ALGEBRAIC MULTIGRID METHODS FOR SOLVING TWO-DIMENSIONAL DIFFUSION EQUATION

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BADIE A.S.; EMAMI M.D.

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Journal: JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL) Year:2012 | Volume:30 | Issue:2 Page(s): 1-19

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Information Journal Paper

Title

ALGEBRAIC MULTIGRID METHODS FOR SOLVING TWO-DIMENSIONAL DIFFUSION EQUATION

Author(s)

BADIE A.S. | EMAMI M.D. | Issue Writer Certificate

Keywords

ALGEBRAIC MULTIGRIDQ2

AMGQ2

COARSENINGQ2

DIFFUSIONQ2

STRONG NEGATIVE COUPLINGQ2

SMOOTHINGQ2

Abstract

Multigrid methods, such as the ALGEBRAIC MULTIGRID methods (AMG), are among the most efficient methods for solving discrete linear equations resulting from elliptic PDEs. In this paper, some classic AMG techniques are used for solving a typical two dimensional DIFFUSION equation. The present work focuses on different COARSENING techniques such as the standard and aggressive COARSENING based on the RS algorithm. Results indicate that the standard COARSENING technique together with direct interpolation minimizes the CPU-time and the computational work. Regarding the memory requirement, using a variant of aggressive COARSENING with direct interpolation minimizes the size of memory usage. In addition, the setup phase time (coarsening process) is minimum in this technique. Nevertheless, the increase in convergence factor results in higher overall time for the solution phase. Analysis of the aspect ratio of the computational cells shows that the convergence rate is affected little by this parameter. However, the COARSENING process work and the total CPU-time are slightly increased when cells with high aspect ratios are used for the numerical simulations. Overall, the standard-coarsening method with direct interpolation is found to be appropriate for two-dimensional DIFFUSION problems.

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APA: Copy

BADIE, A.S., & EMAMI, M.D.. (2012). ALGEBRAIC MULTIGRID METHODS FOR SOLVING TWO-DIMENSIONAL DIFFUSION EQUATION. JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL), 30(2), 1-19. SID. https://sid.ir/paper/173663/en

Vancouver: Copy

BADIE A.S., EMAMI M.D.. ALGEBRAIC MULTIGRID METHODS FOR SOLVING TWO-DIMENSIONAL DIFFUSION EQUATION. JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL)[Internet]. 2012;30(2):1-19. Available from: https://sid.ir/paper/173663/en

IEEE: Copy

A.S. BADIE, and M.D. EMAMI, “ALGEBRAIC MULTIGRID METHODS FOR SOLVING TWO-DIMENSIONAL DIFFUSION EQUATION,” JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL), vol. 30, no. 2, pp. 1–19, 2012, [Online]. Available: https://sid.ir/paper/173663/en

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