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 …

This paper presents a new non-overlapping domain decomposition method for the
Helmholtz equation, whose effective convergence is quasi-optimal. These improved …

Recent advances in graphics processing units (GPUs) technology open a new era in high
performance computing. Applications of GPUs to scientific computations are attracting a lot …

This paper presents a preconditioner for non-overlapping Schwarz methods applied to the
Helmholtz problem. Starting from a simple analytic example, we show how such a …

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

In this paper we are concerned with plane wave discretizations of nonhomogeneous
Helmholtz equation and time-harmonic Maxwell equations. To this end, we design a plane …

The efficient finite element discretization of the Helmholtz equation becomes challenging in
the medium frequency regime because of numerical dispersion, or what is often referred to …

A new hybridizable discontinuous Galerkin method, named the CHDG method, is proposed
for solving time-harmonic scalar wave propagation problems. This method relies on a …

Within the framework of the state-of-the-art, this paper presents a summary of some common
research works carried out by the authors concerning computational methods for the …

Standard numerical methods often fail to solve the Helmholtz equation accurately near
reentrant corners, since the solution may become singular. The singularity has an …