A survey of finite element methods for time-harmonic acoustics

Many of the current issues and methodologies related to finite element methods for time-harmonic acoustics are reviewed. The effective treatment of unbounded domains is a major challenge. Most prominent among the approaches that have been developed for this purpose are absorbing boundary conditions, infinite elements, and absorbing layers. Standard computational methods are unable to cope with wave phenomena at short wave lengths due to resolutions required to control dispersion and pollution errors, leading to prohibitive computational demands. Since computation naturally separates the scales of a problem according to the mesh size, multiscale considerations provide a useful framework for viewing these difficulties and developing methods to counter them. Other issues addressed are related to the efficient solution of systems of specialized algebraic equations, and inverse problems of acoustics. The tremendous progress that has been made in all of the above areas in recent years will surely continue, leading to many more exciting developments.