Acoustic wave simulation by spectral methods

Advantages of dealing with acoustic wave equations by high-order methods are their enhanced accuracy and the possibility of using fewer points per minimum wavelength. On the other hand, they require a more sophisticated mathematical theory. A numerical treatment by spectral weak collocation approximation is presented. Numerical aspects concerning stability, convergence and time-advancing schemes are discussed. Absorbing boundary conditions are introduced to fit realistic physical situations with a suitable mathematical description.