|| IGPM279.pdf October 2007 |
|| Construction of Data-Sparse H2-Matrices by Hierarchical Compression |
||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.
|| hierarchical matrices, data-sparse approximation, non-local operators