Number of non-zero matrix entries in wavelet BEM for steady-state out-of-plane wave propagation problems

Abstract

In the BEM with the non-orthogonal spline wavelets for steady-state out-of-plane wave propagation problems, the relation between the number of non-zero entries of the coefficient matrices and the degree of freedom (DOF) N is theoretically investigated using the information on the size and the arrangement of the support of the basis functions. The coefficient matrices are compressed by truncation with a prescribed threshold value κ. The value of κ is determined so that the amount of storage is minimized without reducing the accuracy of BE solution, and shows κ ≈ ρN^−β (ρ, β > 0). The number of non-zero entries of the matrices G and H, (G) and (H) increases in proportion to O(N log N) or O(N^1+γ) (0 < γ < 1). The low compression rate of the coefficient matrix for a high-frequency problem can be improved using the wavelets with a higher-order vanishing momemt property.