An Algorithm for Tensor Product Approximation of Three-Dimensional Material Data for Implicit Dynamics Simulations [chapter]

Krzysztof Podsiadło, Marcin Łoś, Leszek Siwik, Maciej Woźniak
2018 Lecture Notes in Computer Science  
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
more » ... ity 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 nonstationary problem can be reduced, while the numerical accuracy is preserved.
doi:10.1007/978-3-319-93701-4_12 fatcat:635u775bjndulh3c44eh264dbm