Matrix-Compression Property of Beylkin-Type Truncation Scheme for Wavelet Bem

Abstract

In the present paper, we investigate theoretically and experimentally the number of non-zero matrix entries generated by the wavelet BEM with the Beylkin-type compression algorithm. The Beylkin-type algorithm, which is based on a prescribed level-independent threshold, retains the asymptotic convergence rate of BE solutions, like widely-used level-dependent compression schemes. The coefficient matrix compressed by the Beylkin-type scheme has O(N 1+γ ) (0 < γ < 1, N : degree of freedom (DOF)) non-zero entries; level-dependent schemes enable us to reduce the matrix entries up to O (N (log N ) α ) (α ≥ 1). However, for matrix compression using the Beylkin-type scheme the compression rate is greater than or comparable to that of the Schneider's level-dependent scheme, in the moderate DOF range.