We develop a new approach to the numerical simulation of conduction of heat or electrical charges in a heterogeneous solid material, The morphology of the solid material is characterized by broadly distributed and correlated local conductances. The development of the solution of conduction in such materials has been hampered by the fact that one must utilize a highly detailed and large computational grid if the effect of the distribution of the local conductances and the correlations between them is to be taken into account. In this paper, we describe a method based on the use of wavelet transformations that reduces the computation time very significantly. Starting with a fine-scale computational grid that may contain millions of grid points or blocks, a wavelet transformation is used to systematically coarsen those zones of the grid where a detailed structure is not needed, but preserve the fine details of the grid in the zones that contribute significantly to the conduction process. The coarsening can be static, but can also be dynamic such that the grid structure evolve with the time if, for example, the local conductances are a strong function of the temperature. Utilizing the proposed method, the results of extensive computer simulations of conduction in model composite materials, in which the conductance distribution is broad and contains long-range correlations, are reported. We demonstrate that the wavelet-based grid coarsening reduces, by at least two orders of magnitude, the number of equations to be solved without neglecting any important information about the materials' morphology. Therefore, the proposed method leads to an accurate solution of the conduction problem at greatly reduced (by at least two orders of magnitude) computational cost. (C) 2004 Elsevier Ltd. All rights reserved.