Acoustics

Abstract

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. Three 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; the effective treatment of unbounded domains by domain‐based methods; and parallel iterative methods for large complex, ill‐conditioned and possibly indefinite equation systems for high‐frequency problems. A priori error estimates, including both dispersion (phase error) and global pollution effects for moderate to large wave numbers 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. Numerical methods for direct solution of the acoustic wave equation in the time domain are also reviewed.