Related papers: Spectral Methods for capillary surfaces described …
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic…
A class of surfaces-graphs in a Riemannian 3-space with a prescribed projection of one field of principal directions onto a surface $\Pi$ is considered. A problem of determination of such surfaces when both principal curvatures are given…
The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to…
We characterize all compact embedded stable minimal capillary surfaces with capillary angle close to either $0$ or $\pi$ that are supported on a complete embedded minimal surface with finite total curvature that is not an affine plane.…
In this paper we investigate constant mean curvature surfaces with nonempty boundary in Euclidean space that meet a right cylinder at a constant angle along the boundary. If the surface lies inside of the cylinder, we obtain some results of…
We construct a surface that is obtained from the octahedron by pushing out 4 of the faces so that the curvature is supported in a copy of the Sierpinski gasket in each of them, and is essentially the self similar measure on SG. We then…
In this work, a class of non-linear weakly singular fractional integro-differential equations is considered, and we first prove existence, uniqueness, and smoothness properties of the solution under certain assumptions on the given data. We…
We compare several different methods involving Hodge-theoretic spectra of singularities which produce constraints on the number and type of isolated singularities on projective hypersurfaces of fixed degree. In particular, we introduce a…
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on…
In this paper we develop a class of efficient Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to…
A new approach for integration of the initial value problem for ordinary differential equations is suggested. The algorithm is based on approximation of the solution by a system of functions that contains orthogonal exponential polynomials.
Ruled surfaces play an important role in various types of design, architecture, manufacturing, art, and sculpture. They can be created in a variety of ways, which is a topic that has been the subject of much discussion in mathematics and…
We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…
An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last line segments are enforced to be the head and tail ruling…
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…
Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…
Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
We put forward a new type of spectral method for the direct numerical simulation of flows where anisotropy or very fine boundary layers are present. The mean idea is to take advantage of the fact that such structures are dissipative and…