Numerical Analysis: Gaussian beam approximations
Development and analysis of Gaussian beam methods for high frequency waves.
The goal of this project is to investigate the use of Gaussian beams as a tool for numerical approximation of high frequency wave propagation. This is a classical approximation which has recently attracted much renewed interest. A particular attractive feature is that, in contrast to standard geometrical optics, Gaussian beams remains accurate also at caustics. Our main goals are to obtain a better theoretical understanding of the errors in Gaussian beam approximations, to develop novel numerical Gaussian beam methods and to apply them to new types of problems.