On the non hierarchical matrix representation of the negative, non integer order sobolev norms
Publication Name: Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics
Publication Date: 2006-06-29
Volume: 3743 LNCS
Issue: Unknown
Page Range: 663-670
Description:
In this paper a new cyclic matrix representation of the Sobolev norms Ha, a ∈ (-1, 0) are presented. The matrix-vector multiplication by these matrices requires only O(N · log(N)) arithmetic operations, where N is the number of unknowns, The application of the new H-1/2 norm representation as Schur complement preconditioning matrix requires only matrix-vector multiplication. The efficiency of the construction to elliptic problems has been verified by numerical tests. © Springer-Verlag Berlin Heidelberg 2006.
Open Access: Yes
DOI: 10.1007/11666806_76
