Emeritus Professor Stephen Roberts
Areas of expertise
- Simulation And Modelling 080110
- Numerical Solution Of Differential And Integral Equations 010302
- Water Resources Engineering 090509
- Numerical Computation 080205
- Concurrent Programming 080304
- Numerical Analysis 010301
- Analysis Of Algorithms And Complexity 080201
- Numerical And Computational Mathematics 0103
Research interests
Developer of efficient and robust numerical methods for the modelling of Tsunami and Flood events.
Lead developer at the ANU of the ANUGA hydrodynamic modelling software. ANUGA is a computational tool that models the impact of dam breaks, floods and tsunamis on communities. It is used extensively by councils, governments and consultant engineers. The software is developed in Python and C.
Developer of sparse grid methods for
Multi-dimensional function fitting and approximation of high dimensional probablitiy density functions.
Developing finite element approximation methods for thin plate spline functional smoothing which can scale to millions of data points.
Developer of Computational Science education program at ANU using Python.
Specialties:
Computational Mathematics, Tsunami modelling, Flood modelling, Multi-dimensional approximation, Python programming for Scientific computing.
Biography
Stephen Roberts was Head of the Department of Mathematics at the Australian National University from 2006-2012.
Stephen is heavily involved in the computational science community in Australia. From 2003-2006 he was the national coordinator of the Australian Partnership for Advanced Computing (APAC) Education, Outreach and Training program. He is currently the treasurer of the committee of the Computational Mathematics Group, a special interest group of ANZIAM.
His research area is the application of efficient and robust numerical methods for the solution of partial differential equations.
He is the lead developer at the ANU of the ANUGA hydrodynamic 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.
In the area of data fitting he has developed sparse grid methods for Multidimensional function fitting and approximation of high dimensional probability density functions. He has also developed finite element approximation methods for thin plate spline functional smoothing which can scale to millions of data points.
In 1980, Stephen completed his MSc Science at Flinders Univerisy, supervised by Prof Garth Gaudry, working on A_p spaces and asymmetry of L_p operator norms for convolution operators. In 1985, Stephen completed his 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.
Researcher's projects
High Dimensional Approximation and Uncertainty Quantification:
High Dimensional Approximation and Uncertainty Quantification Uncertainty quantification using sparse grid methods. Multi-dimensional function fitting and approximation of high dimensional probability density functions.
Multi-Fidelity Solution of Tsunami and Flood Models:
We are investigating the use of multi-fidelity solutions of tsunami and flood models to improve the efficiency of uncertainty quantification studies. The multi-fidelity solutions are combined using sparse grid techniques.
Solution of the Serre Equations:
Investigate the use of techniques from the numerical solution of conservation laws (approximate Riemann solvers) to accurately solve the Serre Equation, especially in the presence of large initial gradients in the initial conditions (e.g. in the case of dam breaks).
ANUGA Tsunami and Flood Modelling Software:
The ANUGA package is developed under a collaboration of the Australian National University (ANU) and Geoscience Australia (GA) - hence the name. ANUGA is a Free & Open Source Software (FOSS) package capable of modelling the impact of hydrological disasters such as dam breaks, riverine flooding, storm-surge or tsunamis.
ANUGA is based on a discretization of the Shallow Water Wave Equations onto an unstructured triangular mesh using a finite-volume numerical scheme. A major capability of ANUGA is that it can model the process of wetting and drying as water enters and leaves an area. This means that it is suitable for simulating water flow onto a beach or dry land and around structures such as buildings. ANUGA is also capable of modelling difficult flows involving hydraulic jumps and rapidly changing flow speed regimes (transitions from subcritical to supercritical flows).
The package is available from GitHub github.com//GeoscienceAustralia/anuga_corewhere we average over 200 unique visitors per month, and 30 downloads/month.
Geosciences Australia has used ANUGA extensively to quantify risk from tsunamis around the coast of Australia, It was used to develop ``Last mile evacuation'' plans for Padang, in West Sumatra. It is being used in AusAID (now part of the DFAT) programs to assess risk of flooding in Manila and risk from tsunamis in Papua New Guinea.
In 2016 we developed code to integrate BoM radar rainfall data with ANUGA, and tested the method with a simulation of the full ACT catchment. Also a simple erosion module which models the erosion of sand dunes during a tsunami has been added to ANUGA.
