Abstract
This paper discusses the use of the 4 Point-Explicit Decoupled Group (EDG) iterative method together with a weighted parameter, namely 4 Point-EDGSOR. The effectiveness of this method will be investigated to solve two-dimensional Poisson equations by using the half-sweep triangle finite element approximation equation based on the Galerkin scheme. In fact, formulations of the full-sweep and half-sweep triangle finite element approaches are also shown. Then implementation of the 4 Point-EDGSOR was performed by combining the Red-Black (RB) ordering strategy. Some numerical experiments are conducted to show that the 4 Point-EDGSOR-RB method is superior to the existing 4 Point-EDG method.
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References
Abdullah, A.R.: The Four Point Explicit Decoupled Group (EDG) Method: A Fast Poisson Solver. Intern. Journal of Computer Mathematics 38, 61–70 (1991)
Abdullah, A.R., Ali, N.H.M.: A comparative study of parallel strategies for the solution of elliptic pde’s. Parallel Algorithms and Applications 10, 93–103 (1996)
Evan, D.J., Yousif, W.F.: The Explicit Block Relaxation method as a grid smoother in the Multigrid V-cycle scheme. Intern. Journal of Computer Mathematics 34, 71–78 (1990)
Fletcher, C.A.J.: The Galerkin method: An introduction. In: Noye, J. (pnyt.). Numerical Simulation of Fluid Motion, pp. 113–170. North-Holland Publishing Company, Amsterdam (1978)
Fletcher, C.A.J.: Computational Galerkin method. Springer Series in Computational Physics. Springer, Heidelberg (1984)
Ibrahim, A., Abdullah, A.R: Solving the two-dimensional diffusion equation by the four point explicit decoupled group (EDG) iterative method. Intern. Journal of Computer Mathematics 58, 253–256 (1995)
Lewis, P.E., Ward, J.P.: The Finite Element Method: Principles and Applications. Addison-Wesley Publishing Company, Reading (1991)
Othman, M., Abdullah, A.R.: The Halfsweeps Multigrid Method As A Fast Multigrid Poisson Solver. Intern. Journal of Computer Mathematics 69, 219–229 (1998)
Othman, M., Abdullah, A.R.: An Effcient Multigrid Poisson Solver. Intern. Journal of Computer Mathematics 7, 541–553 (1999)
Othman, M., Abdullah, A.R.: An Efficient Four Points Modified Explicit Group Poisson Solver. Intern. Journal of Computer Mathematics 76, 203–217 (2000)
Othman, M., Abdullah, A.R., Evans, D.J.: A Parallel Four Point Modified Explicit Group Iterative Algorithm on Shared Memory Multiprocessors. Parallel Algorithms and Applications 19(1), 1–9 (2004) (On January 01, 2005 this publication was renamed International Journal of Parallel, Emergent and Distributed Systems)
Parter, S.V.: Estimates for Multigrid methods based on Red Black Gauss-Seidel smoothers. Numerical Mathematics 52, 701–723 (1998)
Sulaiman, J., Hasan, M.K., Othman, M.: The Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) method for diffusion equations. In: Zhang, J., He, J.-H., Fu, Y. (eds.) CIS 2004. LNCS, vol. 3314, pp. 57–63. Springer, Heidelberg (2004)
Sulaiman, J., Othman, M., Hasan, M.K.: Quarter-Sweep Iterative Alternating Decomposition Explicit algorithm applied to diffusion equations. Intern. Journal of Computer Mathematics 81, 1559–1565 (2004)
Twizell, E.H.: Computational methods for partial differential equations. Ellis Horwood Limited, Chichester (1984)
Vichnevetsky, R.: Computer Methods for Partial Differential Equations, vol. I. Prentice-Hall, New Jersey (1981)
Yousif, W.S., Evans, D.J.: Explicit De-coupled Group iterative methods and their implementations. Parallel Algorithms and Applications 7, 53–71 (1995)
Zhang, J.: Acceleration of Five Points Red Black Gauss-Seidel in Multigrid for Poisson Equations. Applied Mathematics and Computation 80(1), 71–78 (1996)
Zienkiewicz, O.C.: Why finite elements? In: Gallagher, R.H., Oden, J.T., Taylor, C., Zienkiewicz, O.C. (eds.) Finite Elements In Fluids-Volume, vol. 1, pp. 1–23. John Wiley & Sons, Chichester (1975)
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Sulaiman, J., Othman, M., Hasan, M.K. (2007). Red-Black EDGSOR Iterative Method Using Triangle Element Approximation for 2D Poisson Equations. In: Gervasi, O., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2007. ICCSA 2007. Lecture Notes in Computer Science, vol 4707. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74484-9_26
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DOI: https://doi.org/10.1007/978-3-540-74484-9_26
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