On Fast Matrix-vector Multiplication In Wavelet Galerkin Bem

摘要

So far, the wavelet boundary element method (BEM) has been recognized as a different kind of fast BEM from the methods based on low-rank approximation, such as fast multipole method, panel clustering method and H~2-matrices.rnWe consider the matrix-vector multiplication in the wavelet Galerkin BEM [Tausch J. A variable order wavelet method for the sparse representation of layer potentials in the non-standard form. J Numer Math 2004;12(3):233-54]. We show that the system matrix of the wavelet Galerkin BEM can be transformed into a matrix with hierarchical structure by combining the forward and inverse wavelet transform in matrix-vector multiplications phase. The new system matrix only involves the data about the scaling functions. Any operations concerning the wavelet functions are thus avoided. A new version of matrix-vector multiplication scheme is proposed. We prove that the complexity of the new scheme never exceeds that of the old scheme.rnThis work: (1) simplifies the implementation wavelet Galerkin BEM; (2) bridges a link between the wavelet BEMs and the methods of low-rank approximation.