相关论文: Laplacian smoothing revisited

Elliptic homogenization is used to determine coarse-grained properties of materials with features on small scales for heat transfer and elasticity. When microstructural features of a material have rapid, periodic fluctuations, the solution…

It is known that the $L^{2}$-norms of a harmonic function over spheres satisfies some convexity inequality strongly linked to the Almgren's frequency function. We examine the $L^{2}$-norms of harmonic functions over a wide class of evolving…

We present a novel approach named TBase for smoothing planar and surface quadrilateral meshes. Our motivation is that the best shape of quadrilateral element (square) can be virtually divided into a pair of equilateral right triangles by…

We develop a theory of surfaces with boundary moving by mean curvature flow. In particular, we prove a general existence theorem by elliptic regularization, and we prove boundary regularity at all positive times under very mild hypotheses.

We show that any generalised smooth distribution on a smooth manifold, possibly of non-constant rank, admits a Riemannian metric. Using such a metric, we attach a Laplace operator to any smooth distribution as such. When the underlying…

In our previous papers we have described efficient and reliable methods of generation of representative volume elements (RVE) perfectly suitable for analysis of composite materials via stochastic homogenization. In this paper we profit from…

An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…

In these notes we give an interdisciplinary result which links the geometric concept of minimal surfaces with generalized harmonic functions.

This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle it is a flow like method in…

This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the…

We investigate in this paper the existence of a metric which maximizes the first eigenvalue of the Laplacian on Riemannian surfaces. We first prove that, in a given conformal class, there always exists such a maximizing metric which is…

Smoothing and sharpening are two fundamental image processing operations. The latter is usually related to the former through the unsharp masking algorithm. In this paper, we develop a new type of filter which performs smoothing or…

The Assouad and lower dimensions and dimension spectra quantify the regularity of a measure by considering the relative measure of concentric balls. On the other hand, one can quantify the smoothness of an absolutely continuous measure by…

A version of the Law of the Iterated Logarithm for smooth functions in the upper-half space is proved. As a consequence, we show that certain size conditions on the gradient and the gradient of the laplacian of a smooth function, lead to…

We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…

Gloss is a quantity used in the optical industry to quantify and categorize materials according to how well they scatter light specularly. With the aid of phase perturbation theory, we derive an approximate expression for this quantity for…

We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…

We prove that the mean curvature of a smooth surface in $\mathbb{R}^n$, $n\geq 2$, arises as the limit of a sequence of functions that are intrinsically related to the difference between an $n$- and $1$-dimensional fractional Laplacian of a…

The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…

The problem of stability in the machining processes is an important task. It is strictly connected with the final quality of a product. In this paper we consider vibrations of a tool-workpiece system in a straight turning process induced by…