Computer models for how waves propagate

Daniel Appelö is an associate professor at the University of Colorado, Boulder,USA. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will be a visiting professor at the Department of Information Technology, Uppsala University.

The project involves the development of methods for computing wave propagation, such as that of acoustic or seismic waves. Perhaps there is a need to simulate how sound spreads from boats or cars, or to predict how much the ground will move during an earthquake in a place where a bridge will be built. The inverse problem is at least as important - determining the location, shape and material properties of the source of the measured waves using measurement data. Intended applications include monitoring the thickness of ice in the Arctic sea or describe the seabed in shallow waters (like the Swedish archipelago).

In order to perform numerical calculations, the commonly used differential equations need to be replaced by an algebraic equation system with a large but finite number of unknowns. For example, for sound waves, which consist of variations in air pressure, one can formulate a very large equation system for the pressure in a huge number of points in space and time, preferably evenly distributed.

The higher the accuracy, the more complicated the equations. It becomes particularly complicated if one wants to take into account the effects of buildings, topography, or differences in sound propagation velocity due to variations in the air temperature or the salinity of the water. Such variations often do not at all fit the model’s evenly spread points. The plan for the project is to investigate how different numerical calculation techniques can be combined to achieve better methods for simulation of wave phenomena.