# Stephen Roberts

Professor, Undergraduate Convenor and Interim MSI Director

I am currently Interim Director of the Mathematical Sciences Institute. From 2006-2012 I was Head of the Department of Mathematics at the ANU.

I am heavily involved in the computational science community in Australia. From 2003-2006 I was the national coordinator of the Australian Partnership for Advanced Computing (APAC) Education, Outreach and Training program. I am currently the treasurer of the Computational Mathematics Group, a special interest group of ANZIAM.

My research area is the application of efficient and robust numerical methods for the solution of partial differential equations.

I am the lead developer at the ANU of the ANUGA hydrodynamic flooding and tsunami modeling software. ANUGA is an open source computational tool that models the impact of dam breaks, floods and tsunamis on communities. It is used extensively by councils, governments and consultant engineers. You can try running the code via our online clinic.

In the area of data fitting I have developed sparse grid methods for Multidimensional function fitting and approximation of high dimensional probability density functions. I also developed a finite element approximation method for thin plate spline functional smoothing which can scale to millions of data points.

In 1980, I completed my MSc at Flinders University, supervised by Prof Garth Gaudry, working on $A_p$ spaces and asymmetry of $L_p$ operator norms for convolution operators. In 1985, I completed my PhD at the University of California, Berkeley, supervised by Prof Alexandre Chorin, working on the Convergence of a random walk method for the Burgers equation.

### Research interests

Research on the efficient and robust numerical methods for the modelling of Tsunami and Flood events, in particular well-balanced finite volume and discontinuous Galerkin methods for the shallow water equations and the Serre equation.

Uncertainty quantification using sparse grid methods. Multi-dimensional function fitting and approximation of high dimensional probability density functions.Efficient methods for the Quantification of Uncertainty in modeling Tsunami and Flood events, in particular Multi-fidelity sparse grid methods.

Finite element approximation methods for thin plate spline functional smoothing which can scale to millions of data points.

Specialties:

Computational Mathematics, Tsunami modelling, Flood modelling, Uncertainty Quantification, Multi-dimensional approximation, Python programming for Scientific computing.

Past PhD Students:

### Projects

In 2020:

In 2019:

Semester 2: MATH1014 Mathematics and Applications 2
Semester 2: MATH3501 Scientific and Industrial Modelling

Semester 1: Reading Course: Mathematical Introduction to the Finite Element Mathod

In 2018:

Semester 2: MATH1014 Mathematics and Applications 2
Semester 2: MATH3501 Scientific and Industrial Modelling

Summer 2017/2018: Reading Course: Pattern Recognition and Machine Learning

In 2017:

Semester 2: MATH3501 Scientific and Industrial Modelling
Semester 2: MATH3512 Matrix Computation

Semester 1: MATH1014 Mathematics and Applications 2

In 2016:

Semester 2: MATH1013 Mathematics and Applications 1
Semester 2: MATH3501 Scientific and Industrial Modelling

Semester 1: MATH4201 Topics in Computational Mathematics. Advanced Finite Element Methods