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 …

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

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

We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous
acoustic media, with online parallel complexity that scales optimally as O (NL), where N is …

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 …

Solving time-harmonic wave propagation problems in the frequency domain and within
heterogeneous media brings many mathematical and computational challenges, especially …

It is well-known that the convergence rate of non-overlapping domain decomposition
methods (DDMs) applied to the parallel finite-element solution of large-scale time-harmonic …

Generalized eigenvalue problems on the overlap (GenEO) is a method for computing an
operator-dependent spectral coarse space to be combined with local solves on subdomains …

Efficient frequency-domain full-waveform inversion (FWI) of long-offset node data can be
designed with a few discrete frequencies, which lead to modest data volumes to be …