Dr. Thai Nhan

I am a Lecturer in the Department of Mathematics and Computer Science at Santa Clara University. I am also a Faculty Research Affiliate at the Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory.  I received my Ph.D. from the National University of Ireland Galway, mentored by Prof. Niall Madden (NUI Galway) and Prof. Scott MacLachlan (formerly at Tufts University, now at the Memorial University of Newfoundland).

I have a wide range of research interests in Computational and Applied Mathematics including, but not limited to, Numerical Analysis, Numerical Linear Algebra, Scientific Computing, Biomath Modeling, and Math Education. 

Contact: 

anhan[at]scu[dot]edu

Department of Mathematics and Computer Science

Santa Clara University

500 El Camino Real, Santa Clara, CA 95053

United States

Research Overview

My overall research goal is to develop novel, fast, and robust numerical methods to efficiently solve scientific problems. I find this field particularly fascinating because recent development in technology has provided computers with greater computational power which has increased the potential to implement large-scale problems with high-performance and even greater parallelism. Therefore, there is a need to develop novel numerical linear algebra and numerical analysis tools to fully exploit this advanced computing potential. I believe that, in the near future, a combination of mathematics and scientific computing will provide even more powerful means to explore and simulate large-scale scientific problems with applications in physics, chemistry, and biology. 

Research Interests 

Numerical Analysis; Scientific Computing; Numerical Linear Algebra; Differential Equations; Preconditioning; Multigrid; Approximations; Modeling of Biological Systems; Mathematics Education. 

Research Grants

* Oct. 2025: Travel Award for faculty to attend the second annual meeting of the Northern and Central California (NCC) Section of SIAM, Lawrence Berkeley National Laboratory.

* Summer 2025: The  U.S. Department of Energy (DOE) Visiting Faculty Program (VFP) at the Lawrence Berkeley National Laboratory (LBNL), funded by the DOE, Office of Science ($20,000 per ten weeks).

 * Oct. 2024: Travel Award (the U.S. National Science Foundation’s Division of Mathematical Sciences grant 2433859) for faculty to attend the first annual meeting of the Northern and Central California (NCC) Section of SIAM, the University of California (UC), Merced.

* Summer 2024: The  U.S. Department of Energy (DOE) Visiting Faculty Program (VFP) at the Lawrence Berkeley National Laboratory (LBNL), funded by the DOE, Office of Science ($27,300 per ten weeks).

* Summer 2023: The  U.S. Department of Energy (DOE) Visiting Faculty Program (VFP) at the Lawrence Berkeley National Laboratory (LBNL), funded by the DOE, Office of Science ($20,000 per ten weeks).

* Summer 2022: The  U.S. Department of Energy (DOE) Visiting Faculty Program (VFP) at the Lawrence Berkeley National Laboratory (LBNL), funded by the DOE, Office of Science ($17,500 per ten weeks).

* The FernUniversität in Hagen President's Travel Award to attend the 18th Workshop on Numerical Methods for Problems with Layer Phenomena, 24--26 March 2022 in Hagen, Germany.

* AY 2020–2021: Awarded a 3-unit teaching release from Holy Names University Faculty Development Program for conducting research beyond the norm.

* Summer 2019, Faculty Trainee, Google New York Headquarter, The Google Applied Computing Series project: the pilot program for two college-level introductory computer science and data science courses and a machine learning intensive. (Skills trained Python, NumPy, SQL).

* The Travel Award for junior researchers to attend the Conference on Computational Mathematics and Applications, University of Nevada Las Vegas, Oct. 2019.

* The Travel Award (from Lawrence Berkeley Lab) for junior researchers to attend the International Conference on the Preconditioning Techniques for Scientific and Industrial Applications, University of Minnesota, Jul. 2019.

* The National Science Foundation (NSF) Travel Award for US junior researchers to attend the International Conference on the Preconditioning Techniques for Scientific and Industrial Applications, UBC, Vancouver, Aug. 2017.

