Trefftz methods are finite element-type schemes whose test and trial functions are (locally)
solutions of the targeted differential equation. They are particularly popular for time …

Computational modeling remains key to the acoustic design of various applications, but it is
constrained by the cost of solving large Helmholtz problems at high frequencies. This paper …

To evaluate the computational performance of high‐order elements, a comparison based on
operation count is proposed instead of runtime comparisons. More specifically, linear versus …

The application of computational modelling to wave propagation problems is hindered by
the dispersion error introduced by the discretisation. Two common strategies to address this …

We propose an original method based on generalized plane waves and approximated
coefficients for the numerical approximation of the Helmholtz equation with a smooth …

Progress in the development of coupled atomistic–continuum methods for simulations of
critical dynamic material behavior has been hampered by a spurious wave reflection …

We have developed two finite element techniques with reduced dispersion for linear
elastodynamics that are used with explicit time-integration methods. These techniques are …

In general, numerical concerns in simulation of time harmonic acoustic waves are mainly
due to the dispersion errors and the demands in modeling the problems with higher number …

A high‐fidelity finite element model is proposed for the complete simulation of the time‐
harmonic acoustic propagation in wind instruments. The challenge is to meet the extremely …

SUMMARY Three Galerkin methods—continuous Galerkin, Compact Discontinuous
Galerkin, and hybridizable discontinuous Galerkin—are compared in terms of performance …