Author:

Keywords:

helmholtz equation, integral equation, wavelet packets, high frequency, boundary-element method, scattering, frequency, bases, Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Helmholtz equation, BOUNDARY-ELEMENT METHOD, SCATTERING, FREQUENCY, BASES, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 0906 Electrical and Electronic Engineering, Numerical & Computational Mathematics, 4613 Theory of computation, 4901 Applied mathematics, 4903 Numerical and computational mathematics

Abstract:

We examine the use of wavelet packets for the fast solution of integral equations with a highly oscillatory kernel. The redundancy of the wavelet packet transform allows the selection of a basis tailored to the problem at hand. It is shown that a well chosen wavelet packet basis is better suited to compress the discretized system than wavelets. The complexity of the matrix-vector product in an iterative solution method is then substantially reduced. A two-dimensional wavelet packet transform is derived and compared with a number of one-dimensional transforms that were presented earlier in literature. By means of some numerical experiments we illustrate the improved efficiency of the two-dimensional approach. (c) 2005 Elsevier B.V. All rights reserved.