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 …
Novel design and analysis of generalized finite element methods based on locally optimal spectral approximations
C Ma, R Scheichl, T Dodwell - SIAM Journal on Numerical Analysis, 2022 - SIAM
In this paper, the generalized finite element method (GFEM) for solving second order elliptic
equations with rough coefficients is studied. New optimal local approximation spaces for …
equations with rough coefficients is studied. New optimal local approximation spaces for …
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 …
Generalized multiscale finite element methods for problems in perforated heterogeneous domains
Complex processes in perforated domains occur in many real-world applications. These
problems are typically characterized by physical processes in domains with multiple scales …
problems are typically characterized by physical processes in domains with multiple scales …
Efficient hybrid explicit-implicit learning for multiscale problems
Splitting method is a powerful method to handle application problems by splitting physics,
scales, domain, and so on. Many splitting algorithms have been designed for efficient …
scales, domain, and so on. Many splitting algorithms have been designed for efficient …
[HTML][HTML] Multiscale modeling of heat and mass transfer in fractured media for enhanced geothermal systems applications
In this work, heat and mass transfer in a hypothetical Enhanced Geothermal System with
complex fracture network is considered. Fracture networks have complex geometries, exist …
complex fracture network is considered. Fracture networks have complex geometries, exist …
[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 …
Fast multiscale reservoir simulations using pod-deim model reduction
In this paper, we present a global-local model reduction for fast multiscale reservoir
simulations in highly heterogeneous porous media with applications to optimization and …
simulations in highly heterogeneous porous media with applications to optimization and …
[HTML][HTML] The multivariate theory of connections
This paper extends the univariate Theory of Connections, introduced in (Mortari, 2017), to
the multivariate case on rectangular domains with detailed attention to the bivariate case. In …
the multivariate case on rectangular domains with detailed attention to the bivariate case. In …
Fast multiscale reservoir simulations with POD-DEIM model reduction
We present a global/local model reduction for fast multiscale reservoir simulations in highly
heterogeneous porous media. Our approach identifies a low-dimensional structure in the …
heterogeneous porous media. Our approach identifies a low-dimensional structure in the …