Related papers: Layer-adapted meshes for weak boundary layers

We propose a novel locally adaptive learning estimator for enhancing the inter- and intra- discriminative capabilities of Deep Neural Networks, which can be used as improved loss layer for semantic image segmentation tasks. Most loss layers…

We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…

We establish the convergence of an adaptive spline-based finite element method of a fourth order elliptic problem.

We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…

We prove the partial regularity of the boundary suitable weak solutions to the MHD system near the plane part of the boundary.

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

A class of quasilinear singularly perturbed boundary value problems with a turning point of attractive type is considered. The problems are solved numerically by a finite-difference scheme on a special discretization mesh which is dense…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is…

We discuss the potential of multilayered plasmonic particles to tailor the optical scattering response. The interplay of plasmons localized in thin stacked shells realizes peculiar degenerate cloaking and resonant states occurring at…

Embedding learning for categorical features is crucial for the deep learning-based recommendation models (DLRMs). Each feature value is mapped to an embedding vector via an embedding learning process. Conventional methods configure a fixed…

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…

A numerical study on the elastic response of single- and multi-layer systems formed by alternating pentamode lattices and stiffening plates is presented. Finite element simulations are conducted to analyze the dependence of the effective…

We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation satisfies an energy inequality and demonstrate numerically,…

A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…

This note is intended as a brief introduction to the theory and practice of perfectly matched layer (PML) absorbing boundaries for wave equations, originally developed for MIT courses 18.369 and 18.336. It focuses on the complex…

Heatmap regression with a deep network has become one of the mainstream approaches to localize facial landmarks. However, the loss function for heatmap regression is rarely studied. In this paper, we analyze the ideal loss function…

This study presents constructions of the space-time Conservation Element and Solution Element (CESE) methods to accommodate adaptive unstructured quadrilateral meshes. Subsequently, a novel algorithm is devised to effectively manage the…

We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely…

This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…

We propose a new architecture for difficult image processing operations, such as natural edge detection or thin object segmentation. The architecture is based on a simple combination of convolutional neural networks with the nearest…