A review of finite-element methods for time-harmonic acoustics

By L. Thompson. 2006

416 citations recorded by the source corpus.

State-of-the-art finite-element methods for time-harmonic acoustics governed by the Helmholtz equation are reviewed. Four major current challenges in the field are specifically addressed: the effective treatment of acoustic scattering in unbounded domains, including local and nonlocal absorbing boundary conditions, infinite elements, and absorbing layers; numerical dispersion errors that arise in the approximation of short unresolved waves, polluting resolved scales, and requiring a large computational effort; efficient algebraic equation solving methods for the resulting complex-symmetric (non-Hermitian) matrix systems including sparse iterative and domain decomposition methods; and a posteriori error estimates for the Helmholtz operator required for adaptive methods. Mesh resolution to control phase error and bound dispersion or pollution errors measured in global norms for large wave numbers in finite-element methods are described. Stabilized, multiscale, and other wave-based discretization methods dev...

Subfields: Electrical and Electronic Engineering, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/31f794b62b1ba231cd42d924769e943c61adb333

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In Electrical and Electronic Engineering

In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

The Boundary Element Method in Acoustics: A Survey (2019, methodology): “The transient acoustic field can be computationally modelled by the finite element method [22,23], the finite difference—time domain method (a particular finite difference method that was originally developed for electromagnetic simulation [24–26]) can also be applied in acoustics [27–30]) and the b”
Duality and unified analysis of discrete approximations in structural dynamics and wave propagation : Comparison of p-method finite elements with k-method NURBS (2008, background): “In [22], Thompson and Pinsky consider the 1D eigenproblem corresponding to the vibration of a fixed-fixed rod of unit length, discretiz d with 21 degreesof-freedom (19 after imposing the boundary conditions) andwith quadratic interpolations; in particular, they study the finite element approximation”