Domain decomposition (DD) methods provide powerful tools for
constructing parallel numerical solution algorithms for large scale
systems of algebraic equations arising from the discretization of
partial differential equations. These methods are well-established
and belong to a fast developing area. In this volume, the reader
will find a brief historical overview, the basic results of the
general theory of domain and space decomposition methods as well as
the description and analysis of practical DD algorithms for
parallel computing. It is typical to find in this volume that most
of the presented DD solvers belong to the family of fast
algorithms, where each component is efficient with respect to the
arithmetical work. Readers will discover new analysis results for
both the well-known basic DD solvers and some DD methods recently
devised by the authors, e.g., for elliptic problems with varying
chaotically piecewise constant orthotropism without restrictions on
the finite aspect ratios.The hp finite element discretizations, in
particular, by spectral elements of elliptic equations are given
significant attention in current research and applications. This
volume is the first to feature all components of
Dirichlet-Dirichlet-type DD solvers for hp discretizations devised
as numerical procedures which result in DD solvers that are almost
optimal with respect to the computational work. The most important
DD solvers are presented in the matrix/vector form algorithms that
are convenient for practical use.
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