Computational mathematics

About

Our group has 6 continuing and 6 contract staff. The group members have wide range of research interests in developing numerical methods for solving various application problems. We focus on algorithm designs, numerical implementation and theoretical analysis.

Capabilities

The group members have long term experience with their research areas. In particular the research of our group addresses the following aspects of computational and applied mathematics:

  • Computational PDEs
  • Computational topology and algebraic geometry
  • Environmental science
  • Inverse problems
  • Modelling
  • Numerical linear algebra
  • Optimisation
  • Plasma physics
  • Theoretical astrophysics

Reasons to work with us

  • Our group members have long term experience with their research areas which typically tie with practical applications and government or industrial partners. Examples include fluid dynamics and the River Darling Basin Authority, inverse problems and the Australian Signals Directorate, fusion energy and the Australian Nuclear and Science and Technology Organisation, and seismology and GeoSciences Australia.
  • Completed HDR students routinely find employment in top international research agencies (e.g. US Department of Energy), or pursue higher degree studies in world leading universities in US and UK (e.g. Oxford).
  • Exposure to broader research challenges through the Mathematics and Computational Sciences Seminar Series, a joint initiative between MSI and Computational Science.
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Project Supervisors
Efficient numerical methods for 3D underwater acoustic wave propagation
Adaptive sparse grids
Advanced computational techniques
Clustering techniques
Computational applications of Multiple Region relaXed MHD (MRxMHD)
Discontinuous Galerkin method for the shallow water wave equation using physics based numerical fluxes
Domain decomposition/Multiscale physics
Edge Localised Modes – linear stability and dynamics
Energetic Particle Physics of the International Thermonuclear Experimental Reactor (ITER)
Equilibrium and stability of ITER configurations with resonant magnetic perturbation
Evaluation of hydrological models
Exploring Adaptive Mesh Refinement strategies for dynamic earthquake rupture modeling with ExaHyPE
Fault tolerant algorithms
High dimensional approximation
Mimetic and stable numerical methods for nonlinear shallow water equations
Navier Stokes equation with free boundaries
Parallel high-dimensional density estimation
Particle orbits in magnetic islands and chaotic magnetic field
Quantum computing of fusion plasmas
Reduced models in Plasma Cylinder
Scalable Fault-tolerant PDE Solvers
Sensitivity Analysis of environmental models
Shaping value of information to real world conditions in water decision making
Statistical shape analysis using algebraic topology
Synthetic diagnostics for global computer networks and fusion power experiments
Synthetic Diagnostics for Prediction, Control and Integrated modelling in ITER
The thermodynamics (and entropy) of redistribution of energetic ions due to wave-particle interaction
Thin plate splines
Tsunami and flood modelling
Upwind summation-by-parts (SBP) finite difference methods for 3D seismic wave propagation in complex geometries
Well-posed and stable boundary conditions for bedload transport equation (the 2D Exner Equation)