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 …

We implement a high-order finite-element application, which performs the numerical
simulation of seismic wave propagation resulting for instance from earthquakes at the scale …

We present forward and adjoint spectral-element simulations of coupled acoustic and (an)
elastic seismic wave propagation on fully unstructured hexahedral meshes. Simulations …

On the line and its tensor products, Fekete points are known to be the Gauss--Lobatto
quadrature points. But unlike high-order quadrature, Fekete points generalize to non-tensor …

We present the main properties of the spectral-element method, which is well suited for
numerical calculations of synthetic seismograms for three-dimensional Earth models. The …

Spectral element approximations for triangles are not yet as mature as for quadrilaterals.
Here we compare different algorithms and show that using an integration rule based on …

We apply a spectral element method based upon a conforming mesh of quadrangles and
triangles to the problem of 2-D elastic wave propagation. The method retains the …

In this paper, we compare a triangle based spectral element method (SEM) with the classical
quadrangle based SEM and with a standard spectral method. For the sake of completeness …

We discuss the application of non-uniform rational B-splines (NURBS) in the scaled
boundary finite element method (SBFEM) for the solution of wave propagation problems at …