An efficient data structure for random walk algorithms in faceted porous media

Modern X-ray Computerized Micro-Tomography (CMT) facilities allow researchers interested in composite materials and porous media to image their samples in 3D with micrometer resolution. The datasets obtained for representative samples are frequently very large (10243 voxels in gray-scale levels). Performing a tessellation on such datasets would produce hundreds millions facets, which would be impossible to handle in memory on rather powerful computers. Various numerical methods are classical for the prediction of some effective properties of porous and other composite media from the phase properties and the micro-structure (diffusivities, conductivities). The choice of a Monte-Carlo random walk scheme is justified by its minimal memory cost in addition to image storage. In order to employ it, one must be able to perform ray-tracing in large and precise 3D images. The new framework we present allows that feature by using a memory-sparing data structure dedicated to such algorithms. We only store in memory the vertices provided by the marching cube algorithm. So, since the facets are not stored, the needed memory size is divided by a factor of five, without any significant increasing of the computation time: the extraction of properties from very large micro-porous media samples is now possible. This study allows us to claim that a simulation making an intensive use of ray-tracing in tessellated media obtained with the marching-cube algorithm is not as expensive (in terms of memory and time cost) as it could seem. We show that the marching-cube algorithm, when it is used dynamically to connect vertices upon request, is still a very powerful mesh generator since it consumes then very few memory, and that it can be trivially implemented.