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 …

We present in this paper a unified framework for analyzing the spectral methods in
unbounded domains using mapped Jacobi, Laguerre and Hermite functions. A detailed …

Along with finite differences and finite elements, spectral methods are one of the three main
methodologies for solving partial differential equations on computers. This book provides a …

Since the middle of the last century, computing power has increased sufficiently that the
direct numerical approximation of Maxwell's equations is now an increasingly important tool …

This chapter is devoted to the finite element analysis of Helmholtz problems on bounded
domains. Speaking of “Finite Element Analysis,” we elaborate on the computational analysis …

While numerically solving a problem initially formulated on an unbounded domain, one
typically truncates this domain, which necessitates setting the artificial boundary conditions …

Artificial boundary method is widely used in the numerical modeling of unbounded wave
problem. However, the accurate modeling of truncated infinite domain with general …

Nonreflecting boundary conditions for problems of wave propagation are nonlocal in space
and time. While the nonlocality in space can be efficiently handled by Fourier or spherical …

A novel artificial boundary method called the scaled boundary perfectly matched layer
(SBPML) is proposed for the transient analysis of elastic wave propagation in unbounded …

Our interest in the study and computation of electromagnetic fields started during the 1990s.
For Franck Assous, it originated from the need to compute precisely the motion of charged …