Parallel Gaussian elimination using OpenMP and MPI

McGinn, S.F.; Shaw, R. E.

doi:10.1109/hpcsa.2002.1019151

Cited by 19 publications

(10 citation statements)

References 4 publications

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“…Let us say that we need to invert matrix A. If B is the inverse of A, then: (13) Where, I is the identity matrix. If we can break A into two matrices such that one is lower triangular matrix and the other is upper triangular matrix then: (14) Where, L is lowering triangular and U is upper triangular matrix.…”

Section: B Decomposition Of the Matrix Problemmentioning

confidence: 99%

Inverse Matrix using Gauss Elimination Method by OpenMP

Alassafi¹,

Alsenani

2016

IJITCS

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OpenMP is an implementation program interface that might be utilized to explicitly immediate multi-threaded and it shared memory parallelism. OpenMP platform for specifications multi-processing via concurrent work between interested parties of hardware and software industry, governments and academia. OpenMP is not needs implemented identically by all vendors and it is not proposed for distributed memory parallel systems by itself. In order to invert a matrix, there are multiple approaches. The proposed LU decomposition calculates the upper and lower triangular via Gauss elimination method. The computation can be parallelized using OpenMP technology. The proposed technique main goal is to analyze the amount of time taken for different sizes of matrices so we used 1 thread, 2 threads, 4 threads, and 8 threads which will be compared against each other to measure the efficiency of the parallelization. The result of interrupting compered the amount of time spent in all the computing using 1 thread, 2 threads, 4 threads, and 8 threads. We came up with if we raise the number of threads the performance will be increased (less amount of time required). If we use 8 threads we get around 64% performance gained. Also as the size of matrix increases, the efficiency of parallelization also increases, which is evident from the time difference between serial and parallel code. This is because, more computations are done parallel and hence the efficiency is high. Schedule type in OpenMP has different behavior, we used static, dynamic, and guided scheme

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Section: B Decomposition Of the Matrix Problemmentioning

confidence: 99%

Inverse Matrix using Gauss Elimination Method by OpenMP

Alassafi¹,

Alsenani

2016

IJITCS

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“…In (15) and (16) [20,21]. Besides, a one-dimensional (1d) element used for links and prestressed anchors is defined in the software.…”

Section: Creep Model Zhumentioning

confidence: 99%

“…The situation has changed since the arrival of a variety of high performance computers and the advances in parallel computing techniques, that is, parallel algorithms and parallel platforms. Parallel algorithms on different platforms, that is, algorithms utilizing OpenMP and MPI, are studied by [13][14][15][16]. Recently, the GPU high performance computing has been popular.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study on Different Parallel Solvers for Nonlinear Analysis of Complex Structures

Zhang

Wang

et al. 2013

Mathematical Problems in Engineering

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The parallelization of 2D/3D software SAPTIS is discussed for nonlinear analysis of complex structures. A comparative study is made on different parallel solvers. The numerical models are presented, including hydration models, water cooling models, modulus models, creep model, and autogenous deformation models. A finite element simulation is made for the whole process of excavation and pouring of dams using these models. The numerical results show a good agreement with the measured ones. To achieve a better computing efficiency, four parallel solvers utilizing parallelization techniques are employed: (1) a parallel preconditioned conjugate gradient (PCG) solver based on OpenMP, (2) a parallel preconditioned Krylov subspace solver based on MPI, (3) a parallel sparse equation solver based on OpenMP, and (4) a parallel GPU equation solver. The parallel solvers run either in a shared memory environment OpenMP or in a distributed memory environment MPI. A comparative study on these parallel solvers is made, and the results show that the parallelization makes SAPTIS more efficient, powerful, and adaptable.

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“…Based on the results of examining various load balancing schemes on both platforms, it shows that in OpenMP, Data can be made available to all processors at all times. But in case of MPI, when authors increase the value of n, the program displays an improvement in performance [1]. The Gauss elimination method without pivoting was introduced to explain the concepts both in OpenMP and MPI where in MPI, communication capabilities between the nodes increases apparently along with the floating point speed [2].Finite algorithms for solving system of linear equations using Gauss elimination method was designed for shared memory, distributed memory and also for their combination.…”

Section: Literature Reviewmentioning

confidence: 99%

Parallel Algorithm for Finding Inverse of a Matrix and its Application in Message Sharing (Coding Theory)

Saraf¹,

Dhingra²,

Pinheiro³

2016

IJCA

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A parallel algorithm for finding the inverse of the matrix using Gauss Jordan method in OpenMP. The Gauss Jordan method has been chosen for this project because it provides a direct method for obtaining inverse matrix and requires approx. 50% fewer operations unlike other methods. Hence forth it is suitable for massive parallelization. Then, authors have analyzed the parallel algorithm for computing the inverse of the matrix and compared it with its perspective sequential algorithm in terms of run time, speed-up and efficiency. Further, the obtained result is used to propose a new method of Message Sharing (called Coding Theory). The proposed method is simple and has a great potential to be applied to other situation where the exchange of messages is done confidentially such as in military operation, banking transactions etc.

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Parallel Gaussian elimination using OpenMP and MPI

Cited by 19 publications

References 4 publications

Inverse Matrix using Gauss Elimination Method by OpenMP

Inverse Matrix using Gauss Elimination Method by OpenMP

A Comparative Study on Different Parallel Solvers for Nonlinear Analysis of Complex Structures

Parallel Algorithm for Finding Inverse of a Matrix and its Application in Message Sharing (Coding Theory)

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