A Parallel Multistage ILU Factorization Based on a Hierarchical Graph Decomposition

A Parallel Multistage ILU Factorization Based on a Hierarchical Graph Decomposition

PHIDAL (Parallel Hierarchical Interface Decomposition ALgorithm) is a parallel incomplete factorization method which exploits a hierarchical interface decomposition of the adjacency graph of the coefficient matrix. The idea of the decomposition is similar to that of the well-known wirebasket techniques used in domain decomposition. However, the method is devised for general, irregularly structu...

Parallel Multistage Preconditioners Based on a Hierarchical Graph Decomposition for SMP Cluster Architectures with a Hybrid Parallel Programming Model

In this work, the Parallel Hierarchical Interface Decomposition Algorithm (PHIDAL) and a hybrid parallel programming model were applied to finite-element based simulations of linear elasticity problems in media with heterogeneous material properties using parallel preconditioned iterative solvers. Reverse Cuthill-McKee reordering with cyclic multicoloring (CM-RCM) was applied for parallelism on...

Multilevel ILU decomposition

In this paper, the multilevel ILU (MLILU) decomposition is introduced. During an incomplete Gaussian elimination process new matrix entries are generated such that a special ordering strategy yields distinct levels. On these levels, some smoothing steps are computed. The MLILU decomposition exists and the corresponding iterative scheme converges for all symmetric and positive deenite matrices. ...

Hierarchical Verb Clustering Using Graph Factorization

Most previous research on verb clustering has focussed on acquiring flat classifications from corpus data, although many manually built classifications are taxonomic in nature. Also Natural Language Processing (NLP) applications benefit from taxonomic classifications because they vary in terms of the granularity they require from a classification. We introduce a new clustering method called Hie...

Parallel Multistage Preconditioners by Extended Hierarchical Interface Decomposition for Ill-Conditioned Problems