The pronounced numerical dispersions and numerical anisotropy make solutions from the
finite element model using low-order elements unreliable for the time-harmonic acoustic …

We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with
approximating spaces made of products of low order VEM functions and plane waves. We …

A new method is introduced for solving Laplace problems on two-dimensional regions with
corners by approximation of boundary data by the real part of a rational function with fixed …

In this paper, a generalized finite element (FE) method with optimal local approximation
spaces for solving high-frequency heterogeneous Helmholtz problems is systematically …

Sound field analysis methods make it possible to characterize and reconstruct a sound field
from a limited set of observations. Classical approaches rely on the use of analytical basis …

We introduce a space–time Trefftz discontinuous Galerkin method for the first-order transient
acoustic wave equations in arbitrary space dimensions, extending the one-dimensional …

It is well known that Galerkin finite element methods suffer from pollution error when solving
wave problems. To reduce the pollution impact on the solution different approaches were …

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for
time-harmonic scattering problems of Helmholtz type with high wavenumber. On a coarse …

We present a space–time ultra-weak discontinuous Galerkin discretization of the linear
Schrödinger equation with variable potential. The proposed method is well-posed and quasi …

We present the first fast solver for the high-frequency Helmholtz equation that scales
optimally in parallel for a single right-hand side. The L-sweeps approach achieves this …