Related papers: Layer-adapted meshes for weak boundary layers
Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived for APME for time-independent diffusion. Anisotropic mesh…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
The increasing complexity of deep learning architectures is resulting in training time requiring weeks or even months. This slow training is due in part to vanishing gradients, in which the gradients used by back-propagation are extremely…
Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…
Triangular meshes are the most popular representations of 3D objects, but many mesh surfaces contain topological singularities that represent a challenge for displaying or further processing them properly. One such singularity is the…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…
Mesh sensitivity of finite element solution for linear elliptic partial differential equations is analyzed. A bound for the change in the finite element solution is obtained in terms of the mesh deformation and its gradient. The bound shows…
Object oriented bounding box tree (OBB-Tree for short) has many applications in collision detection, real-time rendering, etc. It has a wide range of applications. The construction of the hierarchical directed bounding box of the solid mesh…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
Contrastive learning is a discriminative approach that aims at grouping similar samples closer and diverse samples far from each other. It it an efficient technique to train an encoder generating distinguishable and informative…
This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions…
Recent years have witnessed great progress in deep learning based object detection. However, due to the domain shift problem, applying off-the-shelf detectors to an unseen domain leads to significant performance drop. To address such an…
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…
In the present study we consider an example of a boundary value problem for a simple second order ordinary differential equation, which may exhibit a boundary layer phenomenon. We show that usual central finite differences, which are second…
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
Weak gravitational lensing of background galaxies offers an excellent opportunity to study the intervening distribution of matter. While much attention to date has focused on the two-point function of the cosmic shear, the three-point…
The problem of image segmentation is known to become particularly challenging in the case of partial occlusion of the object(s) of interest, background clutter, and the presence of strong noise. To overcome this problem, the present paper…
In potential theory, use of barriers is one of the most important techniques. We construct strong barriers for weighted quasilinear elliptic operators. There are two applications: (i) solvability of Poisson-type equations with boundary…