scholarly journals Matrix Reordering Using Multilevel Graph Coarsening for ILU Preconditioning

2015 ◽  
Vol 37 (1) ◽  
pp. A391-A419 ◽  
Author(s):  
Daniel Osei-Kuffuor ◽  
Ruipeng Li ◽  
Yousef Saad
Keyword(s):  
Matrix Reordering ◽  
Ilu Preconditioning ◽  
Graph Coarsening

Characterization and Coarsening of Autonomous System Networks

2016 ◽  
pp. 148-179 ◽  
Author(s):  
Alberto Garcia-Robledo ◽  
Arturo Diaz-Perez ◽  
Guillermo Morales-Luna
Keyword(s):  
Experimental Study ◽  
Complex Network ◽  
Autonomous System ◽  
The Internet ◽  
Linear Relationships ◽  
Network Properties ◽  
Network Metrics ◽  
Graph Coarsening

This Chapter studies the correlations among well-known complex network metrics and presents techniques to coarse the topology of the Internet at the Autonomous System (AS) level. We present an experimental study on the linear relationships between a rich set of complex network metrics, to methodologically select a subset of non-redundant and potentially independent metrics that explain different aspects of the topology of the Internet. Then, the selected metrics are used to evaluate graph coarsening algorithms to reduce the topology of AS networks. The presented coarsening algorithms exploit the k-core decomposition of graphs to preserve relevant complex network properties.

Iterated Matrix Reordering

2021 ◽  
pp. 745-761
Author(s):  
Gauthier Van Vracem ◽  
Siegfried Nijssen
Keyword(s):  
Matrix Reordering

scholarly journals A Study of Accelerated Adaptive Integral Method Based on Triangle Filling Strategy

2020 ◽  
Vol 38 (3) ◽  
pp. 501-506
Author(s):  
Mingxuan Zheng ◽  
Huiling Zhao ◽  
Zhonghui Zhao
Keyword(s):  
Integral Method ◽  
Large Time ◽  
Impedance Matrix ◽  
Lu Decomposition ◽  
Slow Convergence ◽  
Threshold Criterion ◽  
Simulation Results ◽  
Ilu Preconditioning ◽  
Double Threshold ◽  
Incomplete Lu Decomposition

In order to overcome the shortcomings of large time consuming in the near matrix filling and the slow convergence in iteration of adaptive integral method (AIM), the triangle filling strategy and the double-threshold criterion are combined to accelerate the near matrix filling speed in this paper. This method separates the near matrix filling procedure and the near correction during calculation. With the help of incomplete LU decomposition, the preconditioning matrix is constructed from the sparse near matrix before near correction, which could alleviate the ill-conditioned properties of the impedance matrix. Numerical simulation results show that, the triangle filling strategy with ILU preconditioning could improve the filling speed by 2 times and the iteration converges at most 20 times faster than traditional AIM without any accuracy reduction.

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