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We have divided this book into five main chapters. Chapter 1 gives the motivation for this book and the use of templates. Chapter 2 describes stationary and nonstationary iterative methods. In this chapter we present both historical development and state-of-the-art methods for solving some of the most challenging computational problems facing researchers.… (More)
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Second order elliptic partial differential equations arise in many important applications, including flow through porous media, heat conduction, and the distribution of electrical or magnetic potential. The prototype is the Laplace problem, which in discrete form produces a coefficient matrix that is relatively easy to solve in a regular domain. However,… (More)
A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions, SIAM J. Numer. An optimal preconditioner for a class of saddle point problems with a penalty term, Tech. Howard Elman and Axel Klawonn for many helpful discussions and suggestions.