Abstract
These lecture notes concerns the iterative solution, by domain decomposition methods, of the often huge linear system of algebraic equations which arise when elliptic problems are discretized by finite elements. These algorithms are preconditioned conjugate gradient methods, or more generally, preconditioned Krylov space methods, where the preconditioner is constructed from smaller instances of a given discrete elliptic problem, typically defined by restricting the domain of definition to many small subregions of the given region on which the elliptic problem is defined. These algorithms are designed with parallel computing in mind.
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