相关论文: Adaptive mixed GMsFEM for flows in heterogeneous m…
In this paper, we develop an iterative scheme to construct multiscale basis functions within the framework of the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for the mixed formulation. The…
We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
In this paper, we discuss multiscale methods for nonlinear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are…
A Flow is a collection of component models ("Agents") which constructs the solution to a complex problem via iterative communication. Flows have emerged as state of the art architectures for code generation, and are the raison d'etre for…
Online optimization has emerged as powerful tool in large scale optimization. In this paper, we introduce efficient online algorithms based on the alternating directions method (ADM). We introduce a new proof technique for ADM in the batch…
Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time…
We present two a posteriori error estimators for the virtual element method (VEM) based on global and local flux reconstruction in the spirit of [5]. The proposed error estimators are reliable and efficient for the $h$-, $p$-, and…
One of the biggest challenges in Federated Learning (FL) is that client devices often have drastically different computation and communication resources for local updates. To this end, recent research efforts have focused on training…
In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called…
In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…
Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…
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…
In this work, we propose a novel model order reduction approach for two-phase flow in porous media by introducing a formulation in which the mobility, which realizes the coupling between phase saturations and phase pressures, is regarded as…
The Generalized Finite Element Method (GFEM) is an extension of the Finite Element Method (FEM), where the standard finite element space is augmented with a space of non-polynomial functions, called the enrichment space. The functions in…
In this work, we develop adaptive schemes using goal-oriented error control for a highly nonlinear flow temperature model with temperature dependent density. The dual-weighted residual method for computing error indicators to steer mesh…
We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170…
A hydrogeological model for the spread of pollution in an aquifer is considered. The model consists in a convection-diffusion-reaction equation involving the dispersion tensor which depends nonlinearly of the fluid velocity. We introduce an…
The mathematical formulation of sign-changing problems involves a linear second-order partial differential equation in the divergence form, where the coefficient can assume positive and negative values in different subdomains. These…
We introduce an enriched immersed finite element method for addressing interface problems characterized by general non-homogeneous jump conditions. Unlike many existing unfitted mesh methods, our approach incorporates a homogenization…