* Two week research visit in September 2013, Tufts University, funded by the  Irish Research Council Grant No. RS/2011/179 (5000 euros per 2 weeks).

* 2011–2015, Ph.D. project entitled: “Preconditioning techniques for singularly perturbed differential equations”. The project was funded by the  Irish Research Council Grant No. RS/2011/179 (96,000 euros per four years).

* 2009–2011, M.Sc. project entitled: “Handling Nonlinearity and Uncertainty in Drug Delivery Modelling” funded by  Science Foundation Ireland (SFI) under their Research Frontiers Programme grant SFI RFP/CMS/1254 (37,500 euros per 18 months).

Publications 

31. Govindarao, L.; Al-Ghafri, K.S.; Mohapatra, J.; Nhan, T.A (2025). Stable and Convergent High-Order Numerical Schemes for Parabolic Integro-Differential Equations with Small Coefficients. Symmetry 2025, 17, 1475.

30. R. Vulanović  and T.A. Nhan (2025). Advantages of the Sarmarskii-type schemes on the Shishkin mesh. Journal of Computational and Applied Mathematics, Volume 470, 15 December 2025, 116688.

29. V. Mai, T.A. Nhan (2024). Fractional Modelling of H₂O₂-Assisted Oxidation by Spanish broom peroxidase. Mathematics. 2024; 12(9):1411.

28. T.A. Nhan, R. Vulanovic (2023). Parameter-uniform convergence analysis on a Bakhvalov-type mesh with a smooth mesh-generating function using the preconditioning approach. Letters on Applied and Pure Mathematics, 1(2), 21-34.

27. L. Claus, P. Ghysels, Y. Liu, T.A. Nhan, R. Thirumalaisamy, A.P.S. Bhalla (2023). Sparse Approximate multifrontal factorization with composite compression methods. ACM Transactions on Mathematical Software, Volume 24, Issue 3, Article No.: 24, pp 1-28.  

26. T.A. Nhan and Relja Vulanovic (2023). Analysis of a Second-order Hybrid Scheme on Bakhvalov-type meshes: the Truncation-error and Barrier-function Approach. Applied Numerical Mathematics, Vol 186, April 2023, pp. 84--99. 

25. T.A. Nhan et al. (2023). A new upwind difference analysis of an exponentially graded Bakhvalov-type mesh for singularly perturbed elliptic convection-diffusion problems. Journal of Computational and Applied Mathematics, Vol. 418, Jan. 2023, 114622.

24. S. MacLachlan, N. Madden, and T.A. Nhan (2022). A Boundary-Layer Preconditioner for Singularly Perturbed Convection Diffusion. SIAM Journal on Matrix Analysis and Its Applications (SIMAX), Vol. 43 (2), 561--583.

23. T.A. Nhan and V. Mai (2022). A preconditioning-based analysis for a Bakhvalov-type mesh. In William McLean, Shev Macnamara, and Judith Bunder, editors, Proceedings of the 20th Biennial Computational Techniques and Applications Conference, CTAC-2020, volume 62 of ANZIAM J., pages C146–C162, February 2022.

22. V. Mai, T.A. Nhan, Z. Hammouch (2021). A Mathematical Model of Enzymatic non-competitive inhibition by product and its applications. Physica Scripta 96 (2021) 124062.

21. R. Vulanović  and T.A. Nhan (2021). An Improved Kellogg-Tsan Solution Decomposition in Numerical Methods for Singularly Perturbed Convection-Diffusion Problems. Applied Numerical Mathematics, Volume 170, December 2021, Pages 128-145.

20. T.A. Nhan and V. Mai (2021). On Bakhvalov-type meshes for a linear convection-diffusion problem in 2D. Mathematical Communications 26(2021), 121–130.

