My research is situated in the broad field of computational mathematics. My current work focuses primarily on numerical methods for deterministic and stochastic partial differential equations.
- Create new mathematical theory and efficient numerical methods for solving problems in the physical sciences, engineering, and other fields.
Research in Detail
I have worked with integral equations, partial differential equations (both deterministic and stochastic). Apart from designing numerical methods and proving convergence, I have also designed techniques to accelerate the solution process, the so-called preconditioning techniques. Estimation of errors and adaptivity are other aspects of my research interests.
- ARC Discovery Project 2022-2024: "Novel mathematics and efficient computational techniques for human vision", ($412K; 1st CI: J. Dick, 2nd CI: T. Tran, 3rd CI: Q.T. Le Gia)
- ARC Discovery Project 2020-2022: "Mathematics for breaking limits of speed and density in magnetic memories" ($525K; 1st CI: B. Goldys, 2nd CI: T. Tran, 3rd CI: K-N Le)
- ARC Discovery Project 2019-2021: "Novel mathematics and numerical methods for ferromagnetic problems" ($315K; 1st CI: T. Tran, 2nd CI: J. Dick)
- ARC Discovery Project 2016-2018: "Novel approaches for problems with uncertainties" ($330K; 1st CI: T. Tran, 2nd CI: B. Goldys)
- UNSW Goldstar Award 2015: "Novel approaches for problems with uncertainties".
- ARC Discovery Project 2012-2014: "The mathematics of novel magnetic memory materials" ($330K; 1st CI: B. Goldys, 2nd CI: J.F. Grotowski, 3rd CI: T. Tran)
- Go8-Germany Joint Research Co-operation Scheme 2013: "Shape calculus for interface problems" (German partner: A. Chernov)
- UNSW Goldstar Award 2011: "Stochastic Landau-Lifchitz-Gilbert equation: From flows of harmonic maps to theory of novel magnetic materials" (co-CI, jointly with B. Goldys)
Current Student Projects (PhD and Honours)
Numerical methods for the Maxwell-Landau-Lifshitz-Gilbert equations.
Numerical methods for the stochastic Maxwell-Landau-Lifshitz-Gilbert equations.
Shape calculus for solving exterior boundary value problems.
If you are interested in any of the above topics, please write to me.
Advice for prospective students
The Computational Mathematics Group at UNSW is a vibrant group with extensive international collaborations and connections. If you are an enthusiastic student with strong mathematical talents and minimum skills in mathematical computing, you will find this group an attractive team to be with for a few years of your life.
TEACHING & OUTREACH
Courses I teach
MATH1251 (Mathematics for Actuarial Studies and Finance 1B - Calculus)
MATH3361/5361 (Stochastic Differential Equations: Theory, Applications, and Numerical Methods)
MATH3051 (Applied Real and Functional Analysis)
Professional affiliations and service positions
External Assessor, Universiti Putra Malaysia