Also we are working with Hydrata.com to incorporate ANUGA as the modelling engine for an on-line flood modelling portal as part open collaboration platform http://chennaifloodmanagement.org/en/, a community project to help mitigate the effect of flooding in Chennai, India.
Publications
- Sun, X, Croke, B, Jakeman, A et al. 2022, 'Benchmarking Active Subspace methods of global sensitivity analysis against variance-based Sobol' and Morris methods with established test functions', Environmental Modelling and Software, vol. 149.
- Sun, X, Croke, B, Roberts, S et al. 2021, 'Comparing methods of randomizing Sobolâ€² sequences for improving uncertainty of metrics in variance-based global sensitivity estimation', Reliability Engineering & System Safety, vol. 210.
- Nielsen, O, Roberts, S, Gray, D et al. 2020, 'Hydrodynamic modelling of coastal inundation', 2005 International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, MODSIM 2005, ed. Andre Zerger & Robert M Argent, Modelling and Simulation Society of Australia and New Zealand Inc., Canberra, pp. 518-523.
- Pitt, J, Zoppou, C & Roberts, S 2018, 'Behaviour of the Serre equations in the presence of steep gradients revisited', Wave Motion, vol. 76, pp. 61-77.
- Mungkasi, S, Magdalena, I, Pudjaprasetya, R et al. 2018, 'A STAGGERED METHOD FOR THE SHALLOW WATER EQUATIONS INVOLVING VARYING CHANNEL WIDTH AND TOPOGRAPHY', International Journal for Multiscale Computational Engineering, vol. 16, no. 3, pp. 231-244pp.
- Zoppou, C, Pitt, J & Roberts, S 2017, 'Numerical solution of the fully non-linear weakly dispersive serre equations for steep gradient flows', Applied Mathematical Modelling, vol. 48, pp. 70-95.
- de Baar, J & Roberts, S 2017, 'Multifidelity Sparse-Grid-Based Uncertainty Quantification for the Hokkaido Nansei-oki Tsunami', Pure and Applied Geophysics, vol. 174, no. 8, pp. 3107-3121.
- Sun, X, Roberts, S, Croke, B et al 2017, 'A comparison of global sensitivity techniques and sampling method', 22nd International Congress on Modelling and Simulation (MODSIM2017), ed. Syme, G., Hatton MacDonald, D., Fulton, B. and Piantadosi, J, The Modelling and Simulation Society of Australia and New Zealand Inc., Australia, pp. 57-63.
- Lamichhane, B, Roberts, S & Stals, L 2016, 'A Mixed Finite Element Discretisation of Thin Plate Splines Based on Biorthogonal Systems', Journal of Scientific Computing, vol. 67, no. 1, pp. 20-42.
- Mungkasi, S & Roberts, S 2016, 'A smoothness indicator for numerical solutions to the Ripa model', International Conference on Mathematics, its Applications, and Mathematics Education, ICMAME 2015, ed. Garnadi A.D.Sunkara, IOP Publishing, TBC, pp. 1-9.
- Mungkasi, S & Roberts, S 2016, 'A smoothness indicator for numerical solutions to the Ripa model', International Conference on Mathematics, its Applications, and Mathematics Education, ICMAME 2015, ed. Garnadi A.D.Sunkara, IOP Publishing, TBC, pp. 1-9.
- Lamichhane, B, Roberts, S & Stals, L 2016, 'A Mixed Finite Element Discretisation of Thin Plate Splines Based on Biorthogonal Systems', Journal of Scientific Computing, vol. 67, no. 1, pp. 20-42.
- Zoppou, C & Pitt, J & Roberts, S 2016, 'A SOLUTION OF THE CONSERVATION LAW FORM OF THE SERRE EQUATIONS', Australian and New Zealand Industrial and Applied Mathematics Journal, vol. 57, pp. 385-394.
- Davies, G & Roberts, S 2015, 'Open source flood simulation with a 2D discontinuous-elevation hydrodynamic model', 21st International Congress on Modelling and Simulation (MODSIM2015), ed. Weber, T., McPhee, M.J. and Anderssen, R.S., The Modelling and Simulation Society of Australia and New Zealand Inc., Australia, pp. 2130-2136.