19. T.A. Nhan (2021). A uniform convergence analysis for a Bakhvalov-type mesh with explicitly defined transition point.  In: Garanzha V.A., Kamenski L., Si H. (eds) Numerical Geometry, Grid Generation and Scientific Computing. Lecture Notes in Computational Science and Engineering, Vol 143, pp 213–226. Springer, Cham. https://doi.org/10.1007/978-3-030-76798-3_13

18. V. Mai̇, T.A. Nhan (2021). Numerical analysis of coupled systems of ODEs and applications to enzymatic competitive inhibition by product . Advances in the Theory of Nonlinear Analysis and its Application, 5 (1), 58-71. DOI: 10.31197/atnaa.820590

17. R. Vulanović  and T.A. Nhan (2020). Robust hybrid schemes of higher order for singularly perturbed convection-diffusion problems. Applied Mathematics and  Computation, Volume 386, 1 December 2020, 125495.

16. R. Vulanović  and T.A. Nhan (2020). Using the Kellogg-Tsan solution decomposition in numerical methods for singularly perturbed convection-diffusion problems. Numerical Analysis and Applicable Mathematics, 2020, 1(1), 1-9. 

15. T.A. Nhan and R. Vulanović  (2020). The Bakhvalov mesh: a complete finite-difference analysis of two-dimensional singularly perturbed convection-diffusion problems. Numerical Algorithms 87, 203–-221 (2021). DOI: https://doi.org/10.1007/s11075-020-00964-z

14. T.A. Nhan and N. Madden (2020). An analysis of diagonal and incomplete Cholesky preconditioners for a singularly perturbed problem on a layer-adapted mesh. Journal of Applied  Mathematics and Computing 65, 245–272 (2021). https://doi.org/10.1007/s12190-020-01390-z

13. L.P. Quan and T.A. Nhan (2020).   A closed-form solution to the inverse problem in interpolation by a Bézier-spline curve. Arabian Journal of Mathematics 9, 155–-165 (2020). https://doi.org/10.1007/s40065-019-0241-0

12. T.A. Nhan and R. Vulanović (2019). Analysis of the truncation error and barrier-functions technique for a Bakhvalov-type mesh. Electronic Transactions on Numerical Analysis (ETNA), Volume 51, Pages 315-330.

11. H. Nhan and T.A. Nhan (2019). Different Grouping Strategies for Cooperative Learning in English Majored Seniors and Juniors at Can Tho University, Vietnam. Education Sciences. 2019, 9, 59.

10. T.A. Nhan (2018). Cooperative Learning Activities with a Focus on Geometry Applications in a Basic Math & Pre-Algebra Class. Bay Area Active Learning Workshop, 2018. (Mathematics Education)

9. L.P. Quan and T.A. Nhan (2018). Applying Computer Algebra Systems in Approximating the Trigonometric Functions. Mathematical and Computational Applications. 2018; 23 (3):37.

8. T.A. Nhan and R. Vulanović (2018). A note on a generalized Shishkin-type mesh, Novi Sad Journal of Mathematics.  Vol. 48, No. 2, 2018, 141-150, 2018.  DOI: https://doi.org/10.30755/NSJOM.07880

7. T.A. Nhan, M. Stynes, and R. Vulanović (2018). Optimal Uniform-Convergence Results for Convection-Diffusion Problems in One Dimension Using Preconditioning. Journal of Computational and Applied Mathematics, 2018.

6. T.A. Nhan, S. MacLachlan, and N. Madden (2018). Boundary layer preconditioners for finite-element discretizations of singularly perturbed reaction-diffusion problems. Numerical Algorithms, 2017. (Cite as: Nhan, T.A., MacLachlan, S. & Madden, N. Numer Algor (2018) 79: 281. https://doi.org/10.1007/s11075-017-0437-3 )

5. R. Vulanović and T.A. Nhan (2017). A Numerical Method for Stationary Shock Problems with Monotonic Solutions, Numerical Algorithms, Vol 77 (2018), 1117--1139.

