Related papers: On the circumradius condition for piecewise linear…
Symmetric polynomial quadrature rules for triangles are commonly used to efficiently integrate two-dimensional domains in finite-element-type problems. While the development of such rules focuses on the maximum degree a given number of…
We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the…
We show that any surface of infinite type admits an ideal triangulation. Furthermore, we show that a set of disjoint arcs can be completed into a triangulation if and only if, as a set, they intersect every simple closed curve a finite…
In this paper we prove that a finite triangulation of a connected closed surface is completely determined by its intersection matrix. The \emph{intersection matrix} of a finite triangulation, $K$, is defined as $M_{K}=(dim(s_{i}\cap…
In this paper, we deal with algorithms to solve the finite-sum problems related to fitting over-parametrized models, that typically satisfy the interpolation condition. In particular, we focus on approaches based on stochastic line searches…
The non-conforming linear ($P_1$) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both theoretical and practical senses. Since various error constants must be quantitatively evaluated for…
We define essential and strongly essential triangulations of 3-manifolds, and give four constructions using different tools (Heegaard splittings, hierarchies of Haken 3-manifolds, Epstein-Penner decompositions, and cut loci of Riemannian…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
A new preconditioner is developed for high order finite element approximation of linear elastic problems on triangular meshes in two dimensions. The new preconditioner results in a condition number that is bounded independently of the…
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic…
In this paper we present methods for triangulation of infinite cylinders from image line silhouettes. We show numerically that linear estimation of a general quadric surface is inherently a badly posed problem. Instead we propose to…
Electromagnetic metasurfaces offer the capability to realize almost arbitrary power conserving field transformations. These field transformations are governed by the generalized sheet transition conditions, which relate the tangential…
Intrinsic aberrations are those which occur due to the finite length of the desired field configuration. They are often loosely ascribed to the fringing field. This is misleading as it implies that the effects can be minimized by shaping…
We investigate a spatial random graph model whose vertices are given as a marked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pair of points independently with probability depending on the spatial displacement of the…
In this paper, we investigate the approximation properties of two types of multiscale finite element methods with oversampling as proposed in [Hou \& Wu, {\textit{J. Comput. Phys.}}, 1997] and [Efendiev, Hou \& Wu, \textit{SIAM J. Numer.…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
In two-view geometry, the essential matrix describes the relative position and orientation of two calibrated images. In three views, a similar role is assigned to the calibrated trifocal tensor. It is a particular case of the (uncalibrated)…
We introduce a definition of the electromagnetic chirality of an object and show that it has an upper bound. Reciprocal objects attain the upper bound if and only if they are transparent for all the fields of one polarization handedness…
Complete reliance on the fitted model in response surface experiments is risky and relaxing this assumption, whether out of necessity or intentionally, requires an experimenter to account for multiple conflicting objectives. This work…