This article discusses finite element Galerkin schemes for a number of linear model
problems in electromagnetism. The finite element schemes are introduced as discrete …

A common method for numerically solving wave problems in unbounded domains is based
on truncating the infinite domain via an artificial boundary B, thus defining a finite …

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 …

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

We consider the efficient evaluation of accurate radiation boundary conditions for time
domain simulations of wave propagation on unbounded spatial domains. This issue has …

This lecture presents the perfectly matched layer (PML) absorbing boundary condition (ABC)
used to simulate free space when solving the Maxwell equations with such finite methods as …

The heterogeneous multi-scale method (HMM) is a general strategy for dealing with
problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies …

I review the development of numerical evolution codes for general relativity based upon the
characteristic initial-value problem. Progress in characteristic evolution is traced from the …

A high‐order local transmitting boundary is developed to model the propagation of elastic
waves in unbounded domains. This transmitting boundary is applicable to scalar and vector …

Perhaps the defining feature of waves is the fact that they propagate long distances relative
to their characteristic dimension, the wavelength. This allows us to use them to probe the …