Numerical Methods for High Frequency Acoustic Scattering Problems

Acoustic wave scattering problems arise in application areas as diverse as the modelling of sonar, acoustic noise barriers, and ultrasound. In many practical applications the characteristic length scale L of the domain is large compared to the wavelength  . In such cases the small dimensionless wavelength L /  leads to oscillatory solutions. In order to resolve these solutions, standard numerical schemes with piecewise polynomial approximation spaces are faced with a requirement for a fixed number of degrees of freedom per wavelength, and in order to maintain accuracy this leads to at least a linear growth in the number of degrees of freedom required as L /  decreases. This debilitating restriction has led to much recent research effort focused on the development of schemes whose computational cost does not increase significantly as L /  decreases 1 .