Jacobian-free Newton–Krylov (JFNK) methods are synergistic combinations of Newton-type
methods for superlinearly convergent solution of nonlinear equations and Krylov subspace …

Publisher Summary This chapter discusses the analysis of multigrid methods. It explains
briefly the classical iterative methods for linear systems. This includes the estimate for the …

In the six years that have passed since the publication of the first edition of this book,
iterative methods for linear systems have made good progress in scientific and engineering …

Which of the following statements is true?• Users want “black box” software that they can use
with complete confidence for general problem classes without having to understand the fine …

Abstract Domain decomposition methods are designed to allow the effective numerical
solution of partial differential equations on parallel computer architectures. They comprise a …

In this paper we study diffusion schemes for dynamic load balancing on message passing
multiprocessor networks. One of the main results concerns conditions under which these …

Abstract The Neumann–Neumann algorithm is known to be an efficient domain
decomposition preconditioner with unstructured subdomains for iterative solution of finite …

Domain decomposition refers to divide and conquer techniques for solving partial differential
equations by iteratively solving subproblems defined on smaller subdomains. The principal …

Multigrid methods are among the most efficient iterative methods for the solution of linear
systems which arise in many large scale scientific calculations. Every researcher working …

Although the origins of parallel computing go back to the last century, it was only in the
1970s that parallel and vector computers became available to the scientific community. The …