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 domain decomposition methods are the oldest domain decomposition methods.
They were invented by Hermann Amandus Schwarz in 1869 as an analytical tool to …

This book gives an introduction to iterative methods and preconditioning for solving
discretized elliptic partial differential equations (PDEs) and optimal control problems …

Coarse-grid correction is a key ingredient of scalable domain decomposition methods. In
this work we construct coarse-grid space using the low-frequency modes of the subdomain …

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

Abstract Domain decomposition methods (DDMs) are popular solvers for discretized
systems of partial differential equations (PDEs), with one-level and multilevel variants. These …

Abstract Domain decomposition methods are widely used and effective in the approximation
of solutions to partial differential equations. Yet the\textit {optimal} construction of these …

Optimized Schwarz methods (OSMs) use Robin transmission conditions across the
subdomain interfaces. The Robin parameter can then be optimized to obtain the fastest …

We consider one-level additive Schwarz domain decomposition preconditioners for the
Helmholtz equation with variable coefficients (modelling wave propagation in …