相关论文: On the initial estimate of interface forces in FET…
The velocity, coupling term in the flow and transport problems, is important in the accurate numerical simulation or in the posteriori error analysis for adaptive mesh refinement. We consider Enhanced Velocity Mixed Finite Element Method…
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…
The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
Unfitted finite element methods, e.g., extended finite element techniques or the so-called finite cell method, have a great potential for large scale simulations, since they avoid the generation of body-fitted meshes and the use of graph…
Federated edge learning (FEEL) enables collaborative model training across distributed clients over wireless networks without exposing raw data. While most existing studies assume static datasets, in real-world scenarios clients may…
Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…
Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces…
The enrichment formulation of double-interpolation finite element method (DFEM) is developed in this paper. DFEM is first proposed by Zheng \emph{et al} (2011) and it requires two stages of interpolation to construct the trial function. The…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
Federated learning (FL) enables collaborative model training across distributed devices while preserving data privacy, but deployment on resource-constrained edge nodes remains challenging due to limited memory, energy, and communication…
Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over…
We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…
The fast Fourier transform (FFT) is undoubtedly an essential primitive that has been applied in various fields of science and engineering. In this paper, we present a decomposition method for parallelization of multi-dimensional FFTs with…
We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the…