相关论文: Generalized multiscale finite element method for h…

We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…

This paper introduces an Algebraic MultiScale method for simulation of flow in heterogeneous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and…

The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…

Traditional two level upscaling techniques suffer from a high offline cost when the coarse grid size is much larger than the fine grid size. Thus, multilevel methods are desirable for problems with complex heterogeneities and high contrast.…

In this paper, we propose a rigorous and accurate non-local (in the oversampled region) upscaling framework based on some recently developed multiscale methods [10]. Our proposed method consists of identifying multi-continua parameters via…

We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…

Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…

Knowledge of the underlying mechanisms of multiphase flow dynamics in porous media is crucial for optimizing subsurface engineering applications like geological carbon sequestration. However, studying the micro-mechanisms of multiphase…

In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…

The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…

Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic…

This paper is dedicated to the rigorous numerical analysis of a Multiscale Finite Element Method (MsFEM) for the Stokes system, when dealing with highly heterogeneous media, as proposed in [B.P.~Muljadi et al., arXiv:1404.2837]. The method…

Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…

In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equation. To define the multiscale basis functions, we first build an auxiliary multiscale space by…

Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of compressible two-component flow, and propose a heterogeneous…

Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a…

In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems. It is based on the generalized multiscale finite element method (GMsFEM) and multilevel…

In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…

The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…