Convergence of the CEM-GMsFEM for Stokes flows in heterogeneous perforated domains [PDF]
Journal of Computational and Applied Mathematics, 2021 In this paper, we consider the incompressible Stokes flow problem in a perforated domain and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem.
Hu, Jiuhua, Chung, Eric, Pun, Sai Mang
core +3 more sources
An innovative application of deep learning in multiscale modeling of subsurface fluid flow Reconstructing the basis functions of the mixed Generalized Multiscale Finite Element Method (GMsFEM) [PDF]
Journal of Petroleum Science and Engineering, 2022 In multiscale modeling of subsurface fluid flow in heterogeneous porous media, standard polynomial basis functions are replaced by multiscale basis functions.
Coenen, Frans +3 more
core +3 more sources
CEM-GMsFEM for Poisson equations in heterogeneous perforated domains
Multiscale Modeling & SimulationIn this paper, we propose a novel multiscale model reduction strategy tailored to address the Poisson equation within heterogeneous perforated domains.
Yang, Yin +3 more
core +2 more sources
Prediction of discretization of online GMsFEM using deep learning for Richards equation
Journal of Computational and Applied MathematicsWe develop a new coarse-scale approximation strategy for the nonlinear single-continuum Richards equation as an unsaturated flow over heterogeneous non-periodic media, using the online generalized multiscale finite element method (online GMsFEM) together
Mai, Tina +2 more
core +3 more sources
Dynamic data-driven Bayesian GMsFEM [PDF]
Journal of Computational and Applied Mathematics, 2019 In this paper, we propose a Bayesian approach for multiscale problems with the availability of dynamic observational data. Our method selects important degrees of freedom probabilistically in a Generalized multiscale finite element method framework. Due to scale disparity in many multiscale applications, computational models can not resolve all scales.
Siu Wun Cheung, Nilabja Guha
core +4 more sources
Adaptive Multiscale Model Reduction for Nonlinear Parabolic Equations Using GMsFEM [PDF]
Computational Science – ICCS 2020, 2020 14 pages.
Wang Y, Chung E, Fu S.
europepmc +4 more sources
Mixed GMsFEM for linear poroelasticity problems in heterogeneous porous media [PDF]
Journal of Computational and Applied Mathematics, 2021 Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome this computational challenge, various multiscale methods are developed.
Xia Wang +3 more
openaire +3 more sources
Contrast-Independent, Partially-Explicit Time Discretizations for Nonlinear Multiscale Problems
Mathematics, 2021 This work continues a line of work on developing partially explicit methods for multiscale problems. In our previous works, we considered linear multiscale problems where the spatial heterogeneities are at the subgrid level and are not resolved. In these
Eric T. Chung +3 more
doaj +1 more source
Multiscale Multiphysics Modeling of the Infiltration Process in the Permafrost
Mathematics, 2021 In this work, we design a multiscale simulation method based on the Generalized Multiscale Finite Element Method (GMsFEM) for numerical modeling of fluid seepage under permafrost condition in heterogeneous soils.
Sergei Stepanov +2 more
doaj +1 more source
Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change
Computation, 2023 This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and ...
Dmitry Ammosov, Maria Vasilyeva
doaj +1 more source