We present a review of the application of the spectral-element method to regional and global
seismology. This technique is a high-order variational method that allows one to compute …

We review key ingredients that are needed for high-fidelity simulation of earthquake-
generated seismic waves in large regions. Specifically, we survey existing literature on wave …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

A new class of high-order numerical methods for approximating nonlinear conservation laws
is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on …

The scaled boundary finite element method is extended to solve problems of structural
dynamics. The dynamic stiffness matrix of a bounded (finite) domain is obtained as a …

Spectral and pseudospectral methods have become increasingly popular as higher order
methods for the solution of partial differential and integral equations (Azaïez et al. 2013). A …

In this article, we investigate the behavior of the condition number of the stiffness matrix
resulting from the approximation of a 2D Poisson problem by means of the virtual element …

The purpose of this paper is to give an upscaling tool valid for the wave equation in general
elastic media. This paper is focused on P–SV wave propagation in 2-D, but the methodology …

We present numerical tests of the virtual element method (VEM) tailored for the discretization
of a three dimensional Poisson problem with high-order “polynomial” degree (up to p= 10) …

This paper presents a new approach, referred to here as the two-dimensional spectral-
Tchebychev (2D-ST) technique, to predict the dynamics of thick plates having arbitrary …