This monograph is the first to provide a comprehensive,
self-contained and rigorous presentation of some of the most
powerful preconditioning methods for solving finite element
equations in a common block-matrix factorization framework. Topics
covered include the classical incomplete block-factorization
preconditioners and the most efficient methods such as the
multigrid, algebraic multigrid, and domain decomposition.
Additionally, the author discusses preconditioning of saddle-point,
nonsymmetric and indefinite problems, as well as preconditioning of
certain nonlinear and quadratic constrained minimization problems
that typically arise in contact mechanics. The book presents
analytical as well as algorithmic aspects. This text can serve as
an indispensable reference for researchers, graduate students, and
practitioners. It can also be used as a supplementary text for a
topics course in preconditioning and/or multigrid methods at the
graduate level.
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