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Wavelet based solution of flow and diffusion problems in digital materials. (English) Zbl 1390.65171

Summary: The computation of physical properties in a digital materials laboratory requires significant computational resources. Due to the complex nature of the media, one of the most difficult 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 fictitious 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.

MSC:

65T60 Numerical methods for wavelets
65N85 Fictitious domain methods for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
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