279 IGPM279.pdf        October 2007
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