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Cascadic multigrid for the advection-diffusion equation

Abstract : In this report, the Cascadic Multigrid method (CMG), viewed as a «one-way» multigrid method not involving pre-smoothing or restriction steps, is defined and tested in the case of a simple 2D advection-diffusion problem. Jacobi and Gauss-Seidel smoothers are employed. While the Cascadic Multigrid method is very effective for relatively small Reynolds numbers, the convergenc- e rate deteriorates when advection and diffusion approximately balance each other. However, for larger Reynolds numbers, the method improves somewhat and achieves a mesh-independent convergence rate. In the next step, we recommend that the CMG method should be designed and tested for boundary layers in conjunction with adaptive meshes and/or semi-coarsening.
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https://hal.inria.fr/inria-00072014
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Submitted on : Tuesday, May 23, 2006 - 7:34:08 PM
Last modification on : Thursday, January 20, 2022 - 5:32:13 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:48:50 PM

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  • HAL Id : inria-00072014, version 1

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Xuejun Xu, Ales Janka, Jean-Antoine Desideri. Cascadic multigrid for the advection-diffusion equation. [Research Report] RR-4574, INRIA. 2002. ⟨inria-00072014⟩

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