4. T.A. Nhan and R. Vulanović (2016). Preconditioning and uniform convergence for convection-diffusion problems discretized on Shishkin-type meshes. Advances in Numerical Analysis, vol. 2016, Article ID 2161279, 2016.

3. J. L. Gracia, N. Madden, and T.A. Nhan (2015). Applying a patched mesh method to efficiently solve a singularly perturbed reaction-diffusion problem. In: Bock H., Phu H., Rannacher R., Schlöder J. (eds) Modeling, Simulation and Optimization of Complex Processes HPSC 2015. Springer, Cham.

2. T.A. Nhan and N. Madden (2015). Cholesky factorisation of linear systems coming from finite difference approximations of singularly perturbed problems, Proceedings of BAIL 2014–Boundary and Interior Layers–Computational and Asymptotic Methods, Lecture Notes in Computational Science and Engineering, Springer, Berlin, Vol. 108, 2015.

1. R. Vulanović and T.A. Nhan (2014). Uniform convergence via preconditioning, International Journal of Numerical Analysis and Modeling, Series B 5, 347–356, 2014.

Theses

4. T.A. Nhan (2015). Preconditioning techniques for singularly perturbed differential equations, Ph.D. thesis, National University of Ireland Galway, September 2015. Abstract published in Irish Mathematical Society Bulletin, 76, Winter 2015. (pdf)

3. T.A. Nhan (2011). Numerical solutions of models for glucose and insulin levels in critically ill patients, M.Sc. thesis, National University of Ireland Galway, August 2011. (See here for research publications that cited this thesis)

2. T.A. Nhan (2008). The Unicity Theorem For Meromorphic Maps Of A Complete Kaehler Manifold Into P^N(C), M.Sc. thesis, Hanoi National University of Education, September 2008.

1. T.A. Nhan (2005). On the differential manifolds, B.Sc. thesis, Cantho University, May 2005.

Teaching

• Santa Clara University, Winter 2023–present: CSCI 10: Introduction to Computer Science (Three Lab Sections, Winter 2023); MATH 8: Introduction to Statistics (Spring 2023); MATH 11: Calculus and Analytic Geometry I (Spring 2023); MATH 13: Calculus and Analytic Geometry III (Fall 2023); CSCI 10: Introduction to Computer Science (Lecture and Three Lab Sections, Fall 2023); MATH 13: Calculus and Analytic Geometry III (Winter 2024); MATH 14: Calculus and Analytic Geometry IV (Winter 2024); MATH 14: Calculus and Analytic Geometry IV (Spring 2024, two sections). 
• Holy Names University, Fall 2018–May 2023: Calculus (MATH 11), Computer Coding in Python (CIDS 103), Statistics and Probability (for STEM majors, MATH 60), Statistical Methods (for Business majors, ECON 15), Precalculus (MATH 1), Algebra (MATH A & C).
• Chabot College, Spring 2018: Applied Algebra and Data Analysis (MTH 53), College Algebra (MTH 31).
• Ohlone College, Spring 2016–Summer 2018: Calculus I (MATH 101A), Calculus III (MATH 101C), Introduction to Matlab for Engineers (MATH 111), Trigonometry (MATH 181), Precalculus (MATH 188), Intermediate Algebra (MATH 153), Basic Math & Pre-Algebra (MATH 192).
• National University of Ireland Galway, Fall 2009–Spring 2015: Honours Numerical Analysis I (MA 385), Honours Numerical Analysis II (MA 378), Engineering Numerical Analysis (MA 260), Advanced Calculus I & II (MA 301 and MA 302).
• Hanoi National University of Education, Fall 2006–Spring 2008: Linear Algebra (for Physics majors, TL 18), Multivariable Calculus (TL 3).
• Cantho University, Fall 2005–Spring 2006 and Spring 2009: Analytic Geometry (for Mathematics majors), Differential Geometry and Affine Geometry (for Mathematics majors).