A convergent multigrid cycle for the hybridized mixed method
A convergent multigrid cycle for the hybridized mixed method
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DOI：
10.1002/nla.636
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发表时间：
2009-09
影响因子：
4.3
通讯作者：
Jay Gopalakrishnan;Shuguang Tan
中科院分区：
文献类型：
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作者：
Jay Gopalakrishnan;Shuguang Tan
我们考虑将可变 V 循环多重网格算法应用于二阶椭圆边值问题的混合混合方法。我们的算法与之前混合方法的多重网格工作的不同之处在于，它的目标是有效求解该方法的拉格朗日乘子的矩阵系统。由于混合方法最好通过首先求解拉格朗日乘子并在本地恢复剩余的未知数来实现，因此我们的算法在实践中更有用。该算法的关键要素是合适的网格间传输算子。我们设计了这样一个算子，并证明了可变 V 循环算法的网格独立收敛性。数值实验表明我们的算法具有渐近最优性能，以及某些看似合理的网格间传输算子的失败。版权所有 © 2009 约翰·威利父子有限公司
We consider the application of a variable V‐cycle multigrid algorithm for the hybridized mixed method for second‐order elliptic boundary‐value problems. Our algorithm differs from the previous works on multigrid for the mixed method in that it is targeted at efficiently solving the matrix system for the Lagrange multiplier of the method. Since the mixed method is best implemented by first solving for the Lagrange multiplier and recovering the remaining unknowns locally, our algorithm is more useful in practice. The critical ingredient in the algorithm is a suitable intergrid transfer operator. We design such an operator and prove mesh‐independent convergence of the variable V‐cycle algorithm. Numerical experiments indicating the asymptotically optimal performance of our algorithm, as well as the failure of certain seemingly plausible intergrid transfer operators, are presented. Copyright © 2009 John Wiley & Sons, Ltd.