In the paper, a heuristic algorithm for tensor product approximation with B-spline basis functions of three-dimensional material data is presented. The algorithm has an application as a preconditioner for implicit dynamics simulations of a non-linear flow in heterogeneous media using alternating directions method. As the simulation use-case, a non-stationary problem of liquid fossil fuels exploration with hydraulic fracturing is considered. Presented algorithm allows to approximate the permeability coefficient function as a tensor product what in turn allows for implicit simulations of the Laplacian term in the partial differential equation. In the consequence the number of time steps of the non-stationary problem can be reduced, while the numerical accuracy is preserved.
CITATION STYLE
Podsiadło, K., Łoś, M., Siwik, L., & Woźniak, M. (2018). An Algorithm for Tensor Product Approximation of Three-Dimensional Material Data for Implicit Dynamics Simulations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10861 LNCS, pp. 156–168). Springer Verlag. https://doi.org/10.1007/978-3-319-93701-4_12
Mendeley helps you to discover research relevant for your work.