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 …

The study of rock crack propagation by multi-scale method is of great significance to
comprehensively and accurately understand the law of rock crack evolution. In this paper …

This work proposes a stochastic domain decomposition method for solving steady-state
partial differential equations (PDEs) with random inputs. Specifically, based on the efficiency …

For estimation of the durability of recycled aggregate concrete (RAC) in chloride-rich
environment, it is valuable to investigate the chloride diffusivity in RAC. Because RAC is …

In this paper, we propose a model reduction method for solving multiscale elliptic PDEs with
random coefficients in the multiquery setting using an optimization approach. The …

Elasticity is a fundamental model in mechanics and material sciences. In the article, we
present an ensemble variable-separated multiscale method for elasticity problems in …

We propose a data-driven approach to solve multiscale elliptic PDEs with random
coefficients based on the intrinsic approximate low-dimensional structure of the underlying …

We propose a generalized multiscale finite element method (GMsFEM) based on clustering
algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our …

We propose a reduced-order model-based variational inference method with normalizing
flows for Bayesian elliptic inverse problems. The coefficient of the elliptic PDE is represented …

In this paper, we propose an offline-online strategy based on the Localized Orthogonal
Decomposition (LOD) method for elliptic multiscale problems with randomly perturbed …