The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

This book presents important recent developments in mathematical and computational
methods used in impedance imaging and the theory of composite materials. By augmenting …

Since the early part of the twentieth century, the use of integral equations has developed into
a range of tools for the study of partial differential equations. This includes the use of single …

The fields of photonics and phononics encompass the fundamental science of light and
sound propagation and interactions in complex structures, as well as its technological …

A survey of different representations for lattice sums for the Helmholtz equation is made.
These sums arise naturally when dealing with wave scattering by periodic structures. One of …

In this paper, we present a fast multipole-accelerated integral equation method for solving
the modified Helmholtz equation Δu (x→)-β2u (x→)= f (x→) in two dimensions. The method …

Boundary integral equations are an important class of methods for acoustic and
electromagnetic scattering from periodic arrays of obstacles. For piecewise homogeneous …

The evaluation of the interaction between objects arranged on a lattice requires the
computation of lattice sums. A scenario frequently encountered involves systems governed …

In this paper, we consider band structure calculations governed by the Helmholtz or Maxwell
equations in piecewise homogeneous periodic materials. Methods based on boundary …

We introduce a new methodology, based on new quasi-periodic Green functions which
converge rapidly even at and around Wood-anomaly configurations, for the numerical …