Accurate Predictions In A Limited Calculation Time

A wide variety of flows around us can be modelled, such as traffic flows on motorways, water flows in canals, and gas flows in the atmosphere. A computer can calculate these flows with the help of physics formulae. But even computers have difficulty in calculating, for example, how the air pressure develops over a longer period of time and in large areas.

That is because an area is divided into conceptual pieces for which, for example, the average air pressure and flow rate are calculated. The accuracy of the calculation increases if smaller pieces are used. The downside, however, is that the computer has to calculate for longer because more pieces are needed for the same area.

In his doctoral thesis Van Dam describes a method that automatically reduces the pieces in an ingenious manner. This happens for more complex changes in particular, for example during rapid changes in air pressure, or a rapid increase in traffic density (upon joining a traffic jam). The human eye can easily identify these locations, whereas a computer finds it difficult to find these and to assess their level of complexity. The new method does this in a balanced manner. This automatic focus on interesting areas enables computer simulations to provide highly accurate results within a limited calculation time.

The research was carried out at Utrecht University and funded within the programme Mathematics Applied from NWO Physical Sciences and Technology Foundation STW. This programme aims to strengthen mathematical research that is oriented to social needs.