# Parallel multilevel block ILU preconditioning techniques for large sparse linear systems

@article{Shen2003ParallelMB, title={Parallel multilevel block ILU preconditioning techniques for large sparse linear systems}, author={Chi Shen and Jun Zhang and Kai Wang}, journal={Proceedings International Parallel and Distributed Processing Symposium}, year={2003}, pages={8 pp.-} }

We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU)factorization technique to solve large sparse linear systems on distributed memory parallel computers. The preconditioners are constructed by using the concept of block independent sets. Two algorithms for constructing block independent sets of a distributed sparse matrix are proposed. We compare a few implementations of the parallel multilevel ILU preconditioners with different block…

## 4 Citations

### Scalable Task-Oriented Parallelism for Structure Based Incomplete LU Factorization

- Computer ScienceArXiv
- 2008

This paper presents the first highly scalable parallelILU(k) algorithm, which achieves 50 times speedup with 80 nodes for general sparse matrices of dimension 160,000 that are diagonally dominant.

### Incomplete selected inversion for linear-scaling electronic structure calculations

- Computer ScienceArXiv
- 2020

The resulting incomplete PEXSI (iPEXSI) algorithm is the first linear-scaling algorithm which scales provably better than cubically even in the absence of localization, and it is hoped that this will help to further lower the critical system size where linear- scaling algorithms begin to outperform the diagonalization algorithm.

### Task-Oriented Parallel ILU(k) Preconditioning on Computer Cluster and Multi-core Machine

- Computer Science
- 2008

### A Bit-Compatible Shared Memory Parallelization for ILU(k) Preconditioning and a Bit-Compatible Generalization to Distributed Memory

- Computer Science
- 2008

TPILU(k), the first efficiently parallelized ILU( k) preconditioner that maintains this important stability property, is presented, which shows the ability to efficiently take advantage of many cores will become ever more important as the authors approach an era of many-core computing.

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