TY - JOUR
T1 - On the Influence of the Wavenumber on Compression in a Wavelet Boundary Element Method for the Helmholtz Equation
AU - S. C. Hawkins, K. Chen & P. J. Harris
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 48
EP - 62
PY - 2007
DA - 2007/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/850.html
KW - wavelets, boundary element method, and Helmholtz equation.
AB - <p style="text-align: justify;">We examine how the wavenumber influences the compression in
a wavelet boundary element method for the Helmholtz equation. We show
that for wavelets with high vanishing moments the number of nonzeros in
the resulting compressed matrix is approximately proportional to the
square of the wavenumber. When the wavenumber is fixed, the wavelet
boundary element method as optimal complexity with respect to the number
of unknowns. When the mesh spacing is proportional to the wavelength,
the complexity of the wavelet boundary element method is approximately
proportional to the square of the number of unknowns.</p>