The purpose of this text is to offer an overview of the most popular domain decomposition
methods for partial differential equations (PDEs). The presentation is kept as much as …

Solving time-harmonic wave propagation problems by iterative methods is a difficult task,
and over the last two decades an important research effort has gone into developing …

A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D
Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) …

This paper presents a preconditioner for non-overlapping Schwarz methods applied to the
Helmholtz problem. Starting from a simple analytic example, we show how such a …

This paper deals with the design and validation of accurate local absorbing boundary
conditions set on convex polygonal and polyhedral computational domains for the finite …

This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations
with absorption, where the PDE is discretised using curl-conforming finite-element methods …

Schwarz methods use a decomposition of the computational domain into subdomains and
need to impose boundary conditions on the subdomain boundaries. In domain truncation …

A new construction of an absorbing boundary condition for indefinite Helmholtz problems on
unbounded domains is presented. This construction is based on a near-best uniform rational …

A non-overlapping domain decomposition method (DDM) is proposed for the parallel finite-
element solution of large-scale time-harmonic wave problems. It is well-known that the …

The time-harmonic Maxwell equations describe the propagation of electromagnetic waves
and are therefore fundamental for the simulation of many modern devices we have become …