- de Baar, J, Roberts, S, Dwight, R et al 2015, 'Uncertainty quantification for a sailing yacht hull, using multi-fidelity kriging', Computers and Fluids, vol. 123, pp. 185-201.
- Hossen, M, Cummins, P, Roberts, S et al. 2015, 'Time Reversal Imaging of the Tsunami Source', Pure and Applied Geophysics, vol. 172, no. 3-4, pp. 969-984.
- Mungkasi, S, Li, Z & Roberts, S 2014, 'Weak local residuals as smoothness indicators for the shallow water equations', Applied Mathematics Letters, vol. 30, no. April 2014, pp. 51-55.
- Larson, J, Strazdins, P, Hegland, M et al. 2014, 'Managing complexity in the Parallel Sparse Grid Combination Technique', Parallel Computing, vol. 25, pp. 593-602.
- Van Drie, R, Milevski, P, Roberts, S et al 2014, 'Catchment wide hydrology using radar rainfall', 35th Hydrology and Water Resources Symposium, HWRS 2014, Conference Organising Committee, TBC, pp. 1056-1063.
- Mungkasi, S & Roberts, S 2014, 'Weak local residuals in an adaptive finite volume method for one-dimensional shallow water equations', Journal of the Indonesian Mathematical Society, vol. 20, no. 1, pp. 11-18.
- Mungkasi, S & Roberts, S 2014, 'Well-balanced computations of weak local residuals for the shallow water equations', ANZIAM Journal, vol. 56, pp. 128-147.
- Lamichhane, B, Roberts, S & Hegland, M 2014, 'A new multivariate spline based on mixed partial derivatives and its finite element approximation', Applied Mathematics Letters, vol. 35, pp. 82-85.
- Mungkasi, S & Roberts, S 2013, 'Behaviour of the numerical entropy production of the one-and-a-half- dimensional shallow water equations', 16th Biennial Computational Techniques and Applications, Australia and New Zealand Industrial and Applied Mathematics (ANZIAM), Online, pp. C18-C33.
- Mungkasi, S, Van Drie, R & Roberts, S 2013, 'Predictions on arrival times of water of the St. Francis dam break flood using ANUGA', International Congress on Modelling and Simulation MODSIM 2013, ed. Piantadosi, J., Anderssen, R.S. and Boland J., Modelling and Simulation Society of Australia and New Zealand Inc., Australia, pp. 304-309.
- Jakeman, J & Roberts, S 2013, 'Local and dimension adaptive stochastic collocation for uncertainty quantification', Lecture Notes in Computer Science (LNCS), vol. 88, pp. 181-203.
- Larson, J, Hegland, M, Harding, B et al. 2013, 'Fault-Tolerant Grid-Based Solvers: Combining Concepts from Sparse Grids and MapReduce', International Conference on Computational Science, ICCS 2013, Elsevier B.V., The Netherlands, pp. 130-139.
- Mungkasi, S & Roberts, S 2013, 'Validation of ANUGA hydraulic model using exact solutions to shallow water wave problems', 2013 International Conference on Science and Engineering in Mathematics, Chemistry and Physics, ScieTech 2013, Conference Organising Committee, Jakarta.
- Roberts, S, Oishi, Y & Li, M 2013, 'High Resolution Tsunami Inundation Simulations', International Congress on Modelling and Simulation MODSIM 2013, ed. Piantadosi, J., Anderssen, R.S. and Boland J., Modelling and Simulation Society of Australia and New Zealand Inc., Australia, pp. 310-316.
- Mungkasi, S & Roberts, S 2012, 'Analytical solutions involving shock waves for testing debris avalanche numerical models', Pure and Applied Geophysics, vol. 169, issue 10, pp. 1847-1858.
- Mungkasi, S & Roberts, G 2012, 'ANUGA software for numerical simulations of shallow water flow', Journal of Computer Science and Information, vol. 5, issue 1, pp. 1-8
- Mungkasi, S & Roberts, S 2011, 'A new analytical solution for testing debris avalanche numerical models', ANZIAM Journal, vol. 52, pp. C349-C363.
- Mungkasi, S & Roberts, S 2011, 'Numerical entropy production for shallow water flows', ANZIAM Journal, vol. 52, pp. C1-C17.
