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Title :A practical determination strategy of optimal threshold parameter for matrix compression in wavelet BEM
Authors :Koro, Kazuhiro
Abe, Kazuhisa
Publisher :John Wiley & Sons, Ltd
Issue Date :15-May-2003
Journal Title :International Journal for Numerical Methods in Engineering
Volume :57
Issue :2
Start Page :169
End Page :191
ISSN :0029-5981
Description :A practical strategy is developed to determine the optimal threshold parameter for waveletbased BE analysis. The optimal parameter is determined so that the amount of storage (and computational work) is minimized without reducing the accuracy of BE solution. In the present study, the Beylkin-type truncation scheme is used in the matrix assembly. To avoid unnecessary integration concerning the truncated entries of a coefficient matrix, apriori estimation of the matrix entries is introduced and thus the truncated entries are determined twice: before and after matrix assembly. The optimal threshold parameter is set based on the equilibrium of the truncation and discretization errors. These errors are estimated in the residual sense. For Laplace problems the discretization error is in particular, indicated with the potential's contribution kck to the residual norm kRk used in error estimation for mesh adaptation. Since the normalized residual norm kck/kuk (u: the potential components of BE solution) cannot be computed without main BE analysis, the discretization error is estimated by the approximate expression constructed through subsidiary BE calculation with smaller degree of freedom (DOF). The matrix compression using the proposed optimal threshold parameter enables us to generate a sparse matrix with O(N1+γ) (0 ? γ < 1) non-zero entries. Although the quasi-optimal memory requirements and complexity are not attained, the compression rate of a few percent can be achieved for N ? 1, 000.
Keywords :wavelet BEM
truncation
optimal threshold parameter
non-orthogonal spline wavelet
Type Local :学術雑誌論文
Language :eng
URI :http://hdl.handle.net/10191/4887
fullTextURL :http://dspace.lib.niigata-u.ac.jp/dspace/bitstream/10191/4887/1/ijnme.pdf
DOI :info:doi/10.1002/nme.666
Appears in Collections:10 査読済論文 = Postprint

Please use this identifier to cite or link to this item: http://hdl.handle.net/10191/4887