Partial Learning Using Partially Explicit Discretization for Heterogeneous Transport Problem Simulation.

Autor: Alekseev, V. N., Kalachikova, U. S., Yang, Y.
Zdroj: Lobachevskii Journal of Mathematics; Oct2023, Vol. 44 Issue 10, p4103-4115, 13p
Abstrakt: This article presents a novel approach for learning and simulating multicontinuum/multiscale problems with limited observations. The proposed method, called partial learning with partially explicit discretization, combines hybrid explicit-implicit (HEI) learning techniques with the finite element method to solve the dual continuum transport problem in perforated domains. The mathematical model, including the convection-diffusion for the concentrations and Stokes equations for the velocity field, is described. The problem is approximated using the finite element method on a fine grid and discretized in time using partially explicit scheme. Proper Orthogonal Decomposition (POD) is employed for spatial interpolation and dimensionality reduction, while the Discrete Empirical Interpolation Method (DEIM) determines the interpolation nodes. The effectiveness of the proposed approach in accurately reconstructing the solution using limited observations is demonstrated through numerical results for a two-dimensional model flow and transport problem in a perforated medium. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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