# Efficient Parallel Computing for Solving Linear Systems of Equations

@inproceedings{Allen2003EfficientPC, title={Efficient Parallel Computing for Solving Linear Systems of Equations}, author={K. Allen}, year={2003} }

Linear systems of equations are common throughout the disciplines of science. The conjugate gradient method is a common iterative method used to solve systems with symmetric positive definite system matrices. With a matrix-free implementation, the method is optimal with respect to both memory usage and performance, and we are able to solve problems that are much too large for single processor computers. Using a highperformance Myrinet interconnect, excellent speedup is possible for at least up… Expand

#### 14 Citations

Parallel Solution for Finite Element Linear Systems of Equations on Workstation Cluster

- Computer Science
- 2009

The experiment result shows that the designed parallel algorithm has high speedup and good efficiency on the high performance workstation cluster, illustrating the power of parallel computing in solving large problems much faster than on a single processor. Expand

Large electromagnetic problem on large scale parallel computing systems

- Computer Science
- 2012 International Conference on High Performance Computing & Simulation (HPCS)
- 2012

A prediction model for computing performances on grid, based on a hybrid approach that combines a historic-based prediction and an application profile- based prediction, has been developped and the predicted values are in good agreement with the measured values. Expand

A Comparative Study of the Parallel Performance of the Blocking and Non-Blocking MPI Communication Commands on an Elliptic Test Problem on the Cluster

- 2010

In this report we study the parallel solution of the elliptic test problem of a Poisson equation with homogenous Dirichlet boundary conditions in a two dimensional domain. We use the finite… Expand

Investigating the Use of pMatlab to Solve the Poisson Equation on the Cluster maya

- Mathematics
- 2014

Many physical phenomena can be described by partial dierential equations which can be discretized to form systems of linear equations. We apply the nite dierence method to the Poisson equation with… Expand

Large electromagnetic simulation by hybrid approach on large‐scale parallel computing systems

- Computer Science
- Concurr. Comput. Pract. Exp.
- 2015

A parallel transmission‐line matrix implementation to take the advantage of the distributed architectures and a time prediction model in order to optimize the resource reservation and the simulation execution on the computing nodes. Expand

Study of Free Alternative Numerical Computation Packages

- 2012

Matlab is the most popular commercial package for numerical computations in mathematics, statistics, the sciences, engineering, and other fields. Octave, FreeMat, and Scilab are free numerical… Expand

Parallel Performance Studies for a 3-D Elliptic Test Problem on the 2018 Portion of the Taki Cluster

- Computer Science
- 2020

The hardware used in the computational studies is part of the UMBC High Performance Computing Facility (HPCF), and co-author Carlos Barajas was supported by UMBC as HPCF RA. Expand

IDL : A Possible Alternative to Matlab ?

- 2012

Created by Exelis Visual Information Solutions, IDL (Interactive Data Language) is a commercial package used for data analysis. We compared the usability and efficiency of IDL to that of Matlab to… Expand

A Comparative Evaluation of Matlab , Octave , FreeMat , and Scilab on Tara

- 2011

Matlab is the most popular commercial package for numerical computations in mathematics, statistics, the sciences, engineering, and other fields. Octave, FreeMat, and Scilab are free numerical… Expand

Efficient large electromagnetic simulation based on hybrid TLM and modal approach on grid computing and supercomputer

- Computer Science
- 2012

Electromagnetic modeling of oversized structures by means of different numerical methods, using new resources (hardware and software) to realize yet more performant calculations, is the aim of this work. Expand

#### References

SHOWING 1-8 OF 8 REFERENCES

A Matrix-Free Conjugate Gradient Method for Cluster Computing ?

- Mathematics
- 2003

The conjugate gradient method is applied to a large, sparse, highly structured linear system of equations obtained from a finite dierence discretization of the Poisson equation. The matrix-free… Expand

Coarse-Grained Parallel Matrix-Free Solution of a Three-Dimensional Elliptic Prototype Problem

- Mathematics, Computer Science
- ICCSA
- 2003

The conjugate gradient method with a matrix-free implementation of the matrix-vector product with the system matrix is shown to be optimal with respect to memory usage and runtime performance and justifies the use of this linear solver as the computational kernel for the time-stepping in a system of reaction-diffusion equations. Expand

Parallel programming with MPI

- Computer Science
- 1996

This chapter discusses the design and Coding of Parallel Programs, performance, and grouping data for Communication in the context of parallel computing. Expand

Fundamentals of matrix computations

- Mathematics
- 1991

Preface. Acknowledgments. 1 Gaussian Elimination and Its Variants. 1.1 Matrix Multiplication. 1.2 Systems of Linear Equations. 1.3 Triangular Systems. 1.4 Positive Definite Systems Cholesky… Expand

MPI: A message - passing interface standard

- Geology
- 1994

In rock drilling utilizing mechanical destruction of the rock and circulation of drilling fluid for removing debris from the cutting face, the drilling fluid is directed on to the cutting face in the… Expand

A parallel matrix-free implementation of the conjugate gradient method for the Poisson equation

- A parallel matrix-free implementation of the conjugate gradient method for the Poisson equation
- 2003

PETSc users manual

- PETSc users manual
- 2002

1 (Version 6.1). The MathWorks, Inc

- MATLAB Release