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.

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.

scholarly journals A nested decomposition algorithm for parallel computations of very large sparse systems

1995 ◽  
Vol 1 (1) ◽  
pp. 41-57 ◽  
Author(s):  
D. D. Šiljak ◽  
A. I. Zečević
Keyword(s):  
Parallel Computation ◽  
Linear Equations ◽  
Parallel Computations ◽  
Decomposition Algorithm ◽  
Parallel Solution ◽  
Engineering Problems ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Block Diagonal ◽  
Large Sparse Systems

In this paper we present a generalization of the balanced border block diagonal (BBD) decomposition algorithm, which was developed for the parallel computation of sparse systems of linear equations. The efficiency of the new procedure is substantially higher, and it extends the applicability of the BBD decomposition to extremely large problems. Examples of the decomposition are provided for matrices as large as250,000×250,000, and its performance is compared to other sparse decompositions. Applications to the parallel solution of sparse systems are discussed for a variety of engineering problems.

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