On the use of discrete wavelet transform for solving integral equations of acoustic scattering

In this paper, the discrete wavelet transform (DWT) is used to solve the dense system of equations which arises from integral equation of acoustic scattering. The DWT using appropriate wavelet family for acquiring larger sparsification of the system matrix is used to obtain a sparse approximation to the transformed matrix that is used in place of the original matrix in an iterative solver. Alternatively DWT is also used to design sparse preconditioners for an iterative method. Also, DWT-based preconditioners are constructed to accelerate iterative Krylov subspace methods. Convergence rates and number of operations are discussed for each case.