Numerical performance of preconditioning techniques for the solution of complex sparse linear systems

2002 ◽  
Vol 19 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Annamaria Mazzia ◽  
Giorgio Pini
Keyword(s):  
Linear Systems ◽  
Sparse Linear Systems ◽  
Preconditioning Techniques ◽  
Numerical Performance

scholarly journals Preconditioning for Sparse Linear Systems at the Dawn of the 21st Century: History, Current Developments, and Future Perspectives

2012 ◽  
Vol 2012 ◽  
pp. 1-49 ◽  
Author(s):  
Massimiliano Ferronato
Keyword(s):  
Linear Systems ◽  
Specific Problem ◽  
General Purpose ◽  
Sparse Linear Systems ◽  
System Matrix ◽  
Preconditioning Techniques ◽  
Key Factor ◽  
Recent Developments ◽  
Approximate Inverses ◽  
Linear Systems Of Equations

Iterative methods are currently the solvers of choice for large sparse linear systems of equations. However, it is well known that the key factor for accelerating, or even allowing for, convergence is the preconditioner. The research on preconditioning techniques has characterized the last two decades. Nowadays, there are a number of different options to be considered when choosing the most appropriate preconditioner for the specific problem at hand. The present work provides an overview of the most popular algorithms available today, emphasizing the respective merits and limitations. The overview is restricted to algebraic preconditioners, that is, general-purpose algorithms requiring the knowledge of the system matrix only, independently of the specific problem it arises from. Along with the traditional distinction between incomplete factorizations and approximate inverses, the most recent developments are considered, including the scalable multigrid and parallel approaches which represent the current frontier of research. A separate section devoted to saddle-point problems, which arise in many different applications, closes the paper.

scholarly journals Preconditioning Techniques for Sparse Linear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-3
Author(s):  
Massimiliano Ferronato ◽  
Edmond Chow ◽  
Kok-Kwang Phoon
Keyword(s):  
Linear Systems ◽  
Sparse Linear Systems ◽  
Preconditioning Techniques

Preliminary Application of Software Package GPPS to Spare Linear Systems from Meso Scale Simulation of Concrete Specimen

2014 ◽  
Vol 580-583 ◽  
pp. 2907-2911
Author(s):  
Jian Ping Wu ◽  
Huai Fa Ma ◽  
Jun Zhao ◽  
Shu Chang Wang
Keyword(s):  
Linear Systems ◽  
Software Package ◽  
Concrete Specimen ◽  
Sparse Linear Systems ◽  
Preconditioning Techniques ◽  
Subspace Iteration ◽  
Computational Performance ◽  
Parallel Preconditioning ◽  
Simple Interface ◽  
Meso Scale

The general parallel preconditioning subspace iteration software GPPS is developed based on the integration of various preconditioning methods, parallelization techniques, and subspace iterations, to solve general sparse linear systems. The software has several characteristics, including high computational performance, good readability, simple interface, and excellent scalability. In this paper, the functions of the software are outlined, and then it is used to solve the sparse linear systems from meso-scale simulation of concrete specimens. The numerical experiments show that GPPS is clearly superior to the software package AZTEC, which is used in the simulation up to now, and in addition, ICT and the parallelization technique based on factors combination outperform other preconditioning techniques integrated in the software.

Parallel algorithm for solving sparse linear systems

1996 ◽  
Vol 32 (19) ◽  
pp. 1766
Author(s):  
K.N. Balasubramanya Murthy ◽  
C. Siva Ram Murthy
Keyword(s):  
Parallel Algorithm ◽  
Linear Systems ◽  
Sparse Linear Systems

Discretisation of sparse linear systems: An optimisation approach

2015 ◽  
Vol 80 ◽  
pp. 42-49 ◽  
Author(s):  
M. Souza ◽  
J.C. Geromel ◽  
P. Colaneri ◽  
R.N. Shorten
Keyword(s):  
Linear Systems ◽  
Sparse Linear Systems
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