 indexed citations

Farrell, Paul A. & Hong Ong. (2003). Factors involved in the performance of computations on Beowulf clusters.. 15. 211–224.

Farrell, Paul A., Alan F. Hegarty, John J. H. Miller, Eugene O’Riordan, & G. I. Shishkin. (2003). Singularly perturbed convection–diffusion problems with boundary and weak interior layers. Journal of Computational and Applied Mathematics. 166(1). 133–151. 84 indexed citations

Farrell, Paul A., Alan F. Hegarty, John J. H. Miller, Eugene O’Riordan, & G. I. Shishkin. (2003). Numerical techniques for flow problems with singularities. International Journal for Numerical Methods in Fluids. 43(8). 915–936. 3 indexed citations

Zhu, Yang‐Ming & Paul A. Farrell. (2002). A vector grouping algorithm for liquid crystal tensor field visualization. Liquid Crystals. 29(10). 1259–1264. 3 indexed citations

Farrell, Paul A., Eugene O’Riordan, John J. H. Miller, & G. I. Shishkin. (2001). Parameter–uniform Fitted Mesh Method for Quasilinear Differential Equations with Boundary Layers. Computational Methods in Applied Mathematics. 1(2). 154–172. 10 indexed citations

10.

Farrell, Paul A., Alan F. Hegarty, John Miller, Eugene O’Riordan, & G. I. Shishkin. (2000). Robust Computational Techniques for Boundary Layers. 704 indexed citations breakdown →

11.

Ong, Hong & Paul A. Farrell. (2000). Performance comparison of LAM/MPI, MPICH, and MVICH on a linux cluster connected by a gigabit ethernet network. 31–31. 12 indexed citations

12.

Farrell, Paul A., John J. H. Miller, Eugene O’Riordan, & G. I. Shishkin. (1998). On the non-existence of 𝜀-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems. Mathematics of Computation. 67(222). 603–617. 24 indexed citations

13.

Farrell, Paul A., Piet Hemker, & G. I. Shishkin. (1996). Discrete Approximations for Singularly Perturbed Boundary Value Problems with Parabolic Layers, III. Journal of Computational Mathematics. 14(3). 273–290. 9 indexed citations

14.

Farrell, Paul A., John J. H. Miller, Eugene O’Riordan, & G. I. Shishkin. (1996). A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation. SIAM Journal on Numerical Analysis. 33(3). 1135–1149. 32 indexed citations

15.

Farrell, Paul A., Piet Hemker, & G. I. Shishkin. (1995). Discrete Approximations for Singularly Perturbed Boundary Value Problems with Parabolic Layers. Journal of Computational Mathematics. 14(1). 1–44. 1 indexed citations

16.

Farrell, Paul A., et al.. (1993). Algorithms for LU decomposition on a shared memory multiprocessor. Parallel Computing. 19(8). 925–937. 5 indexed citations

17.

Vulanović, Relja & Paul A. Farrell. (1993). Continuous and Numerical Analysis of a Multiple Boundary Turning Point Problem. SIAM Journal on Numerical Analysis. 30(5). 1400–1418. 33 indexed citations

18.

Webb, Ralph L. & Paul A. Farrell. (1990). Improved Thermal and Mechanical Design of Copper/Brass Radiators. SAE technical papers on CD-ROM/SAE technical paper series. 1. 4 indexed citations

19.

Farrell, Paul A.. (1988). Sufficient Conditions for the Uniform Convergence of a Difference Scheme for a Singularly Perturbed Turning Point Problem. SIAM Journal on Numerical Analysis. 25(3). 618–643. 36 indexed citations

20.

Farrell, Paul A.. (1987). Uniform and optimal schemes for stiff initial-value problems. Computers & Mathematics with Applications. 13(12). 925–936. 16 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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