Adaptive multiscale model reduction with generalized multiscale finite element methods
In this paper, we discuss a general multiscale model reduction framework based on
multiscale finite element methods. We give a brief overview of related multiscale methods …
multiscale finite element methods. We give a brief overview of related multiscale methods …
Deep multiscale model learning
The objective of this paper is to design novel multi-layer neural networks for multiscale
simulations of flows taking into account the observed fine data and physical modeling …
simulations of flows taking into account the observed fine data and physical modeling …
Efficient deep learning techniques for multiphase flow simulation in heterogeneous porousc media
We present efficient deep learning techniques for approximating flow and transport
equations for both single phase and two-phase flow problems. The proposed methods take …
equations for both single phase and two-phase flow problems. The proposed methods take …
[图书][B] Multiscale Model Reduction
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …
impact of computer technology, the growing importance of computer modeling and the …
Generalized multiscale finite element treatment of a heterogeneous nonlinear strain-limiting elastic model
M Vasilyeva, SM Mallikarjunaiah - Multiscale Modeling & Simulation, 2024 - SIAM
In this work, we consider a nonlinear strain-limiting elastic model in heterogeneous
domains. We investigate heterogeneous material with soft and stiff inclusions and …
domains. We investigate heterogeneous material with soft and stiff inclusions and …
Fast online generalized multiscale finite element method using constraint energy minimization
Local multiscale methods often construct multiscale basis functions in the offline stage
without taking into account input parameters, such as source terms, boundary conditions …
without taking into account input parameters, such as source terms, boundary conditions …
Multiscale solver for multi-component reaction–diffusion systems in heterogeneous media
Coupled nonlinear system of reaction–diffusion equations describing multi-component
(species) interactions with heterogeneous coefficients is considered. Finite volume method …
(species) interactions with heterogeneous coefficients is considered. Finite volume method …
[HTML][HTML] Generalized Multiscale Finite Element method for multicontinua unsaturated flow problems in fractured porous media
In this paper, we present a multiscale method for simulations of the multicontinua
unsaturated flow problems in heterogeneous fractured porous media. The mathematical …
unsaturated flow problems in heterogeneous fractured porous media. The mathematical …
[HTML][HTML] Multiscale model reduction for transport and flow problems in perforated domains
Convection-dominated transport phenomenon is important for many applications. In these
applications, the transport velocity is often a solution of heterogeneous flow problems, which …
applications, the transport velocity is often a solution of heterogeneous flow problems, which …
Reduced-order deep learning for flow dynamics. The interplay between deep learning and model reduction
In this paper, we investigate neural networks applied to multiscale simulations of porous
media flows and discuss a design of a novel deep neural network model reduction approach …
media flows and discuss a design of a novel deep neural network model reduction approach …