Operator‐based interpolation for bootstrap algebraic multigrid
Operator‐based interpolation for bootstrap algebraic multigrid
复制标题
基于算子的自举代数多重网格插值
DOI：
10.1002/nla.711
复制
发表时间：
2010
影响因子：
4.3
通讯作者：
J. Ruge
中科院分区：
文献类型：
--
作者：
T. Manteuffel;S. McCormick;Minho Park;J. Ruge
Bootstrap代数多重网格(BAMG)是一种基于多重网格的矩阵方程Ax=b的求解器。它的目的是通过局部拟合一组测试向量来自动确定代数多重网格(AMG)中使用的插值权重，这些测试向量被松弛为对应的齐次方程Ax=0的解，然后可能使用多级特征解算器进行改进。本文介绍了一种灵活的BAMG算法，它通过“折叠”“算子内插”中不需要的连接来间接确定内插权重。与BAMG方法相比，这种间接BAMG方法(IBAMG)更符合经典AMG方法的精神，它基于平滑误差是局部恒定的(限制性)假设，消除了算子内插中不需要的连接。本文研究了iBAMG格式的数值性能，并在一定的假设条件下，建立了它与一个稍作修改的(标准)BAMG格式的等价性。为了比较BAMG和iBAMG，并揭示它们随着问题规模的增长而表现出来的行为，数值实验集中在类Poisson标量问题上。版权所有©2010 John Wiley&Sons，Ltd.
Bootstrap algebraic multigrid (BAMG) is a multigrid‐based solver for matrix equations of the form Ax=b. Its aim is to automatically determine the interpolation weights used in algebraic multigrid (AMG) by locally fitting a set of test vectors that have been relaxed as solutions to the corresponding homogeneous equation, Ax=0, and are then possibly improved later using a multilevel eigensolver. This paper introduces a flexible variant of BAMG that determines the interpolation weights indirectly by ‘collapsing’ the unwanted connections in ‘operator interpolation’. Compared to BAMG, this indirect BAMG approach (iBAMG) is more in the spirit of classical AMG, which collapses unwanted connections in operator interpolation based on the (restrictive) assumption that smooth error is locally constant. This paper studies the numerical performance of iBAMG and establishes an equivalence, under certain assumptions, between it and a slightly modified (standard) BAMG scheme. To focus on camparing BAMG and iBAMG and exposing their behavior as the problem size grows, the numerical experiments concentrate on Poisson‐like scalar problems. Copyright © 2010 John Wiley & Sons, Ltd.