279	RWTH Publication No: 47192        2007        IGPM279.pdf
TITLE	Construction of Data-Sparse H2-Matrices by Hierarchical Compression
AUTHORS	Steffen Börm
ABSTRACT	Discretizing an integral operator by a standard finite element or boundary element method typically leads to a dense matrix. Since its storage complex- ity 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.
KEYWORDS	hierarchical matrices, data-sparse approximation, non-local operators
DOI	10.1137/08072069
PUBLICATION	SIAM Journal on Scientific ComputingVol. 31, Iss. 3 (2009)