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- Xiao-Chuan Cai, Marcus Sarkis
- SIAM J. Scientific Computing
- 1999

We introduce some cheaper and faster variants of the classical additive Schwarz preconditioner (AS) for general sparse linear systems and show, by numerical examples, that the new methods areâ€¦ (More)

- Xiao-Chuan Cai, David E. Keyes
- SIAM J. Scientific Computing
- 2002

Inexact Newton algorithms are commonly used for solving large sparse nonlinear system of equations F (uâˆ—) = 0 arising, for example, from the discretization of partial differential equations. Evenâ€¦ (More)

- Xiao-Chuan Cai, Olof B. Widlund
- SIAM J. Scientific Computing
- 1992

Iterative methods for linear systems of algebraic equations arising from the finite element discretization of nonsymmetric and indefinite elliptic problems are considered. Methods previously known toâ€¦ (More)

This paper begins with an introduction to additive and multiplicative Schwarz methods. A two-level method is then reviewed and a new result on its rate of convergence is established for the case whenâ€¦ (More)

- Xiao-Chuan Cai, William Gropp, David E. Keyes
- Numerical Lin. Alg. with Applic.
- 1994

In recent years competitive domain decomposed preconditioned iterative tech niques have been developed for nonsymmetric elliptic problems In these tech niques a large problem is divided into manyâ€¦ (More)

- Xiao-Chuan Cai
- 1991

In this paper, we consider the solution of linear systems of algebraic equations that arise from parabolic finite element problems. We introduce three additive Schwarz type domain decompositionâ€¦ (More)

- Xiao-Chuan Cai, Yousef Saad
- Numerical Lin. Alg. with Applic.
- 1996

Domain decomposition methods for Finite Element problems using a partition based on the underlying nite element mesh have been extensively studied In this paper we discuss algebraic extensions of theâ€¦ (More)

Iterative methods for linear systems of algebraic equations arising from the nite element discretization of nonsymmetric and indeenite elliptic problems are considered. Methods previously known toâ€¦ (More)

We introduce some cheaper and faster variants of the classical additive Schwarz preconditioner (AS) for general sparse linear systems and show, by numerical examples, that the new methods areâ€¦ (More)

- Jinchao Xu, Xiao-Chuan Cai
- 1992

A preconditioning technique is proposed for nonsymmetric or indefinite linear systems of equations. The main idea in our theory, roughly speaking, is first to use some "coarser mesh" space to correctâ€¦ (More)