This paper seeks to present a wavelet Galerkin boundary element method (WGBEM) for solving 2D Laplace's equation in which the coefficient matrices are exactly computed through fast Fourier transform (FFT).
When Daubechies periodized wavelets are used to approximate smooth functions the wavelet coefficients can be exactly computed through FFT, and numerical evaluation of wavelet integrations is discarded. The same methods for computing the expansion coefficients of 2D function and singular function are derived.
For Daubechies periodized wavelets based WGBEM, two remarkable advantages over the existing WGBEM are: the coefficient matrices can be exactly calculated through FFT; a linear system with potential and flux values at dyadic points as unknowns can be gained. Thus, the mixed boundary condition can be enforced with ease. Sparse matrices with only O(N log N) nonzero entries are obtained by performing the fast wavelet transform (FWT) and the truncation of matrix entries.
A wavelet‐integration‐free method for computing the wavelet coefficients is introduced into the WGBEM. The conventional numerical evaluation of wavelet integrations is avoided. Good performance and accuracy are obtained.
