Related papers: Adaptive Mesh Refinement for Variational Inequalit…
We demonstrate a practical differentiable programming approach for acoustic inverse problems through two applications: admittance estimation and shape optimization for resonance damping. First, we show that JAX-FEM's automatic…
Visual anomaly detection aims to identify anomalous regions in images through unsupervised learning paradigms, with increasing application demand and value in fields such as industrial inspection and medical lesion detection. Despite…
The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…
Visual-Inertial Odometry (VIO) algorithms typically rely on a point cloud representation of the scene that does not model the topology of the environment. A 3D mesh instead offers a richer, yet lightweight, model. Nevertheless, building a…
This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic…
Adaptive Mesh Refinement (AMR) enables efficient computation of flows by providing high resolution in critical regions while allowing for coarsening in areas where fine detail is unnecessary. While early AMR software packages relied solely…
Facial Expression Recognition (FER) is a classification task that points to face variants. Hence, there are certain affinity features between facial expressions, receiving little attention in the FER literature. Convolution padding, despite…
Free space ground segmentation is essential to navigate autonomous robots, recognize drivable zones, and traverse efficiently. Fine-grained features remain challenging for existing segmentation models, particularly for robots in indoor,…
We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
An adaptive mesh refinement and error estimation method for numerically solving optimal control problems is developed using Legendre-Gauss-Radau direct collocation. In regions of the solution where the desired accuracy tolerance has not…
This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…
Adaptive Mesh Refinement (AMR) is becoming a prevalent data representation for scientific visualization. Resulting from large fluid mechanics simulations, the data is usually cell centric, imposing a number of challenges for high quality…
An implicit method for the ohmic dissipation is proposed. The proposed method is based on the Crank-Nicolson method and exhibits second-order accuracy in time and space. The proposed method has been implemented in the SFUMATO adaptive mesh…
We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the…
Coarsely-labeled semantic segmentation annotations are easy to obtain, but therefore bear the risk of losing edge details and introducing background pixels. Impeded by the inherent noise, existing coarse annotations are only taken as a…
Spectral element methods (SEM), which are extensions of finite element methods (FEM), are important emerging techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver better accuracy due…
I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell…