Construction of Data-Sparse H2-Matrices by Hierarchical Compression
Construction of Data-Sparse H2-Matrices by Hierarchical Compression
复制标题
通过分层压缩构建数据稀疏 H2 矩阵
DOI：
10.1137/080720693
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
S. Börm
中科院分区：
文献类型：
--
作者：
S. Börm
通过标准有限元或边界元素方法将积分运算符离散，通常会导致密集的矩阵，因为其存储复杂性随着自由度的数量而增长，因此无法将矩阵的标准表示形式应用于二维数组大型问题大小。本文提出了一种相对简单的算法，可以使用任何流行的低级别近似方案（例如，交叉近似）来找到“初始猜测”，并构建了一个匹配的多级结构。与竞争方法一样快，需要较大的存储空间才能获得大问题。
Discretizing an integral operator by a standard finite element or boundary element method typically leads to a dense matrix. Since its storage complexity grows quadratically with the number of degrees of freedom, the standard representation of the matrix as a two-dimensional array cannot be applied to large problem sizes. H2-matrix techniques use a multilevel approach to represent the dense matrix in a more efficient data-sparse format. We consider the challenging task of finding a good multilevel representation of the matrix without relying on a priori information of its contents. This paper presents a relatively simple algorithm that can use any of the popular low-rank approximation schemes (e.g., cross approximation) to find an “initial guess” and constructs a matching multilevel structure on the fly. Numerical experiments show that the resulting technique is as fast as competing methods and requires far less storage for large problem dimensions.