AMGe - Coarsening Strategies and Application to the Oseen Equations
AMGe - Coarsening Strategies and Application to the Oseen Equations
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DOI：
10.1137/040610350
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发表时间：
2005-12
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通讯作者：
M. Wabro
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文献类型：
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作者：
M. Wabro
对基于单元内插的代数多重网格法(AMGE)在凝聚过程、非协调元的应用以及Oseen线性化的Navier-Stokes方程的混合有限元离散等方面进行了扩展。最后一点，将AMGE用于混合有限元，由于粗略级别的拓扑的存在，变得直接了当。对于Crouzeix-Raviart元，我们举例说明了这一点(包括一个稳定性结果)。数值结果表明，仔细研究集聚战略确实是有回报的。一个“错误”的选择可能导致整体多重网格法的不充分收敛甚至发散。
We provide some extensions to the algebraic multigrid method based on element interpolation (AMGe), concerning the agglomeration process, the application to nonconforming elements, and the application to the mixed finite element discretization of the Oseen linearized Navier--Stokes equations. This last point, using AMGe for mixed finite elements, becomes straightforward because of the availability of coarse-level topologies. We show this exemplarily for the Crouzeix--Raviart element (including a stability result). The numerical results show that it really pays off to take a closer look at the agglomeration strategy. A "wrong" choice can lead to insufficient convergence or even divergence of the overall multigrid method.