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MiS Preprint
54/1999
${\cal H}$-matrix approximation on graded meshes
Wolfgang Hackbusch and Boris N. Khoromskij
Abstract
In a preceding paper, a class of matrices (${\cal H}$-matrices) has been introduced which are data-sparse and allow an approximate matrix arithmetic of almost linear complexity. Several types of ${\cal H}$-matrices were analysed which are able to approximate integral (nonlocal) operators in FEM and BEM applications in the case of quasi-uniform unstructured meshes. In the present paper, the special class of ${\cal H}$-matrices on graded meshes is analysed. We investigate two types of separation criteria for the construction of the cluster tree which allow to optimise either the approximation power (cardinality-balancing strategy) or the complexity (distance-balancing strategy) of the ${\cal H}$-matrices under consideration. For both approaches, we prove the optimal complexity and approximation results in the case of composite meshes and tensor-product meshes with polynomial/exponential grading in Rd, d=1,2,3.
fast algorithms, hierarchical matrices, data-sparse matrices, mesh refinement, bem, fem
Related publications
inBook
2000
Repository Open Access
Wolfgang Hackbusch and Boris N. Khoromskij
\( \mathscr{H} \)-matrix approximation on graded meshes
In: The mathematics of finite elements and applications X, MAFELAP 1999 : proceedings of the 10th conference, Brunel Univ., Uxbridge, Middlesex, GB, June 22-25, 1999 / J. R. Whiteman (ed.) Amsterdam [u. a.] : Elsevier, 2000. - pp. 307-316
