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## Data Approximation

A mathematical model is the key to understanding the behaviour of a measurement system and interpreting the data it produces. Models are developed on the basis of physical theory and from the analysis of data.

## What We Do

Our discrete and continuous mathematical modelling activity encompasses:

• modelling of physical systems
• development of empirical models
• simulation
• data visualisation
• mathematical modelling for biotechnology applications
• running training courses

### Discrete Modelling

Discrete modelling involves the modelling of discrete data, i.e., data that represent a finite number of attributes of a system in a finite number of states, typically described by algebraic equations. It covers such areas as model construction, data approximation and smoothing and signal processing. The classic example is the fitting of a straight line to measurement data.

### Continuous Modelling

Continuous models describe a physical problem using ordinary or partial differential equations. In general, such models do not have analytic solutions and so they require approximate solution methods such as finite elements, finite differences, boundary elements, and finite volumes. Typically these methods involve splitting the region of interest into a set of small elements, producing a discrete approximation of the differential equation in each element, and solving all of the discrete approximations simultaneously. Continuous modelling is used in many fields, including stress analysis, heat flow, acoustic and electromagnetic wave propagation, and vibrational analysis.

## Background Material

Last Updated: 13 Apr 2012
Created: 5 Jun 2007