The spatially and temporally variable parameters and inputs to complex groundwater
models typically result in long runtimes which hinder comprehensive calibration, sensitivity …

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 …

Hydraulic conductivity exhibits a high spatial variability due to the heterogeneity and
discontinuity of the geologic environments and their constituent materials. Representing …

In this paper, we derive an a-posteriori error indicator for the Generalized Multiscale Finite
Element Method (GMsFEM) framework. This error indicator is further used to develop an …

The construction of local reduced-order models via multiscale basis functions has been an
area of active research. In this paper, we propose online multiscale basis functions which …

In this paper, we propose oversampling strategies in the generalized multiscale finite
element method (GMsFEM) framework. The GMsFEM, which has been recently introduced …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

In this paper, we discuss the application of generalized multiscale finite element method
(GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity …

Discrete fracture networks (DFN) are often used to model flow and transport in fractured
porous media. The accurate resolution of flow and transport behavior on a large DFN …

In this work, we combine the generalized multiscale finite element method (GMsFEM) with a
reduced model based on the discrete fracture model (DFM) to resolve the difficulties of …