- Lamichhane, B, Roberts, S & Stals, L 2011, 'A mixed finite element discretisation of thin-plate splines', ANZIAM Journal, vol. 52, pp. C518-C534.
- Roberts, S & Wilson, P 2011, 'A well balanced scheme for the shallow water wave equations in open channels with (discontinuous) varying width and bed', ANZIAM Journal, vol. 52, pp. C967-C987.
- Mungkasi, S & Roberts, S 2011, 'A finite volume method for shallow water flows on triangular computational grids', IEEE International Conference on Advanced Computer Science and Information Systems 2011, Faculty of Computer Science, Universitas Indonesia, Depok Indonesia, pp. 79-84.
- Mungkasi, S & Roberts, S 2012, 'Approximations of the Carrier-Greenspan periodic solution to the shallow water wave equations for flows on a sloping beach', International Journal for Numerical Methods in Fluids, vol. 69, issue 4, pp. 763-780.
- Mungkasi, S & Roberts, S 2010, 'On the best quantity reconstructions for a well balanced finite volume method used to solve the shallow water wave equations with a wet/dry interface', ANZIAM Journal, vol. 51, pp. C48-C65.
- Roberts, S & Bolt, S 2009, 'A note on the convergence analysis of a sparse grid multivariate probability density estimator', ANZIAM Journal, vol. 50, no. SUPPL., pp. C858-C870.
- Roberts, S, Nielsen, O & Jakeman, J 2008, 'Simulation of Tsunami and Flash Floods', International Conference on High Performance Scientific Computing (HPSC 2006), ed. Hans Georg Bock, Ekaterina Kostina, Hoang Xuan Phy, Rolf Rannacher, Springer, Berlin, Germany, pp. 489-498.
- Stals, L & Roberts, S 2008, 'Smoothing and Filling Holes with Dirichlet Boundary Conditions', International Conference on High Performance Scientific Computing (HPSC 2006), ed. Hans Georg Bock, Ekaterina Kostina, Hoang Xuan Phy, Rolf Rannacher, Springer, Berlin, Germany, pp. 521-531.
- Stals, L & Roberts, S 2008, 'Preconditioners for low order thin plate spline approximations', in T.J. Barth, M. Griebel, D.E. Keyes, R.M. Nieminen, D. Roose, and T Schlick (ed.), Domain Decomposition Methods in Science and Engineering XVII, Springer, Germany, pp. 639-646.
- Roberts, S, Stals, L & Nielsen, O 2007, 'Parallelisation of a finite volume method for hydrodynamic inundation modelling', Computational Techniques and Applications Conference (CTAC 2006), ed. Wayne Read, A.J. Roberts, Australian Mathematical Society, Australia, pp. 558-572.
- Stals, L & Roberts, S 2006, 'Smoothing large data sets using discrete thin plate splines', Computing and Visualization in Science, vol. 9, no. 3, pp. 185-195.
- Nielsen, A, Adamantidis, C, Roberts, S et al 2006, 'A finite volume solution for a ring tank failure parametric study', Australasian Journal of Water Resources, vol. 10, no. 1, pp. 1-9.
- Stals, L & Roberts, S 2005, 'Verifying convergence rates of discrete thin-plate splines in 3{D}', Computational Techniques and Applications Conference (CTAC 2002), ed. Rob May and A. J. Roberts, Australian Mathematics Publishing Association, Australia, pp. C515-C529.
- Nielsen, O, Roberts, S, Gray, D et al. 2005, 'Hydrodymamic modelling of coastal inundation', 2005 International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, MODSIM 2005, ed. Andre Zerger & Robert M Argent, Modelling and Simulation Society of Australia and New Zealand Inc., Canberra, pp. 518-523.
- Roberts, S & Stals, L 2004, 'Discrete thin plate spline smoothing in 3d', Computational Techniques and Applications Conference (CTAC 2003), ed. Jagoda Crawford, Tony Roberts, Australian Mathematical Society, Electronic Supplement, pp. c646-c659.
- Geiger, S, Roberts, S, Matthai, S et al 2004, 'Combining finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media', Geofluids, vol. 4, pp. 284-299.
