# Overlapping Blocks by Growing a Partition with Applications to Preconditioning

@article{Fritzsche2013OverlappingBB, title={Overlapping Blocks by Growing a Partition with Applications to Preconditioning}, author={David Fritzsche and Andreas Frommer and Stephen D. Shank and Daniel B. Szyld}, journal={SIAM J. Sci. Comput.}, year={2013}, volume={35} }

Starting from a partitioning of an edge-weighted graph into subgraphs, we develop a method which enlarges the respective sets of vertices to produce a decomposition with overlapping subgraphs. The vertices to be added when growing a subset are chosen according to a criterion which measures the strength of connectivity with this subset. By using our method on the (directed) graph associated with a matrix, we obtain an overlapping decomposition of the set of variables which can be used for…

## 6 Citations

### Overlapping for preconditioners based on incomplete factorizations and nested arrow form

- Computer ScienceNumer. Linear Algebra Appl.
- 2015

The effect of the overlapping technique on the convergence of two classes of preconditioners, on the basis of nested factorization and block incomplete LDU factorization are discussed.

### Overlapping clusters for distributed computation

- Computer ScienceWSDM '12
- 2012

This work describes a graph decomposition algorithm for the paradigm where the partitions intersect and describes a framework for distributed computation across a collection of overlapping clusters and how this framework can be used in various algorithms based on the graph diffusion process.

### Parallel alternating iterative algorithms with and without overlapping on multicore architectures

- Computer ScienceAdv. Eng. Softw.
- 2016

### Schwarz Preconditioners for Krylov Methods : Theory and Practice PI :

- Computer Science
- 2013

This work worked on combinatorial problems to help define the algebraic partition of the domains, with the needed overlap, as well as PDE-constraint optimization using the above-mentioned inexact Krylov subspace methods.

### A class of linear solvers based on multilevel and supernodal factorization

- Mathematics
- 2018

De oplossing van grote en schaarse lineaire systemen is een kritieke component van moderne wetenschap en technische simulaties. Iteratieve methoden, namelijk de klasse van moderne…

### Recycling Preconditioners for Sequences of Linear Systems and Matrix Reordering

- Computer Science
- 2015

## References

SHOWING 1-10 OF 31 REFERENCES

### Extensions of Certain Graph-based Algorithms for Preconditioning

- Computer ScienceSIAM J. Sci. Comput.
- 2007

Experiments are presented showing that for certain classes of matrices, the block Gauss-Seidel preconditionser used with the system permuted with the new algorithm can outperform the best ILUT preconditioners in a large set of experiments.

### A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs

- Computer ScienceSIAM J. Sci. Comput.
- 1998

This work presents a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of theSize of the final partition obtained after multilevel refinement, and presents a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening.

### Weighted max norms, splittings, and overlapping additive Schwarz iterations

- Computer ScienceNumerische Mathematik
- 1999

Weighted max-norm bounds are obtained for Algebraic Additive Schwarz Iterations with overlapping blocks for the solution of Ax = b, when the coefficient matrix A is an M-matrix and a new theorem concerning P-regular splittings is presented which provides a useful tool for the A- norm bounds.

### A Block Ordering Method for Sparse Matrices

- Computer ScienceSIAM J. Sci. Comput.
- 1990

A method is presented based on combinatorial considerations which permutes the rows and columns of a general matrix in such a way that relatively dense blocks of various sizes appear along the diagonal.

### ILUT: A dual threshold incomplete LU factorization

- Computer ScienceNumer. Linear Algebra Appl.
- 1994

This ILUT factorization extends the usual ILU(O) factorization without using the concept of level of fill-in, and is a compromise between these two extremes.

### An Algebraic Convergence Theory for Restricted Additive Schwarz Methods Using Weighted Max Norms

- Computer Science, MathematicsSIAM J. Numer. Anal.
- 2001

A comparison theorem with respect to the classical additive Schwarz method makes it possible to indirectly get quantitative results on rates of convergence which otherwise cannot be obtained by the theory.

### Domain decomposition methods : algorithms and theory

- Mathematics
- 2005

The purpose of this text is to offer a comprehensive and self-contained presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element…

### The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices

- Computer ScienceSIAM J. Matrix Anal. Appl.
- 1999

This work considers techniques for permuting a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value and indicates several cases where such a permutation can be useful.

### Solving unsymmetric sparse systems of linear equations with PARDISO

- Computer ScienceFuture Gener. Comput. Syst.
- 2002

### Iterative Solution of Large Sparse Systems of Equations

- Computer Science
- 1993

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods…