Wavelet based solution of flow and diffusion problems in digital materials

The computation of physical properties in a digital materials labora- tory requires significant computational resources. Due to the complex nature of the media, one of the most diffcult problems to solve is the multiphase flow problem, and traditional methods such as Lattice Boltzmann are not attractive as the computational demand for the solution is too high. A wavelet based algorithm reduces the amount of information required for computation. Here we solve the Poisson equation for a large three dimensional data set with a second order finite difference approximation. Constraints and factitious domains are used to capture the complex geometry. We solve the discrete system using a discrete wavelet transform and thresholding. We show that this method is substantially faster than the original approach and has the same order of accuracy.