A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation

Sahimi, M. S.; Mansor, Noreliza Abu; Nor, Norhalena Mohd; Nusi, Noraini Md; Alias, Norma

doi:10.1504/ijspm.2006.009011

Cited by 5 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In reference to Sahimi et al [38], more reasons for DS-MF performance compared with ADI of P-R have been given. Similar reasons show that DS-MF is more accurate than the ADI in [27,37].…”

Section: Numerical Experimentssupporting

confidence: 65%

See 1 more Smart Citation

Armadillo generation distributed system with geranium Cadcam cluster for solving 2D telegraphic problem

Uzezi

Shariffudin

2011

International Journal of Computer Mathematics

View full text Add to dashboard Cite

In this paper, the parallel implementation of the iterative alternating direction explicit method by D'Yakonov (IADE-DY) and the Mitchell and Fairweather double sweep method (DS-MF) compared with the alternative direction implicit (ADI) method for solving the 2D telegraphic problem on a distributed system ofArmadillo cluster and geranium Cadcam cluster using the parallel virtual machine and message passing interface is presented. We implement the scheduling of n tridiagonal system of equations with the above methods to show improvement on speedup and efficiency with parallel strategies across the two platforms. The single program multiple data model was employed for the implementation. The IADE-DY, DS-MF and ADI are developed by the splitting of the implicit equation using the finite difference discretization on the 2D telegraphic problem. The implementation is discussed in relation to means of the performance parallel strategies and analysis. The model enhances overlap communication and computation to avoid unnecessary synchronization, hence, the method yields significant speedup by the use of the non-blocking communication. We present some analyses that are helpful for speedup and efficiency.

show abstract

“…In reference to Sahimi et al [38], more reasons for DS-MF performance compared with ADI of P-R have been given. Similar reasons show that DS-MF is more accurate than the ADI in [27,37].…”

Section: Numerical Experimentssupporting

confidence: 65%

“…The second term N 0 /N 1 in the right-hand side of Equation (37) represents the increase in the number of iterations required by the parallel method to achieve a specified accuracy compared with the serial method.…”

Section: Speedup Efficiency and Effectivenessmentioning

confidence: 99%

Armadillo generation distributed system with geranium Cadcam cluster for solving 2D telegraphic problem

Uzezi

Shariffudin

2011

International Journal of Computer Mathematics

View full text Add to dashboard Cite

show abstract

“…GSRB method is based on domain decomposition for each odd sub domain, Ω R and even sub domain, Ω H [9]. GSRB calculation is as follows, , ,…”

Section: Gauss-seidel Red Black (Gsrb) Methodsmentioning

confidence: 99%

The parallel AGE variances method for temperature prediction on laser glass interaction

Yusuf

Alias

Ghouse

et al. 2011

2011 IEEE Symposium on Computers &Amp; Informatics

View full text Add to dashboard Cite

This paper describes the formula of threedimensional parabolic equations for cylindrical coordinate glass that is used for mathematical simulation in simulating the temperature behavior of the laser glass cutting. There are three methods have been used for the simulation purposes which is the Alternating Group Explicit (AGE) which compromises two variances that is Brian and Douglas variant, and Gauss Seidel Red Black method. The simulation for these three methods is conducted in a parallel computing environment in order to speed up the calculation process and to achieve an accurate and convergence results. From the simulation, the results will be compared by conducting parallel performance measurement, which include execution time, speedup, efficiency, effectiveness and temporal performance.

show abstract

“…Several studies have later been developed based on the IADE method. Sahimi et al [3,4] The studies showed that the accuracies of the IADEDY and the IADEMG are comparable to the IADEMF. Alias [5] studied the parallel implementation of the IADEMF on distributed parallel computing using the parallel virtual machine.…”

Section: ( ) ( ) O T X   mentioning

confidence: 99%

A Distributed Memory Parallel Fourth-Order IADEMF Algorithm

Mansor¹,

Alias²,

Zulkifle³

et al. 2019

IJACSA

View full text Add to dashboard Cite

The fourth-order finite difference Iterative Alternating Decomposition Explicit Method of Mitchell and Fairweather (IADEMF4) sequential algorithm has demonstrated its ability to perform with high accuracy and efficiency for the solution of a one-dimensional heat equation with Dirichlet boundary conditions. This paper develops the parallelization of the IADEMF4, by applying the Red-Black (RB) ordering technique. The proposed IADEMF4-RB is implemented on multiprocessor distributed memory architecture based on Parallel Virtual Machine (PVM) environment with Linux operating system. Numerical results show that the IADEMF4-RB accelerates the convergence rate and largely improves the serial time of the IADEMF4. In terms of parallel performance evaluations, the IADEMF4-RB significantly outperforms its counterpart of the second-order (IADEMF2-RB), as well as the benchmarked fourth-order classical iterative RB methods, namely, the Gauss-Seidel (GS4-RB) and the Successive Overrelaxation (SOR4-RB) methods.

show abstract

A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation

Cited by 5 publications

References 4 publications

Armadillo generation distributed system with geranium Cadcam cluster for solving 2D telegraphic problem

Armadillo generation distributed system with geranium Cadcam cluster for solving 2D telegraphic problem

The parallel AGE variances method for temperature prediction on laser glass interaction

A Distributed Memory Parallel Fourth-Order IADEMF Algorithm

Contact Info

Product

Resources

About