A Sparse ℋ-Matrix Arithmetic.
A Sparse ℋ-Matrix Arithmetic.
复制标题
稀疏ℋ-矩阵算术。
作者：
W. Hackbusch;B. Khoromskij
本文的前一部分介绍了一类数据稀疏的矩阵（n-矩阵），它允许近似的矩阵算法的近似线性复杂度。在第一部分中讨论的矩阵能够近似离散积分算子的情况下，一维。在本第二部分中，构造的矩阵的有限元和边界元法的应用在二维和三维空间的解释。各种矩阵运算的复杂性顺序与第一部分完全相同。特别是，它示出的适用性的矩阵不需要一个规则的网格。我们讨论了准均匀非结构网格和组合曲面的情况。
Abstract The preceding Part I of this paper has introduced a class of matrices (ℋ-matrices) which are data-sparse and allow an approximate matrix arithmetic of almost linear complexity. The matrices discussed in Part I are able to approximate discrete integral operators in the case of one spatial dimension.In the present Part II, the construction of ℋ-matrices is explained for FEM and BEM applications in two and three spatial dimensions. The orders of complexity of the various matrix operations are exactly the same as in Part I. In particular, it is shown that the applicability of ℋ-matrices does not require a regular mesh. We discuss quasi-uniform unstructured meshes and the case of composed surfaces as well.