Wavelet-based SPAI pre-conditioner using local dropping

In this work we performed an experimental study to determine if a wavelet basis can be used to build and apply a highly parallel and low density pre-conditioner known as sparse approximation of the inverse(SPAI), to solve large and sparse linear systems. Test matrices arising from discretizing a second order 3D elliptic scalar operator and from fluid flow simulation in porous media were used as test cases. The results show that low density wavelet-based SPAI pre-conditioners can be built and applied to yield good results.