Geodesic
Numerical estimation of electrical resistivity in digital rocks using GPUs
Numerical methods and programming, Tome 21 (2020) no. 3, pp. 306-318

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We present a numerical algorithm for computing the electric field in digital rock samples and estimating their electrical resistivity (conductivity). The main peculiarity of the algorithm is its applicability tostrongly heterogeneous models including partially saturated and multi-mineral rock samples. The algorithm is based on the iterative Krylov-type solver preconditioned by the inverse Laplace operator for homogeneous media. The preconditioner is computed using the spectral method in directions orthogonal to the direction of the main electric current, whereas the series of 1D problems are solved by the Thomas algorithm. We implement the algorithm using GPUs, which allows us to use a single GPU to solve the problems for samples whose size is up to $400^3$ voxels.
Keywords: digital rock physics; finite-difference method; iterative methods; electrical resistivity; numerical upscaling. 
@article{VMP_2020_21_3_a8,
     author = {T. S. Khachkova and V. V. Lisitsa and G. V. Reshetova and V. A. Tcheverda},
     title = {Numerical estimation of electrical resistivity in digital rocks  using {GPUs}},
     journal = {Numerical methods and programming},
     pages = {306--318},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a8/}
}
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T. S. Khachkova; V. V. Lisitsa; G. V. Reshetova; V. A. Tcheverda. Numerical estimation of electrical resistivity in digital rocks  using GPUs. Numerical methods and programming, Tome 21 (2020) no. 3, pp. 306-318. http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a8/