- Roberts, S, Gardner, H, Press, S et al 2004, 'Teaching computational science using vpython and virtual reality', Lecture Notes in Computer Science (LNCS), vol. 3039, pp. 1218-1225.
- Roberts, S, Hegland, M & Altas, I 2003, 'Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions', SIAM Journal of Numerical Analysis, vol. 41, no. 1, pp. 208-234.
- Zoppou, C & Roberts, S 2003, 'Explicit schemes for dam-break simulations', Journal of Hydraulic Engineering, vol. 129, pp. 11-34.
- Geiger, S, Roberts, S, Matthai, S et al 2003, 'Combining finite volume and finite element methods to simulate fluid flow in geologic media', ANZIAM Journal, vol. 44, pp. C180-C201.
- Christen, P, Hegland, M, Nielsen, O et al. 2001, 'Scalable parallel algorithms for surface fitting and data mining', Parallel Computing, vol. 27, pp. 941-961.
- Christen, P, Hegland, M, Nielsen, O et al. 2001, 'Towards a Parallel Data Mining Toolbox', International Workshop on Parallel and Distributed Data Mining in conjunction with International Parallel and Distributed Processing Symposium (IPDPS 2001), ed. Pradip Srimani, Institute of Electrical and Electronics Engineers (IEEE Inc), Piscataway, USA.
- Hegland, M, Hooker, G & Roberts, S 2000, 'Finite Element Thin Plate Splines in Density Estimation', ANZIAM Journal, vol. 42, pp. C712-C734.
- Ding, K, Kalyanasundaram, S, Grosz, L et al. 2000, 'Development of a new integration algorithm for parallel implementation of the finite element elasto-plastic analysis', ANZIAM Journal, vol. 42, pp. C561-C585.
- Zoppou, C & Roberts, S 2000, 'Numerical Solutions of the Two-Dimensional Unsteady Dam Break', Applied Mathematical Modelling, vol. 24, pp. 457-475.
- Zoppou, C, Roberts, S & Renka, R 2000, 'Exponential Spline Interpolation in Characteristic Based Scheme for Solving the Advective-Diffusion Equation', International Journal for Numerical Methods in Fluids, vol. 33, pp. 429-452.
- Christen, P, Hegland, M, Nielsen, O et al. 2000, 'Algorithms for Predictive Modelling', IEEE International Conference on Data Mining (ICDM 2000), ed. Ebecken, N and Brebbia, CA, WIT Press, Southampton, UK, pp. 423-434.
- Ding, K, Kalyanasundaram, S, Grosz, L et al. 2000, 'A Parallel three-dimensional elasto-plastic finite element analysis in a workstation cluster environment', International Symposium on Structural Failure and Plasticity (IMPLAST 2000), ed. Grzebieta, Zhao &, Pergamon-Elsevier Ltd, Oxford, UK, pp. 801 - 812.
- Roberts, S 1999, 'Comment on Space-Time Conservative Method applied to the SV Equations', Journal of Hydraulic Engineering, vol. 125, no. 8, pp. 891-892.
- Zoppou, C & Roberts, S 1999, 'Comment on Refined numerical scheme for advective transport in diffusion simulation', Journal of Hydraulic Engineering, vol. 124, no. 7, pp. 765-767.
- Zoppou, C & Roberts, S 1999, 'Catastrophic Collapse of Water Supply Reservoirs in Urban Areas', Journal of Hydraulic Engineering, vol. 125(7), pp. 686-695.
Projects and Grants
Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.
- ANUGA Enhancement: Parallelisation, Validation and Optimisation. (Note:Linked to#25733 GLC-Q4810016) (Primary Investigator)
- Detection of Co2 leaks from a geological storage site using atmospheric measurements (Primary Investigator)
- ANUGA Enhancements:Validation (Primary Investigator)
- ANUGA enhancements: parallelisation validation and optimisation (Primary Investigator)
- Robust numerical solution of partial differential equations on petascale computer systems with applications to tsunami modelling and plasma physics (Secondary Investigator)
- ANUGA Enhancements: Implementation of functionality and parallelisation for 1D structures to ANUGA (Primary Investigator)
- ANUGA Enhancements: Kinematic Viscosity, 1-D Pipe Flow and Parallelisation (Primary Investigator)
- CSIRO Flagship Top-up Scholarship for John Jakeman (Primary Investigator)