Related papers: Provably size-guaranteed mesh generation with supe…
The formalism of language generation in the limit studies generative models by requiring an algorithm, given strings from a hidden true language, to eventually generate new valid strings. A core issue is the tension between validity and…
The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions,…
Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…
In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties,…
The generalization ability of kernel interpolation in large dimensions (i.e., $n \asymp d^{\gamma}$ for some $\gamma>0$) might be one of the most interesting problems in the recent renaissance of kernel regression, since it may help us…
We give a Dirichlet form approach for the construction of distorted Brownian motion in a bounded domain $\Omega$ of $\mathbb{R}^d$, $d \geq 1$, with boundary $\Gamma$, where the behavior at the boundary is sticky. The construction covers…
We show that optimal $L^2$-convergence in the finite element method on quasi-uniform meshes can be achieved if, for some $s_0 > 1/2$, the boundary value problem has the mapping property $H^{-1+s} \rightarrow H^{1+s}$ for $s \in [0,s_0]$.…
Delaunay has shown that the Delaunay complex of a finite set of points $P$ of Euclidean space $\mathbb{R}^m$ triangulates the convex hull of $P$, provided that $P$ satisfies a mild genericity property. Voronoi diagrams and Delaunay…
The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order…
This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes…
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…
A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic…
This paper provides the currently best known upper bound on the density of a packing in three-dimensional Euclidean space of two types of spheres whose size ratio is the largest one that allows the insertion of a small sphere in each…
The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…
This paper develops a unified theory of natural superconvergence points for polynomial spline approximations to second-order elliptic problems. Beginning with the one-dimensional case, we establish that when a point $x_0$ is a local…
The Ordered Upwind Method (OUM) is used to approximate the viscosity solution of the static Hamilton-Jacobi-Bellman (HJB) with direction-dependent weights on unstructured meshes. The method has been previously shown to provide a solution…
We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency…
We prove that a planar $C^2$-regular boundary $\Gamma$ can always be parameterized with its closest point projection $\pi$ over a certain collection of edges $\Gamma_h$ in an ambient triangulation, by making simple assumptions on the…
In this paper, the author derives an $O(h^4)$-superconvergence for the piecewise linear Ritz-Galerkin finite element approximations for the second order elliptic equation $-\nabla \cdot(A\nabla u)= f$ equipped with Dirichlet boundary…
The Hilbert metric is a distance function defined for points lying within the interior of a convex body. It arises in the analysis and processing of convex bodies, machine learning, and quantum information theory. In this paper, we show how…