Exploiting Task-Parallelism in Message-Passing Sparse Linear System Solvers Using OmpSs

2016 ◽  
pp. 631-643 ◽  
Author(s):  
José I. Aliaga ◽  
María Barreda ◽  
Matthias Bollhöfer ◽  
Enrique S. Quintana-Ortí
Keyword(s):  
Linear System ◽  
Message Passing ◽  
Task Parallelism ◽  
Sparse Linear System

scholarly journals Solutions of reaction-diffusion equations using similarity reduction and HSSOR iteration

2019 ◽  
Vol 16 (3) ◽  
pp. 1430
Author(s):  
Nur Afza Mat Ali ◽  
Rostang Rahman ◽  
Jumat Sulaiman ◽  
Khadizah Ghazali
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Iterative Method ◽  
Iterative Methods ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Sparse Linear System ◽  
Successive Over Relaxation ◽  
Number Of Iterations

<p>Similarity method is used in finding the solutions of partial differential equation (PDE) in reduction to the corresponding ordinary differential equation (ODE) which are not easily integrable in terms of elementary or tabulated functions. Then, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is applied in solving the sparse linear system which is generated from the discretization process of the corresponding second order ODEs with Dirichlet boundary conditions. Basically, this ODEs has been constructed from one-dimensional reaction-diffusion equations by using wave variable transformation. Having a large-scale and sparse linear system, we conduct the performances analysis of three iterative methods such as Full-sweep Gauss-Seidel (FSGS), Full-sweep Successive Over-Relaxation (FSSOR) and HSSOR iterative methods to examine the effectiveness of their computational cost. Therefore, four examples of these problems were tested to observe the performance of the proposed iterative methods.  Throughout implementation of numerical experiments, three parameters have been considered which are number of iterations, execution time and maximum absolute error. According to the numerical results, the HSSOR method is the most efficient iterative method in solving the proposed problem with the least number of iterations and execution time followed by FSSOR and FSGS iterative methods.</p>

scholarly journals Leveraging task-parallelism in message-passing dense matrix factorizations using SMPSs

2014 ◽  
Vol 40 (5-6) ◽  
pp. 113-128 ◽  
Author(s):  
Alberto F. Martín ◽  
Ruymán Reyes ◽  
Rosa M. Badia ◽  
Enrique S. Quintana-Ortí
Keyword(s):  
Message Passing ◽  
Matrix Factorizations ◽  
Task Parallelism ◽  
Dense Matrix

scholarly journals Parallelization of the solve phase in a task-based Cholesky solver using a sequential task flow model

2019 ◽  
Vol 34 (3) ◽  
pp. 340-356
Author(s):  
Sébastien Cayrols ◽  
Iain S Duff ◽  
Florent Lopez
Keyword(s):  
Linear System ◽  
Flow Model ◽  
State Of The Art ◽  
Direct Methods ◽  
Dramatic Reduction ◽  
Multicore Architecture ◽  
Sequential Task ◽  
Sparse Linear System ◽  
Parallel Version ◽  
Two Phases

We describe the parallelization of the solve phase in the sparse Cholesky solver SpLLT when using a sequential task flow model. In the context of direct methods, the solution of a sparse linear system is achieved through three main phases: the analyse, the factorization and the solve phases. In the last two phases, which involve numerical computation, the factorization corresponds to the most computationally costly phase, and it is therefore crucial to parallelize this phase in order to reduce the time-to-solution on modern architectures. As a consequence, the solve phase is often not as optimized as the factorization in state-of-the-art solvers, and opportunities for parallelism are often not exploited in this phase. However, in some applications, the time spent in the solve phase is comparable to or even greater than the time for the factorization, and the user could dramatically benefit from a faster solve routine. This is the case, for example, for a conjugate gradient (CG) solver using a block Jacobi preconditioner. The diagonal blocks are factorized once only, but their factors are used to solve subsystems at each CG iteration. In this study, we design and implement a parallel version of a task-based solve routine for an OpenMP version of the SpLLT solver. We show that we can obtain good scalability on a multicore architecture enabling a dramatic reduction of the overall time-to-solution in some applications.

Solving a very large-scale sparse linear system with a parallel algorithm in the Gaia mission

2014 ◽  
Author(s):  
Ugo Becciani ◽  
Eva Sciacca ◽  
Marilena Bandieramonte ◽  
Alberto Vecchiato ◽  
Beatrice Bucciarelli ◽  
...  
Keyword(s):  
Linear System ◽  
Parallel Algorithm ◽  
Large Scale ◽  
Sparse Linear System

scholarly journals Development and Application of a New High-Efficiency Sparse Linear System Solver in the Thermal-Hydraulic System Analysis Code

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Li Ge ◽  
Wei Liu ◽  
Jianqiang Shan
Keyword(s):  
Linear System ◽  
Hydraulic System ◽  
Large Scale ◽  
System Analysis ◽  
High Efficiency ◽  
Oriented Graph ◽  
Lu Factorization ◽  
Analysis Program ◽  
Lower Upper ◽  
Sparse Linear System

This paper presents a faster solver named NRLU (Node Reordering Lower Upper) factorization solver to improve the solution speed for the pressure equations, which are formed by RELAP5/MOD3.3. The NRLU solver uses the oriented graph method and minimal fill-ins rule to reorder the structure of the nonsymmetry sparse pressure matrix. It solves the pressure matrix by LU factorization. Then the solver is embedded into the large scale advanced thermal-hydraulic system analysis program RELAP5/MOD3.3. The comparisons of the original solver and the NRLU solver show that the NRLU solver is faster than the original solver in RELAP5/MOD3.3, and the rate enhancement can be 44.44%. The results also show that the NRLU solver can reduce the number of fill-ins effectively. This can improve the calculation speed.

Design of generic direct sparse linear system solver in C++ for power system analysis

2001 ◽  
Vol 16 (4) ◽  
pp. 647-652 ◽  
Author(s):  
S. Pandit ◽  
S.A. Soman ◽  
S.A. Khaparde
Keyword(s):  
Linear System ◽  
Power System ◽  
System Analysis ◽  
Power System Analysis ◽  
Sparse Linear System
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