相关论文: Analysis of a New Harmonically Enriched Multiscale…

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…

Feature matching between image pairs is a fundamental problem in computer vision that drives many applications, such as SLAM. Recently, semi-dense matching approaches have achieved substantial performance enhancements and established a…

Holographic displays hold the promise of providing authentic depth cues, resulting in enhanced immersive visual experiences for near-eye applications. However, current holographic displays are hindered by speckle noise, which limits…

Convolutional Neural Networks (CNNs) have achieved high accuracy for cardiac structure segmentation if training cases and testing cases are from the same distribution. However, the performance would be degraded if the testing cases are from…

The Generalized Finite Element Method (GFEM) is an effective unfitted numerical method for handling interface problems. By augmenting the standard FEM space with an appropriate enrichment space, GFEM can accurately capture C^0 solutions…

Deep learning-based methods for low-light image enhancement typically require enormous paired training data, which are impractical to capture in real-world scenarios. Recently, unsupervised approaches have been explored to eliminate the…

This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization…

A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…

In this paper, we introduce the Fully Homomorphic Integrity Model (HIM), a novel approach designed to enhance security, efficiency, and reliability in encrypted data processing, primarily within the health care industry. HIM addresses the…

In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the Generalized Multiscale Finite Element Method (GMsFEM). In order…

The hierarchical equations of motion (HEOM) provide a numerically exact approach for computing the reduced dynamics of a quantum system linearly coupled to a bath. We have found that HEOM contains temperature-dependent instabilities that…

The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E and B. Engquist, \emph{Commun. Math. Sci.},…

In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…

In this paper, we consider local multiscale model reduction for problems with multiple scales in space and time. We developed our approaches within the framework of the Generalized Multiscale Finite Element Method (GMsFEM) using space-time…

The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the…

Fully Homomorphic Encryption (FHE) allows for computation directly on encrypted data and enables privacy-preserving neural inference in the cloud. Prior work has focused on models with dense inputs (e.g., CNNs), with less attention given to…

In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically studied. The local spaces are built from selected eigenvectors…

Hashing is an efficient method for nearest neighbor search in large-scale data space by embedding high-dimensional feature descriptors into a similarity preserving Hamming space with a low dimension. However, large-scale high-speed…

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…

We are interested in time-harmonic acoustic scattering by an impenetrable obstacle in a medium where the wavenumber is constant in an exterior unbounded subdomain and is possibly heterogeneous in a bounded subdomain. The associated…