**Industrial Mathematics: Process tomography**

## The Kate Edger Department of Mathematics

# Industrial Mathematics: Process tomography

If we take industrial mathematics to refer to solving actual industrial problems, it may well be the most challenging field in applied mathematics. If we take into account the actual environment such as typically enormous disturbances, often highly variable operating conditions, unavoidable uncertainties and the constraints such as very limited computational time and memory, things do not get simpler.

For example, when considering imaging or control of high velocity flows, the computational times may be of the order of ten milliseconds while solution with standard approaches would typically take minutes. Thus, severe model reduction and approximations have to be made, which lead to often extensive stochastic modelling or the associated errors.

With industrial mathematics, we have concentrated in tomographic imaging of processes in chemical, pulp and paper and mining industry. Similar problems are also found in the food processing industry. With accurate imaging, the energy consumption can often be reduced significantly. Often, the amount of waste can also be reduced since more efficient mixing facilitates the use of fewer chemicals. The algorithms that were developed by the research consortium have been implemented in the technologically most advanced commercial impedance tomography systems.

### Researchers at The University of Auckland

### Other collaborators

- University of Eastern Finland, Department of Physics and Mathematics
- Numcore Ltd, Finland
- Outotec Ltd, Finland and Australia
- Metso Ltd, Finland

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**