Wavelet-weighted Gauss quadrature formula for reduction of computational work in wavelet BEM

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  • Wavelet基底を用いた境界要素解析の効率化のためのwavelet重み付きGauss積分公式
  • Wavelet キテイ オ モチイタ キョウカイ ヨウソ カイセキ ノ コウリツカ ノ タメ ノ wavelet オモミツキ Gauss セキブン コウシキ

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Abstract

Awavelet-weighted Gauss quadrature formula is developed to reduce computational work in wavelet BEM. The non-orthogonal wavelet constructed by the authors is used as the basis. This wavelet is defined as a spline, which requires us to divide an interval into several subintervals in calculation of integrals corresponding to the basis. Besides, the number of the subintervals increases in propotion to the order of vanishing moments. The computational work for generating matrices thus is expensive, in particular, in application of numerical integration. The present formula enables us to carry out numerical integrations without division of the interval, since the wavelet is also employed as a weighting function of the formula. The number of integration points is determined a priori based on estimation of the integration error and a prescribed accuracy. In wavelet BEM, the error tolerance can be given by a threshold for matrix compression. Through numerical experiments, availability of the present method is verified.

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