scholarly journals PARALLEL APPROACH TO SOLVE OF THE DIRECT SOLUTION OF LARGE SPARSE SYSTEMS OF LINEAR EQUATIONS

2017 ◽  
Vol 13 ◽  
pp. 16
Author(s):  
Michal Bošanský ◽  
Bořek Patzák
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Distributed Memory ◽  
Linear Equations ◽  
Direct Solution ◽  
Parallel Solution ◽  
Finite Element Software ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Symmetric Systems

The paper deals with parallel approach for the numerical solution of large, sparse, non-symmetric systems of linear equations, that can be part of any finite element software. In this contribution, the differences between the sequential and parallel solution are highlighted and the approach to efficiently interface with distributed memory version of SuperLU solver is described.

Accelerated GPMHSS Method for Solving Complex Systems of Linear Equations

2017 ◽  
Vol 7 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Jing Wang ◽  
Xue-Ping Guo ◽  
Hong-Xiu Zhong
Keyword(s):  
Complex Systems ◽  
Linear Systems ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Splitting Method ◽  
Complex Symmetric Linear Systems ◽  
Systems Of Linear Equations ◽  
Complex Symmetric ◽  
Symmetric Systems

AbstractPreconditioned modified Hermitian and skew-Hermitian splitting method (PMHSS) is an unconditionally convergent iteration method for solving large sparse complex symmetric systems of linear equations, and uses one parameter α. Adding another parameter β, the generalized PMHSS method (GPMHSS) is essentially a twoparameter iteration method. In order to accelerate the GPMHSS method, using an unexpected way, we propose an accelerated GPMHSS method (AGPMHSS) for large complex symmetric linear systems. Numerical experiments show the numerical behavior of our new method.

Evaluation of Different Approaches to Solution of the Direct Solution of Large, Sparse Systems of Linear Equations

2017 ◽  
Vol 1144 ◽  
pp. 97-101
Author(s):  
Michal Bošanský ◽  
Bořek Patzák
Keyword(s):  
High Performance ◽  
Linear Equations ◽  
Object Oriented ◽  
General Purpose ◽  
Finite Element Code ◽  
Direct Solution ◽  
Iterative Solver ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Symmetric Systems

The aim of this paper is to the evaluate efficiency of differentapproaches to solution of large, sparse, non-symmetric systems of linearequations on high performance machines, that can be found in any finiteelement software. The different approaches based on direct or iterativealgorithms for solution of linear equations are compared. In particular,directs solver using Skyline sparse storage, direct solver from SuperLUlibrary, iterative solver from Iterative Method Library(IML)are compared. SuperLU is a general purpose library for the directsolution of large, sparse, nonsymmetric systems of linear equations.Additionally, the performance and scalability of parallel SuperLU solveris studied, based on OpenMP. The paper shows thatparallelization can efficiently exploit the power of modern availablehardware, significantly reducing the needed computation time.The different strategies were implemented in OOFEM which is afree finite element code with object oriented architecture for solvingmechanical, transport and fluid mechanics problems that operates onvarious platforms.

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