Acoustics

State-of-the-art computational methods for linear acoustics are reviewed. The equations of linear acoustics are summarized and then transformed to the frequency domain for time-harmonic waves governed by the Helmholtz equation. Two major current challenges in the field are specifically addressed: Numerical dispersion errors that arise in the approximation of short unresolved waves, polluting resolved scales, and requiring a large computational effort; and the effective treatment of unbounded domains by domain-based methods. A discussion of the indefinite sesquilinear forms in the corresponding weak form are summarized. A priori error estimates, including both dispersion (phase error) and global pollution effects for moderate to large wave numbers in finite element methods are discussed. Stabilized and other wave-based discretization methods are reviewed. Domain based methods for modeling exterior domains are described including Dirichlet-to-Neumann (DtN) methods, absorbing boundary conditions, infinite elements, and the perfectly matched layer (PML). Efficient equation solving methods for the resulting complex-symmetric, (non-Hermitian) matrix systems are discussed including parallel iterative methods and domain decomposition methods including the FETI-H method. Numerical methods for direct solution of the acoustic wave equation in the time-domai