On the non hierarchical matrix representation of the negative, non integer order sobolev norms

Authors:
Béla Kiss
Affiliations:
Széchenyi István University, Hungary
Venue:
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Year:
2005

Citing 5
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Abstract

In this paper a new cyclic matrix representation of the Sobolev norms Ha, a ε (−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.