GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
SIAM Journal on Scientific and Statistical Computing
Dynamic load balancing for distributed memory multiprocessors
Journal of Parallel and Distributed Computing
An analysis of some element-by-element techniques
Computer Methods in Applied Mechanics and Engineering
Some domain decomposition algorithms for elliptic problems
Iterative methods for large linear systems
A taxonomy for conjugate gradient methods
SIAM Journal on Numerical Analysis
Performance of dynamic load balancing algorithms for unstructured mesh calculations
Concurrency: Practice and Experience
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
A parallel implementation of an iterative substructuring algorithm for problems in three dimensions
SIAM Journal on Scientific Computing
Parallel efficiency of domain decomposition methods
Parallel Computing
An improved spectral graph partitioning algorithm for mapping parallel computations
SIAM Journal on Scientific Computing
PARMESH—a parallel mesh generator
Parallel Computing
SIAM Journal on Numerical Analysis
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
SIAM Journal on Scientific Computing
The Incomplete Factorization Multigraph Algorithm
SIAM Journal on Scientific Computing
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Parallel optimisation algorithms for multilevel mesh partitioning
Parallel Computing - Special issue on graph partioning and parallel computing
Parallel preconditioners based upon domain decomposition
Parallel and distributed processing for computational mechanics
SIAM Journal on Scientific Computing
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Object oriented implementation of distributed finite element analysis in .NET
Advances in Engineering Software
Object-oriented programming of distributed iterative equation solvers
Computers and Structures
Advances in Engineering Software
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Domain decomposition methods have been applied to the solution of engineering problems for many years. Over the past two decades however the growth in the use of parallel computing platforms has ensured that interest in these methods, which offer the possibility of parallelism in a very natural manner, has become greater than ever. This interest has led to research that has yielded significant advances in both the theoretical understanding of the underlying mathematical structure behind domain decomposition methods and in the variety of domain decomposition algorithms that are available for use by the engineering community. In this paper we provide a brief overview of some of the main categories of domain decomposition algorithm and then focus on a particular variant of the overlapping Schwarz algorithm that is based upon the use of a hierarchy of finite element grids. Throughout the paper we consider domain decomposition methods as preconditioners for standard, Krylov subspace, iterative solvers however they may also be used directly as iterative methods in their own right. All of the theoretical results that are described apply equally in both cases.