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Overview

We focus on developing and analysing mathematical models and solving mathematical problems using numerical methods and computer simulation.

Our applied and computational mathematics discipline is devoted to:

  • teaching mathematics with an emphasis on mathematical modelling and numerical simulation
  • research to develop new fundamental knowledge in mathematics
  • applying new models, algorithms and software to solve complex problems for our partners in academia, industry and government.
Professor Scott McCue
Discipline Leader, Applied and Computational Mathematics

Our experts

Our discipline brings together a diverse team of experts who deliver world-class education and achieve breakthroughs in research.

Explore our staff profiles to discover the amazing work our researchers are contributing to.

Meet our experts

Professor Kevin Burrage
Position
Professor of Computational Maths
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Statistics
Email
Professor Fawang Liu
Position
Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Numerical and Computational Mathematics
Applied Mathematics
Email
Professor Scott McCue
Position
Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research field
Applied Mathematics
Email
Professor Matthew Simpson
Position
Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Other Mathematical Sciences
Email
Professor Ian Turner
Position
Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Numerical and Computational Mathematics
Applied Mathematics
Email
Associate Professor Michael Bode
Position
Associate Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Email
Associate Professor Timothy Moroney
Position
Associate Professor in Mathematics
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research field
Numerical and Computational Mathematics
Email
Dr Wang Jin
Position
Vice Chancellor's Research Fellow in Mathematical Biology
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Email
Dr Pamela Burrage
Position
Senior Lecturer
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Numerical and Computational Mathematics
Applied Mathematics
Email
Dr Elliot Carr
Position
Senior Lecturer
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Email
Dr Petrus van Heijster
Position
Senior Lecturer
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Pure Mathematics
Numerical and Computational Mathematics
Email
Dr Robyn Araujo
Position
Lecturer
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Email

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Teaching

We offer a major that provides students the opportunity to combine their studies in mathematics with real-world applications and computational simulations.

Students can use these computer simulation and visualisation techniques in many research projects, from bone fracture and wound healing to modelling saltwater intrusion in coastal systems.

Bachelor of Mathematics (Applied and Computational Mathematics)

Industry learning

Students in our capstone unit have worked with Australasian Groundwater and Environmental Consultants (AGE) to model and analyse groundwater flow in aquifer systems used for crop irrigation across regional Queensland.

Through a combination of mathematical modelling and computational algorithms, students simulated different groundwater pumping scenarios and devised strategies to ensure this natural resource was being used sustainably.

This project brought together three years of learning in modelling and computation and provided valuable experience in teamwork, communication, the nature and language of industry projects.

Research

Our discipline’s research has contributed to new advancements and insights into a wide variety of practical applications, including:

  • agrichemical spraying of plants
  • battery technology
  • coal seam gas production
  • electrical activity of the heart
  • growth of cancerous tumours
  • management of coastal aquifers.
  • sugar cane production
  • wood drying processes
  • wound healing.

Research themes

Mathematical modelling of physical processes with industrial applications

  • electrochemical systems and solar cells
  • fluid dynamics, bubbles and droplets
  • heat and mass transfer
  • hydrology and groundwater flow
  • multi-scaled modelling
  • porous materials
  • phase-change phenomena
  • transport theory.

Computational simulation of large, multi-scaled or complex systems

  • computational efficiency
  • high performance computing
  • parallel computing with GPU hardware
  • numerical linear algebra
  • numerical methods
  • quantifying uncertainty
  • scientific computing and visualisation
  • stochastic simulation.

Modelling processes in biology, ecology and medicine

  • cardiac modelling
  • collective cell motion
  • computational biology
  • fracture healing
  • gene regulation
  • infectious disease modelling
  • intra-cellular processes
  • pattern formation
  • regulation of musculoskeletal tissues
  • tissue engineering
  • tumour growth and invasion
  • wound healing processes.

New mathematical techniques and analysis of mathematical models

  • analysis of differential equations
  • analysis of stochastic models
  • applied complex analysis
  • asymptotic analysis and perturbation methods
  • geometric singular perturbation theory
  • mathematical cryptology
  • numerical analysis.

Projects

Mathematical and computational analysis of ship wakes

Project leaders
Dates

2018-2020

Project summary

This project aims to develop mathematical and computational tools to compute the energy in a given ship wake and to determine a range of properties of a ship by taking simple measurements of the water height as the ship travels past.

The expected outcomes should have direct implications for measuring damage to coastal zones by ship wakes and for surveillance of shipping channels.

A unifying framework for generalised distributed-order fractional models

Project leaders
Dates

2018-2020

Project summary
This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous media.

Expected outcomes of the project include an evaluation of dimensionality and/or complexity reduction of the governing equations in fractional transport models with a focus on groundwater applications.

Mathematical models of cell migration in three-dimensional living tissues

Project leader

Professor Matthew Simpson

Dates

2017-2020

Project summary
This project aims to develop mathematical models of cell migration in crowded, living tissues. Existing models rely solely on stochastic simulations, and therefore provide no general mathematical insight into how properties of the crowding environment (obstacle shape, size, density) affect the migration of cells through that environment.

This project will produce mathematical analysis, mathematical calculations and exact analytical tools that quantify how the crowding environment in threedimensional living tissues affects the migration of cells within these tissues. Long term effects will be the translation of this new mathematical knowledge into decision support tools for researchers from the life sciences.

Mathematical and computational models for agrichemical retention on plants

Project leader

Professor Scott McCue

Dates

2016-2019

Project summary
This project aims to build interactive software that simulates agrichemical spraying for multiple virtual plants reconstructed from scanned data. Mathematical modelling and computer simulation could offer an alternative to expensive experimental programs for agrichemical spraying of plants.

This project will use contemporary fluid mechanics to build practical mathematical models for droplet impaction, spreading and evaporation on leaf surfaces, and experimentally calibrate and validate the models.

View our student topics

Partnerships

Our industry and community partners have included:

Industry and community

Universities and institutes

Ask us about becoming a partner

Contact us