Related papers: Multi-scale spectral methods for bounded radially …
Calculating the spectral function of two dimensional systems is arguably one of the most pressing challenges in modern computational condensed matter physics. While efficient techniques are available in lower dimensions, two dimensional…
This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…
We prove that the index of a CMC surface with capillary boundary is bounded from above linearly by its genus, number of boundary components, and branching order, and also by some Willmore-type energy involving the area, mean curvature,…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of…
We develop minimal slicing via capillary hypersurfaces to understand positive scalar curvature metric on manifolds with boundary. The method provides rigidity statements once the regularity of minimizers of capillary area functional holds.…
In this work we deal with a scalar spectral mixed boundary value problem in a spacial junction of thin rods and a plate. Constructing asymptotics of the eigenvalues, we employ two equipollent asymptotic models posed on the skeleton of the…
By variational methods, for a kind of Webster scalar curvature problems on the CR sphere with cylindrically symmetric curvature, we construct some multi-peak solutions as the parameter is sufficiently small under certain assumptions. We…
We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…
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…
We generalize the closest point method (CPM) to solve surface partial differential equations with general boundary conditions. The proposed extrapolation method provides a unified framework for treating a broad class of inhomogeneous…
To enhance the ability of neural networks to extract local point cloud features and improve their quality, in this paper, we propose a multiscale graph generation method and a self-adaptive graph convolution method. First, we propose a…
We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin…
For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale approximations. There are no assumptions of periodicity involved…
We consider spectral approximations to the conservative form of the two-sided Riemann-Liouville (R-L) and Caputo fractional differential equations (FDEs) with nonhomogeneous Dirichlet (fractional and classical, respectively) and Neumann…
This proceeding is intended to be a first introduction to spectral methods. It is written around some simple problems that are solved explicitly and in details and that aim at demonstrating the power of those methods. The mathematical…
We introduce the conformally-invariant scalar product, originally devised for radiation fields, to the study of the modes of optical resonators. This scalar product allows one to normalize and compare resonant modes using their…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
We develop and demonstrate two numerical methods for solving the class of open cavity problems which involve a curved, cylindrically symmetric conducting mirror facing a planar dielectric stack. Such dome-shaped cavities are useful due to…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…