Wavelet BEMにおける特異・擬似特異積分の計算

抄録

Application of the wavelet-weighted Gaussian quadrature formula to the singular and nearly singular integrals is attempted in the context of implementation of the wavelet BEM. To achieve this, the singular or nearly singular integrand is decomposed into a singular or nearly singular but simple term and a regular part. The former is integrated analytically and the integral of the latter is calculated by the wavelet-weighted quadrature method. Moreover, in order to avoid the calculation of the Jacobian, the bases such as wavelets are described with respect to the arc length of each subboundary, and then the simplification of analytical integrals is attained. Numerical examples are presented to validate the developed method. It is concluded that the proposed method can shorten the computation time for matrix coefficients by a factor of 3 irrespective of the degrees of freedom.