Multiple Galerkin Adaptive Algebraic Multigrid Algorithm for the Helmholtz Equations
Multiple Galerkin Adaptive Algebraic Multigrid Algorithm for the Helmholtz Equations
复制标题
亥姆霍兹方程组的多重伽辽金自适应代数多重网格算法
DOI：
10.1137/140975310
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
I. Livshits
中科院分区：
文献类型：
--
作者：
I. Livshits
本文提出了一种求解线性离散方程组的多重Galerkin自适应代数多重网格算法，该算法是由具有丰富多样近核的偏微分算子离散化而产生的。标准的多重网格方法由于无法对所有近核分量产生精确的粗校正而难以求解这样的方程。激励模型问题在这里是不确定的亥姆霍兹算子的近核组件的字符是，至少近似地，已知的。在该算法中，这些组件中的一些被用来创建多个延拓算子和连续的粗略描述，共同近似整个近核。该算法由两部分组成，多个Galerkin校正加速一个标准的多重网格V-循环。这两个部分主要采用标准的多重网格技术。由此产生的算法，然后用于预处理GMRES。在一个和两个维度的数值实验，.
Introduced in this paper is a multiple Galerkin adaptive algebraic multigrid algorithm for solving linear discrete equations arising from discretization of partial differential operators with a rich and diverse near-kernel. Standard multigrid methods struggle with solving such equations due to their inability to produce accurate coarse correction to all near-kernel components. The motivating model problem here is the indefinite Helmholtz operators for which the character of near-kernel components is, at least approximately, known. In the algorithm, some of these components are used to create multiple prolongation operators and consecutive coarse descriptions which collectively approximate the entire near-kernel. The algorithm consists of two parts, with multiple Galerkin corrections accelerating a standard multigrid V-cycle. Both parts largely employ standard multigrid techniques. The resulting algorithm is then used to precondition the GMRES. Numerical experiments in one and two dimensions are presented,...