Spectral AMGe (ρAMGe)
Spectral AMGe (ρAMGe)
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DOI：
10.1137/s106482750139892x
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发表时间：
2003-01-01
影响因子：
3.1
通讯作者：
Vassilevski, PS
中科院分区：
文献类型：
--
作者：
Chartier, T;Falgout, RD;Vassilevski, PS
我们介绍了基于谱元素的代数多重网格（rhoAMGe），一个新的代数多重网格方法求解系统的代数方程，出现在Ritz型有限元离散偏微分方程。该方法需要访问单元刚度矩阵，这使得能够精确地近似代数“平滑”向量（即，松弛不能有效消除的误差分量）。大多数其他代数多重网格方法以某种方式基于预定义的平滑度概念。例如，粗网格选择和延伸通常是假设平滑误差在“强”连接（算子矩阵中相对较大的系数）的方向上变化缓慢。rhoAMGe的一个目的是扩大该方法可以成功应用的问题的范围，避免任何隐含的前提下的性质的平滑误差。rhoAMGe使用元素刚度矩阵的小集合的谱分解来确定代数平滑误差分量的局部表示。这为粗水准的生成和粗水准的确定提供了基础。有效的插值。本文提出了一个理论基础rhoAMGe沿着与数值实验证明其鲁棒性。
We introduce spectral element-based algebraic multigrid (rhoAMGe), a new algebraic multigrid method for solving systems of algebraic equations that arise in Ritz-type finite element discretizations of partial differential equations. The method requires access to the element stiffness matrices, which enables accurate approximation of algebraically "smooth" vectors (i.e., error components that relaxation cannot effectively eliminate). Most other algebraic multigrid methods are based in some manner on predefined concepts of smoothness. Coarse-grid selection and prolongation, for example, are often defined assuming that smooth errors vary slowly in the direction of "strong" connections (relatively large coefficients in the operator matrix). One aim of rhoAMGe is to broaden the range of problems to which the method can be successfully applied by avoiding any implicit premise about the nature of the smooth error. rhoAMGe uses the spectral decomposition of small collections of element stiffness matrices to determine local representations of algebraically smooth error components. This provides a foundation for generating the coarse level and for de. ning effective interpolation. This paper presents a theoretical foundation for rhoAMGe along with numerical experiments demonstrating its robustness.