A note on wave number dependence of wavelet matrix compression for integral equations with oscillatory kernel

Authors:
Daan Huybrechs;Jo Simoens;Stefan Vandewalle
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, Leuven B-3001, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, Leuven B-3001, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, Leuven B-3001, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

This paper analyzes the effect of large wave numbers on the wavelet method for integral equations arising in electromagnetic applications. It is shown that the compression of the stiffness matrix deteriorates with increasing wave number, a characteristic that has been reported before in the literature. Here, however, the exact dependence on the wave number is calculated analytically for the two-dimensional Helmholtz problem.